High Accuracy Gravimetric Winkler Method for Determination of Dissolved Oxygen

DISSERTATIONES CHIMICAE UNIVERSITATIS TARTUENSIS 118

IRJA HELM

High accuracy gravimetric Winkler method for determination of dissolved oxygen

Institute of Chemistry, Faculty of Science and Technology, University of Tartu

Dissertation is accepted for the commencement of the Degree of Doctor philosophiae in Chemistry on June 14, 2012 by the Doctoral Committee of the Institute of Chemistry, University of Tartu.

Supervisors: Research Fellow Lauri jalukse (PhD) Professor Ivo Leito (PhD)

Opponent: Associate professor Jens Enevold Thaulov Andersen (D.Sc.) Technical University of Denmark

Commencement: August 31, 2012 at 10:00, Ravila 14a, room 1021

This work has been partially supported by the ETF grant No 7449. This work has been partially supported by Graduate School „Functional materials and technologies” receiving funding from the European Social Fund under project 1.2.0401.09-0079 in University of Tartu, Estonia

ISSN 1406–0299 ISBN 978–9949–32–069–1(trükis) ISBN 978–9949–32–070–7(PDF)

Autoriõigus Irja Helm, 2012

Tartu Ülikooli Kirjastus www.tyk.ee Tellimus nr 344 TABLE OF CONTENTS

LIST OF ORIGINAL PUBLICATIONS ...... 7 ABBREVATIONS ...... 8 1. INTRODUCTION ...... 9 2. PRINCIPLE OF THE WINKLER METHOD ...... 12 3. EXPERIMENTAL ...... 13 3.1. General notes ...... 13 3.2. Syringe gravimetric Winkler ...... 15 3.2.1. Measurement model of the syringe gravimetric Winkler ...... 15 3.2.2. Preparing of working solution of KIO3 ...... 17 3.2.3. Determination of the concentration of the Na2S2O3 titrant ...... 17 3.2.4. Sample preparation ...... 18 3.2.5. Titration of the sample with the Na2S2O3 titrant ...... 18 3.2.6. Determination of parasitic oxygen...... 19 3.2.7. Determination of iodine volatilization ...... 20 3.3. Flask gravimetric Winkler ...... 21 3.3.1. Measurement model of flask gravimetric Winkler ...... 22 3.3.2. Preparing of standard working solutions of KIO3 ...... 24 3.3.3. Determination of the concentration of the Na2S2O3 titrant ...... 24 3.3.4. Sampling and sample preparation ...... 25 3.3.5. Titration of the sample with the Na2S2O3 titrant ...... 26 3.3.6. Determination of the correction for oxygen introduced from the reagents ...... 26 3.3.7. Determination of Parasitic Oxygen ...... 28 3.3.8. Iodine volatilization ...... 29 3.4. Saturation method for obtaining the reference DO values ...... 32 3.5. Differences between gravimetric Winkler carried out in syringes and in flasks ...... 34 4. RESULTS AND DISCUSSION ...... 36 4.1. Validation of the methods ...... 36 4.2. Measurement uncertainties ...... 38 4.3. Comparison with the uncertainties of other Winkler methods published in the literature ...... 40 4.4. Comparison of the Gravimetric Winkler method with saturation method for calibration of DO sensors ...... 42 CONCLUSIONS ...... 43 SUMMARY ...... 44 SUMMARY IN ESTONIAN ...... 45

5 2 REFERENCES ...... 46 ACKNOWLEDGEMENTS ...... 49 APPENDIX 1 ...... 50 APPENDIX 2 ...... 52 APPENDIX 3 ...... 54 APPENDIX 4 ...... 57 APPENDIX 5 ...... 64 PUBLICATIONS ...... 69

6 LIST OF ORIGINAL PUBLICATIONS

This thesis consists of four articles listed below and a review. The articles are referred in the text by Roman numerals I–IV. The review summarizes and supplements the articles. I. I. Helm, L. Jalukse, I. Leito, Measurement Uncertainty Estimation in Amperometric Sensors: A Tutorial Review. Sensors, 2010, 10, 4430–4455. DOI:10.3390/s100504430 II. L. Jalukse, I. Helm, O. Saks, I. Leito, On the accuracy of micro Winkler titration procedures: a case study, Accredit. Qual. Assur. 2008, 13, 575– 579. DOI: 10.1007/s00769-008-0419-1 III. I. Helm, L. Jalukse, M. Vilbaste, I. Leito, Micro-Winkler titration method for dissolved oxygen concentration measurement. Anal. Chim. Acta, 2009, 648, 167–173. DOI:10.1016/j.aca.2009.06.067 IV. I. Helm, L. Jalukse, I. Leito, A new primary method for determination of dissolved oxygen: gravimetric Winkler method. Analytica Chimica Acta, 2012, 741, 21–31. DOI: 10.1016/j.aca.2012.06.049

Author’s contribution

Paper I: Main person responsible for planning and writing the manuscript. Paper II: Performed literature search and wrote large part of the text. Paper III: Main person responsible for planning and writing the manuscript. Performed all the experimental work. Paper IV: Main person responsible for planning and writing the manuscript. Performed all the experimental work.

7 ABBREVATIONS

DO Dissolved oxygen FGW Gravimetric Winkler titration method, where sample preparation is performed in flasks GUM The Guide to the Expression of Uncertainty in Measurement ISO International Organization for Standardization PTFE Polytetrafluoroethene SGW Gravimetric Winkler titration method, where sample preparation is performed in syringes SI International System of Units WM Winkler titration method

8 1. INTRODUCTION

Dissolved oxygen (DO) content in natural waters is an indispensable quantity whenever background data is collected for investigations of nature from hydrobiological, ecological or environmental protection viewpoint [1]. Suffi- cient concentration of DO is critical for the survival of most aquatic plants and animals [2] as well as in waste water treatment. DO concentration is a key parameter characterizing natural and wastewaters and for assessing the state of environment in general. Besides dissolved CO2, DO concentration is an important parameter shaping our climate. It is increasingly evident that the concentration of DO in oceans is decreasing [3–6]. Even small changes in DO content can have serious consequences for many marine organisms, because DO concentration influences the cycling of nitrogen and other redox-sensitive elements [3]. Decrease of DO concentration leads to formation of hypoxic regions (or dead zones) in coastal seas, in sediments, or in the open ocean, which are uninhabitable for most marine organisms [3,7]. DO concentration is related to the changes in the ocean circulation and to the uptake of CO2 (including anthropogenic) by the ocean [8]. All these changes in turn have relation to the climate change. Accurate measurements of DO concentration are very important for studying these processes, understanding their role and predicting climate changes. These processes are spread over the entire vast area of the world's oceans and at the same time are slow and need to be monitored over long periods of time. This invokes serious requirements for the measurement methods used to monitor DO. On one hand, the results obtained at different times need to be comparable to each other. This means that the sensors used for such measurements need to be highly stable and reproducible [9]. The performance of oxygen sensors – amperometric and (especially) optical – has dramatically improved in recent years [10]. On the other hand, measurements made in different locations of the oceans have to be comparable to each other. The latter requirement means that the sensors have to be rigorously calibrated so that the results produced with them are traceable to the SI. The sensors need to be calibrated with solutions of accurately known oxygen concentration in order to correct for sensor drift, temperature, salinity and pressure influences [I,11]. Oxygen is an unstable analyte thus significantly complicating sensor calibration. It has been established that if every care is taken to achieve as accurate as possible results then the accuracy of DO measurements by amperometric sensors is limited by calibration [11] and specifically by the accuracy of the reference DO concentration(s) that can be obtained [I]. This is similar with optical sensors: their lower intrinsic uncertainty may make the relative contribution of calibration reference values even larger [10]. The issues with sensors, among them issues with calibration, have caused a negative perception about the data using sensors in the oceanography commu-

9 3 nity and because of this the recent issue of the World Ocean Atlas [12] was compiled with taking into account only DO concentrations obtained with chemical titration methods (first of all the Winkler titration method, WM) and rejecting all sensor-based data. Similar decision was taken in a recent study of DO decline rates in coastal ocean [6]. It is nevertheless clear that there is need for large amounts of data, so that the slow and clumsy titration method cannot satisfy this need. It is necessary to be able to collect data automatically and in large amounts. It is thus expected that eventually sensors will be “back in business”. In order to achieve this the accuracy of their calibration needs to be improved. There are two ways to prepare DO calibration solutions with known concentrations: (1) saturating water with air at fixed temperature and air pressure and using the known saturation concentrations [13–15] and (2) preparing a DO solution and using some primary measurement method for measuring DO concentration. The premier method for the second way is the WM [16] which was first described by Winkler [17] more than hundred years ago. Nowadays the use of WM as the standardizing method is even more important than measurements in the real samples [1]. Also gasometry is an old method for DO determinations, but it is a partly physical method requiring quite specific and complex experimental setup and is therefore not routinely used nowadays. DO measurement practitioners currently almost exclusively use the saturation method for calibration of DO measurement instruments. This method gives quite accurate results when all assumptions made are correct. DO values obtained with the saturation method are also used in this work for comparison with the WM values. Nevertheless, the saturation method uses ambient air – a highly changing medium – as its reference, thereby relying on the assumption that the oxygen content of the Earth’s atmosphere is constant, which is not entirely true [4]. The oxygen content of air depends on air humidity and CO2 content, which both can change over a wide range of values. Also, this method needs careful accounting for air pressure, humidity and water temperature. It is customary to use published values of DO concentrations in air-saturated water at different temperatures. At the same time, different published values are in disagreement by up to 0.11 mg dm–3 at 20 oC and even up to 0.19 mg dm–3 at 40 oC [15]. Thus the saturation method has many factors that influence the results and it is difficult to realize it in a highly accurate way. An independent primary method, such as WM, would be free from these shortcomings. The Winkler method is known for a long time, it has been extensively studied and numerous modifications have been proposed [16,18–23]. There have, however, been very few studies using WM that report combined uncertainties taking into account both random and systematic factors influencing the measurement [II]. Usually repeatability and/or reproducibility data are presented that do not enable complete characterization of the accuracy of the methods and tend to leave too optimistic impression of the methods. Very illuminating in this respect are the results of an interlaboratory comparison

10 study [24] where the between-lab reproducibility standard deviation is as large as 0.37 mg dm–3 [24]. In light of this data three original publications [20–22] of so-called micro Winkler procedures (sample volumes 1 to 10 ml instead of 100 to 200 ml for classical Winkler titration) were taken under examination [II] and using the experimental data from those publications uncertainty estimates were calculated by using the Nordtest [25] method. As a result, uncertainty estimates of these three methods were obtained ranging from 0.13 to 0.27 mg dm–3 (k = 2 expanded uncertainty), which are quite high [II]. These uncertainty estimates reveal that there is a lot of room for improvement of the Winkler method. Winkler method is the primary method of DO concentration measurement: the obtained mass DO in the sample is traceable to the SI via mass measurement. In this work a realization of the Winkler method with the highest possible accuracy and a careful analysis of the method for its uncertainty sources is presented. First, a very precise and accurate WM for small samples (9–10 ml) is developed. By using this method the uncertainty decreased in the range of 0.08–0.13 mg dm–3 (k = 2 expanded uncertainty) [III]. Uncertainty analysis was carried out on the basis of ISO GUM [26]. It was comprehensive and gave information about uncertainty sources and their contribution. By analyzing the results of this uncertainty estimation it was seen, that there were still some opportunities for decreasing the uncertainty by modifying the procedure and equipment. As a result of this, the method was further refined and uncertainty in the range of 0.023 to 0.035 mg dm–3 (0.27 to 0.38% relative, k = 2 expanded uncertainty) was achieved [IV]. This work prepares the ground for putting the DO measurements as such onto a more reliable metrological basis, enabling lower uncertainties and allowing detection of trends and relationships that may remain obscured with the current level of accuracy achievable for DO determination.

11 2. PRINCIPLE OF THE WINKLER METHOD

The Winkler method is based on quantitative oxidation of Mn2+ to Mn3+ by oxygen in alkaline medium and on the subsequent quantitative oxidation of iodide to iodine by Mn3+ in acidic medium [18,27]. The formed iodine is titrated with thiosulphate. First, two solutions (Winkler reagents) are added to the oxygen-containing sample: one containing KI and KOH and the other containing MnSO4. Oxygen reacts under alkaline conditions with Mn2+ ions forming manganese(III)- hydroxide [18,27]:

2+ – 4Mn + O2 + 8OH + 2H2O → 4Mn(OH)3 ↓ (1)

The solution is then acidified. Under acidic conditions Mn3+ ions oxidize iodide – – to iodine, which eventually forms I3 ions with the excess of I [18, 27]:

+ 3+ 2Mn(OH)3 (s) + 6H → 2Mn + 3H2O (2)

3+ – 2+ 2Mn + 2I →2Mn + I2 (3)

– – I2 + I →I3 (4)

– The concentration of the formed tri-iodide ions I3 (below termed simply as iodine) is usually determined by titration with sodium thiosulphate solution:

I – + 2S O 2– → 3I– + S O 2– (5) 3 2 3 4 6

Thiosulphate solution is standardized using potassium iodate (KIO3). Under acidic conditions iodine is formed quantitatively according to the following reaction:

– – + IO3 + 5I + 6H  3I2 + 3H2O (6)

All the above reactions are fast and proceed quantitatively.

12 3. EXPERIMENTAL

In this section two developed gravimetric Winkler methods and their mathematical models are described in detail. These methods are called here and below syringe gravimetric Winkler (SGW) [III] and flask gravimetric Winkler (FGW) [IV], respectively. In the first one the sample treatment is carried out in the syringe, in the second one in the flask. As a result of the SGW and its uncertainty analysis it was found, that there is still room for improvements and it is possible to decrease the uncertainty even more. This is done in this work. Photos visualizing the steps of the methods are presented in Appendix 1.

3.1. General notes In this section also essential uncertainty sources and ways of their estimates of two developed gravimetric Winkler methods are described. Uncertainty esti- mations for both methods have been carried out according to the ISO GUM modeling approach [26]. If the output quantity Y is dependent on a number of input quantities as follows

Y  F(X1, X 2 , ... , X n ) (7)

then the combined standard uncertainty of the estimate y of the output quantity is found by combining the uncertainty components Y (termed below u(xi ) X i

also as absolute uncertainty components) of the input quantities Xi according to the following equation [26]:

2 2 2  Y   Y   Y  (8) uC (y)   u(x1)   u(x2 )  .....   u(xn ) X1  X 2  X n 

Technically the uncertainty evaluation was carried out using the Kragten spreadsheet method [36]. The measurands are concentration of DO in the water –3 sample (CO2_s) expressed in mg dm . The measurement models are presented in eqs 11–14 and 16–18 for SGW and FGW, respectively. All molecular masses and their uncertainties were found from atomic masses according to ref 37. In all cases where uncertainty estimates are obtained as ±X without additional information on the probability distribution was assumed rectangular distribution (the safest assumption) and converted such uncertainty estimates to the respective standard uncertainties by dividing with square root of 3 [26]. The uncertainty of water density is sufficiently low to be negligible for our purposes.

13 4 Γ mX Both methods’ mathematical models use the value of mY . This quantity is calculated by the general equation 9 and are the average (of six or seven parallel determinations for SGW and FGW, respectively, in the equation marked as n) ratios of the amounts of X and Y solutions, used in the analysis.

m  X _ i i mY _ i Γ mX  (9) mY n

Such approach is needed (differently from volumetry), because it is impossible to take exactly the same mass of KIO3 for titration in all parallel titrations. The m uncertainties of Γ X take into account the repeatability of titrations. Titrations mY were carried out gravimetrically to lessen the uncertainty caused by volumetric operations [28]. Detailed description of the calculations and the full uncertainty budget can be found in Appendixes 4 and 5 for SGW (in 22.02.2008) and FGW (in 30.01.2012), respectively. It has been stressed [18,29] that loss of iodine may be an important source of uncertainty in Winkler titration, however, concrete experimental data on the extent of this effect are rare. In the literature more sources of iodine-related errors have been described [30], such as hydrolysis of iodine by formation of oxyacid anions, which are not capable of oxidizing thiosulphate at the pH of the titration and iodine adsorption on glass surfaces. All these effectively lead to the loss of the iodine. At the same time under strongly acidic conditions additional iodine may form via light-induced oxidation of iodide by air oxygen [18,31]:

– + 4I + 4H + O2 → 2I2 + 2H2O (10)

This process leads to the increase of iodine concentration. All these factors can have influence both during titration of the sample and during titrant standardization. In present work iodine volatilization is determined by additional experiments. While titration conditions are different for two gravimetric Winkler methods, then also the volatilized iodine amounts are different. At SGW titration vessel is capped with plastic cap and it makes iodine difficult to vaporize because vapor pressure above the solution is high. At FGW for the end-point determination an electrode is used and that’s why it is not convenient to cap the titration vessel, so that the amount of volatilized iodine is about 16 times higher (it depends highly also on stirring speed). That is why iodine volatilization is differently handled at two gravimetric Winkler methods: at SGW it is accounted only as an uncertainty component, at FGW the amount of volatilized iodine is added or subtracted (depending on where the iodine is coming from) and accounted also as uncertainty sources.

14 Due to the small sample volume the possible sources of parasitic oxygen have to be determined and their influence minimized. The concentration of oxygen in air per volume unit is more than 30 times higher than in water saturated with air. Therefore avoiding air bubbles is extremely important when taking the samples and when adding the reagent solutions. The two main sources of parasitic oxygen are: DO in Winkler reagent solutions (with possible additional effect from the adding procedure) and sample contamination by the atmospheric oxygen.

3.2. Syringe gravimetric Winkler All weighings were done on a Mettler Toledo B204-S analytical balance (resolution 0.0001 g). This balance was regularly adjusted using the external adjustment (calibration) weight (E2, 200 g, traceable to the Estonian National mass standard). Uncertainty components of all weighings are: rounding of the digital reading (±0.00005 g, u(rounding)=0.000029 g); linearity of the balance (±0.0002 g, u(linearity)=0.000115 g); drift of the balance (determined in five separate days during 8 hours, relative quantity, u(drift)=0.00024%); and repeatability (determined on two days weighing different weights or their combinations for ten times, calculated as pooled standard deviation, u(repeatability)=0.00016 g). Latter one is used for weighing solid KIO3 only, the repeatability of weighing during the titrations is accounted for by the  factors based on the actual parallel titrations data, see eq 9. Thereat weighing systematic components are considered as factors, which have unity values and uncertainties corresponding to the relative uncertainties of the effects they account for. All solutions were prepared using distilled water.

3.2.1. Measurement model of the syringe gravimetric Winkler

Potassium iodate (KIO3) was used as standard titrimetric substance. The stock solution concentration was found according to eq 11

m  P C  KIO3 _ s KIO3 (11) KIO3 M V   KIO3 flask KIO3

–1 where CKIO3 [mol kg ] is the concentration of the KIO3 solution, mKIO3_s [g] is –1 the mass of the KIO3, PKIO3 [–] is the purity of KIO3, MKIO3 [g mol ] is molar 3 –3 mass of KIO3, Vflask [dm ] is the volume of the flask, ρKIO3 [kg dm ] is the density of 0.0285% KIO3 solution. KIO3 solution density was calculated based

15 on the data on water density from ref 32 and data of KIO3 solution density from refs 33 and 34. Concentration of the Na2S2O3 titrant was found by titrating iodine liberated from the KIO3 standard substance in acidic solution of KI. The titrant concentration was found according to eq 12:

m KIO3 CNa S O  6CKIO m  Fm  Fm  Fm  FI (12) 2 2 3 3 Na2S2O3 _ KIO3 KIO3 Na2S2O3 _ KIO3 KIO3 _ endp 2

–1 where CNa2S2O3 is the titrant concentration [mol kg ], mKIO3 [g] is the mass of the KIO3 solution taken for titration, mNa2S2O3_KIO3 [g] is the mass of the Na2S2O3 titrant used for titrating the iodine liberated from KIO3. FmKIO3 [–] and FmNa2S2O3_KIO3 [–] are factors taking into account the uncertainties of these solutions weighing. FmKIO3_endp [–] is the factor taking into account the uncertainty of determining the titration end-point, FI2 [–] is the factor taking into account evaporation of iodine from the solution. These factors have values of unity and uncertainties corresponding to the relative uncertainties of the effects they account for. –1 The concentration of parasitic DO in the reagents CO2_reag [mg kg ] was found as follows:

1 m O2_syringe Na2S2O3_reag (13) CO _reag   M O CNa S O m  Fm  Fm  Fm  FI  2 2 2 2 3 reag reag Na2S2O3 _ reag reag _ endp 2 4 mreag

–1 where MO2 [mg mol ] is the molar mass of oxygen, mNa2S2O3_reag [g] is the amount of titrant consumed for titration, mreag [g] is the overall mass of the solutions of the alkaline KI and MnSO4 and O2_syringe [μg] is the mass of oxygen introduced by the syringe plunger. Fmreag [–] and FmNa2S2O3_reag [–] are factors taking into account the uncertainties of these solutions weighing. Fmreag_endp [–] is the factor taking into account the uncertainty of determining the titration end-point. These factors have values of unity and uncertainties corresponding to the relative uncertainties of the effects they account for. The DO concentration in the sample was found according to eq 14:

(14)  m m O  1 Na2S2O3_s reag_s 2_syringe CO _s     M O CNa S O m  Fm  Fm  Fm  FI  CO _reag m   2  2 2 2 3 s s Na2S2O3 _ s s _ endp 2 2 s   4 ms 

–3 –3 where CO2_s [mg dm ] is the DO concentration in the sample, ρ [kg dm ] is the density of water saturated with air, found according to ref 35, mNa2S2O3_s [g] is the mass of Na2S2O3 solution consumed for sample titration, ms [g] is the sample mass, mreag_s [g] is the overall mass of the added reagent solutions.

16 Fm_s [–] and FmNa2S2O3_s [–] are factors taking into account the uncertainties of these solutions weighing. Fm_s_endp [–] is the factor taking into account the uncertainty of determining the titration end-point. These factors have unity values and uncertainties corresponding to the relative uncertainties of the effects they account for.

3.2.2. Preparing of working solution of KIO3 Potassium iodate solution with concentration of ca 0.0013 mol kg–1 was pre- 3 pared from 0.28 g (known with the accuracy of 0.0001 g) of KIO3 in a 1000 cm volumetric flask. Uncertainty components of the 1 dm3 volumetric flask volume are: uncertainty of the nominal volume as specified by the manufacturer (no calibration was done at our laboratory):  0.4 cm3 (u(cal)=0.23 cm3); uncertainty due to the imprecision of filling of the flask: ± 10 drops or ± 0.3 cm3, u(filling)=0.17 cm3; uncertainty due to the temperature effect on solution 3 density: u(temperature)=0.24 cm . The standard uncertainty of the KIO3 3 solution volume was found as u(Vflask)=0.38 cm . The minimum purity of the KIO3 was given 99.7 %, so it was assumed that actual purity is 99.85 with the rectangular distribution (the safest assumption) and  0.15% as the uncertainty, giving the relative standard uncertainty as 0.00087.

3.2.3. Determination of the concentration

of the Na2S2O3 titrant 3 Iodine solution was prepared as follows. 2 cm of the standard KIO3 solution (0.0013 mol kg–1) was transferred using a plastic syringe through plastic septum into a dried and weighed titration vessel. The vessel was weighed again. Using another syringe 0.1 cm3 of solution containing KI (2.1 mol dm–3) and KOH (8.7 mol dm–3) (alkaline KI solution) was added. Using a third syringe ca 3 –3 0.1 cm of H2SO4 solution (5.3 mol dm ) was added carefully, until the color of the solution did not change anymore. Under acidic conditions iodine is formed according to the reaction 6. The care in adding H2SO4 solution is necessary in order to avoid over-acidification of the solution because under strongly acidic conditions additional iodine may form via oxidation of iodide by air oxygen (see the reaction 10). The iodine formed from KIO3 was titrated immediately (to –3 avoid loss of iodine by evaporation) with ca 0.0025 mol dm Na2S2O3 solution (reaction 5). Titration was carried out using a glass syringe filled with titrant and weighed. After titration the syringe was weighed again to determine the consumed titrant mass. Six parallel measurements were carried out according to the described procedure and the average result was used as the titrant concentration. Repeatability of the titration and repeatabilities of the masses are

17 5 m KIO3 taken into account by the standard deviation of the mean ratio m Na2S2O3 _ KIO3 (according to eq 9). Possible systematic effects on the titration end-point are taken into account by the factor FmKIO3_endp (see eq 12). The end-point was determined using a visual starch indicator. The uncertainty of end-point determination was estimated as ± 1 drop. Mass of one drop with the used needle was 0.017 g and thus the standard uncertainty was u = 0.01 g.

3.2.4. Sample preparation Samples were prepared in 10 cm3 glass syringes with PTFE plungers (Hamilton 1010LT 10.0 cm3 Syringe, Luer Tip). Masses of all syringes were determined beforehand. Six parallel samples were taken as follows: a) The syringe and the needle were rinsed with sample solution. b) Air bubbles were eliminated by gently tapping the syringe. DO concentration decreases when doing this, therefore the syringe was emptied again so that only its dead volume was filled. c) The syringe was rinsed again avoiding air bubbles. d) 9.4 cm3 of the sample was aspirated into the syringe. e) The tip of the needle was poked into a rubber septum.

When six syringes were filled with samples and weighed the reagents were 3 3 added. Ca 0.2 cm of the alkaline KI solution and ca 0.2 cm of MnSO4 solution (2.1 mol dm–3) was aspirated into each syringe. The needle tip was again sealed, the sample was intensely mixed and the Mn(OH)3 precipitate was let to form during 45±10 minutes (according to eq 1). The syringe was weighed again to determine the net amount of the added reagents. This is necessary because the reagents also contain DO, which is taken into account. After 45 minutes ca 3 0.2 cm of H2SO4 solution was aspirated into the syringe. Tri-iodide complex is formed according to reactions 2, 3 and 4. At this stage the air bubbles do not interfere anymore.

3.2.5. Titration of the sample with the Na2S2O3 titrant The formed iodine solution is transferred through a plastic cap to the titration vessel. Simultaneously titrant is added from a pre-weighed glass syringe (to avoid possible evaporation of iodine). The sample syringe was rinsed twice with distilled water and the rinsing water was added to the titration vessel. The solution was titrated with Na2S2O3 using a syringe until the solution was pale yellow. Then ca 0.2 cm3 of 1% starch solution was added and titration was continued until the formed blue color disappeared. The titration syringe was weighed again. The amount of the consumed titrant was determined from mass

18 difference. Six parallel titrations were carried out. Repeatability of the titration and repeatabilities of the masses were taken into account by the standard

ms uncertainty of the mean ratio Γm (according to eq 9). Possible systematic Na2S2O3 _ s effect in finding titration end-point is taken into account by Fm_s_endp (see eq 14). This uncertainty has been estimated as ± 1 drop. Mass of one drop is 0.017 g leading to the standard uncertainty of 0.01 g.

3.2.6. Determination of parasitic oxygen

The overall amount of oxygen introduced by the MnSO4 and the alkaline KI solutions was determined daily by aspirating into the glass syringe ca 2 cm3 of 3 3 the solution of KI and KOH, ca 2 cm of MnSO4 and after 45 minutes 2 cm of H2SO4 solution was aspirated. The titration was carried out as described above. Repeatability of the titration and repeatabilities of the masses were taken into

mreag account by the standard deviation of the mean ratio Γm (according to Na2S2O3 _ reag eq 9). Possible systematic effect in finding titration end-point has been estimated as ± 2 drops of titrant. Mass of one drop is 0.017 g leading to the standard uncertainty of 0.02 g. All polymeric materials can dissolve oxygen. In this work the oxygen dissolved in the PTFE plunger is important. If there is no diffusion of oxygen inside the sample the oxygen concentration should decrease to zero if the sample mass is decreased to zero. If some oxygen diffuses into the sample from the environment (not from the sample itself), then the value of the intercept of the graph equals the amount of parasitic oxygen (axes: amount of oxygen – y-axis, sample mass – x-axis). In order to determine the amount of oxygen introduced from the plunger the DO amount in different quantities of the same sample was determined. The mass of DO found in the sample was plotted against the sample mass. The mass of the parasitic oxygen introduced from the plunger was found as the intercept of the graph (see Graph 1). From the measurement results it can be concluded that some oxygen diffuses into the sample from the PTFE plunger and possibly from the narrow space between the plunger and the syringe barrel. The air-saturated distilled water at 20 °C was used in this experiment and the samples were allowed to precipitate for 45±10 minutes. The mass of the parasitic oxygen introduced from the plunger was found as the intercept of the graph. The measurements were carried out on six different days and the following results were obtained: 2.69; 1.62; 3.00; 1.23; 2.03; 2.08 μg. The amount of parasitic oxygen introduced from the plunger was found as 2.11 µg (O2_syringe) with standard uncertainty of 0.27 µg (u(O2_syringe). The Mn(OH)3 precipitate was let to form during 45±10 minutes in this experiment.

Graph 1. Determination of parasitic oxygen O2_syringe.

3.2.7. Determination of iodine volatilization An additional experiment was carried out to determine the iodine volatilization amount. The experimental conditions were the same as when standardizing the titrant. Averaged quantity of iodine moles was 7.8 μmol. The measurements were carried out in parallel in two ways: if the titration vessels were covered with plastic caps and if the vessels were open. Altogether six iodine solutions were prepared – three of them were capped in waiting period and three of them were open. The time gaps used were one minute, two hours and three hours. See the Graph 2.

Graph 2. Determination of iodine volatilization.

20 The slope of the graph equals the number of volatilized iodine moles in one minute. The results showed that the amount of iodine volatilized in one minute are 0.0028 μmol and 0.011 μmol if capped titration vessel and open vessel were used, respectively. It makes 0.04% and 0.14% of the whole iodine amount (7.78 µmol), respectively. The titration of iodine solution takes time approximately one minute. The uncertainty of iodine volatilization expressed according to eq 15:

0.0028mol u(F )   0.00021 I2 (15) 3  7.78mol

In the case of determination of DO in reagents and sample the concentration of iodine solution was lower. Nevertheless it was assumed the same relative volatilization of iodine. So this uncertainty component may be overestimated to some extent.

3.3. Flask gravimetric Winkler All solutions where accurate concentration was important were prepared by weighing. The amounts of the solutions were measured by weighing. In case of transfers where it was necessary to avoid contact with air oxygen glass syringes with tight plungers and cemented needles were used. In other cases plastic syringes were used. All amounts of reagents, which directly influenced the result, were measured by weighing. Weighing was done on a Precisa XR205SM-DR balance. The balance was regularly adjusted using the internal adjustment (calibration) weight. This adjustment was additionally checked using 5 independent reference weights in 9 different combinations resulting in masses ranging from 0.01 g to 200 g (and traceable to the SI via the Estonian National mass standard). The obtained differences of the readings from the masses of the weights were too small to justify correction, however they were taken into account in evaluation of mass measurement uncertainty. The balance has two measurement ranges: low: 0–92 g and high: 92–205 g with 4 and 5 decimal places, respectively. So, some of the components of weighing uncertainties have two different values – for higher and for lower range. Which one is used depends on the mass of the object together with tare. The uncertainty components of weighing are: repeatability, rounding of the digital reading, drift of the balance and calibration of the balance. The repeatability uncertainty components for the two ranges were determined as u(repeatability_low)=0.000043 g and u(repeatability_high)=0.000057 g. These estimates are used for weighing of KIO3 and its solutions. The repeatability of weighing during titration is accounted for by the  factors based on the actual parallel titrations data as detailed in section 3.1, see eq 9 there. Rounding of the digital reading is taken

21 6 into account in the conventional way, as half of the last digit of the reading assuming rectangular distribution leading to standard uncertainty estimates u(rounding_low)=0.0000029 g and u(rounding_high)=0.000029 g. To estimate the drift of balance three weights (m1 = 50 g, m2 = 100 g and m3 = 100 g) were weighed daily before and after making the Winkler titration. This experiment was carried out on 17 different days. The instrument was adjusted (internal calibration) on every morning before the start of the measurements. The drift of the balance was found to be proportional to the mass and was quantified as u(drift)=0.000064 %. Additional experiment has been done by weighing reference weights. The biggest difference between mass of the reference weight and reading of the used scale was 0.0003 g and it was divided with the mass it was attained (120 g) to get a relative quantity and divided by the square root of three. This gave uncertainty of the calibration of the balance, u(calibration)=0.000042 %. Two additional uncertainty sources related to weighing were taken into account: possible partial evaporation of water from the KIO3 solution (u = 0.002 g) and the “warm hand” effect when weighing the titrant syringe after titration (u = 0.00046 g). The latter leads to lower mass of the syringe because it has been warmed by hand during titration and this causes ascending air flow in the balance compartment. The water used for all operations was produced with a Millipore Milli-Q Advantage A10 setup (resistivity 18.2 M cm). The reagents used were of the highest purity available.

3.3.1. Measurement model of flask gravimetric Winkler

Potassium iodate (KIO3) was used as the standard substance. The working solution concentration was found according to eq 16.

mKIO _ s 10001000mKIO _ I _ transf mKIO _ II _transf  PKIO C  3 3 3 3 (16) KIO3III M m m m KIO3 KIO3 _ I KIO3 _ II KIO3 _ III

–1 where CKIO3_III [mol kg ] is the concentration of the KIO3 working solution, mKIO3_s [g] is the mass of the solid KIO3, PKIO3 [–] is the purity (mass fraction) –1 of KIO3, MKIO3 [mg mol ] is molar mass of KIO3, mKIO3_I [g], mKIO3_II [g] and mKIO3_III [g] are the masses of the prepared solutions, respectively, mKIO3_I_transf [g] and mKIO3_II_transf [g] are the masses of the transferred solutions for diluting the previous solution. Concentration of the Na2S2O3 titrant was found by titrating iodine liberated from the KIO3 standard substance in acidic solution of KI. The titrant concentration was found according to eq 17.

22 m 2n KIO3 I2 _ vol _ t CNa S O  6CKIO  Γm  Fm  Fm  Fm  (17) 2 2 3 3 Na2S2O3 _ KIO3 KIO3 Na2S2O3 _ KIO3 KIO3 _ endp m Na2S2O3 _ KIO3

–1 where CNa2S2O3 is the titrant concentration [mol kg ], mKIO3 [g] is the mass of the KIO3 working solution taken for titration, mNa2S2O3_KIO3 [g] is the mass of the Na2S2O3 titrant used for titrating the iodine liberated from KIO3, nI2_vol_t [mmol] evaporated iodine from the solution during the titration for determination of titrant concentration. In order to account for the remaining uncertainty sources three factors F are introduced. FmKIO3 [–] and FmNa2S2O3_KIO3 [–] are factors taking into account the uncertainties of weighing of these solutions. FmKIO3_endp [–] is the factor taking into account the uncertainty of determining the titration end- point. These factors have unity values and their uncertainties correspond to the m KIO3 respective relative uncertainty contributions to Γ m . Na2S2O3 _ KIO3 The DO concentration in the sample was found according to eq 18:

 1  m 2  nI _ vol _ s  p  C    M   C  Γ Na2S2O3_s  F  F  F  2   Int  CF   O2 _ s O2 Na2S2O3 ms ms mNa S O _ s ms _ endp O2 O2 (18)  4  2 2 3 m  p    s  n 

–3 –3 where CO2_s [mg dm ] is the DO mass concentration in the sample, [kg dm ] is the density of water saturated with air, calculated according to ref 35. m Γ Na2S2O3 _ s is the average (from seven parallel determinations) ratio of the ms masses of Na2S2O3 and sample solutions, used in the analysis and is defined m analogously to eq 9. The uncertainty of Γ Na2S2O3 _ s takes into account only the ms repeatability of titration, nI2_vol_s [mmol] is the estimated amount evaporated iodine from the solution during the transfer from sample flask to the titration vessel and during the titration, ms is the average mass of the sample. In order to account for the remaining uncertainty sources three factors F are introduced. Fm_s [–] and FmNa2S2O3_s [–] are factors taking into account the uncertainties of weighing of these solutions weighing. Fm_endp [–] is the factor taking into account the uncertainty of determining the titration end-point. These factors have unity values and uncertainties corresponding to the relative uncertainties of –1 the effects they account for. IntO2 [mg kg ] is the input quantity taking into account the contamination of the sample by the parasitic oxygen introduced –1 through the junction between the stopper and the flask neck. CFO2 [mg kg ] is the correction accounting for the parasitic oxygen introduced with reagent solutions. Both these effects lead to apparent increase of DO concentration in the sample (therefore the negative signs of the corrections). CFO2 is normalized to the sea-level pressure by multiplying it with the ratio of pressures p [Pa] and pn [Pa], which are air pressures in the measurement location at the time of the measuring and the normal sea-level pressure, respectively.

23 3.3.2. Preparing of standard working solutions of KIO3 Standard solutions were prepared gravimetrically using the highest purity standard substance KIO3 available (declared purity: 99.997% on metals basis, Sigma-Aldrich). This purity was considered as too optimistic and it was used the following purity estimate: 100.0% ± 0.1%. The true content of KIO3 in the substance was assumed to be rectangularly distributed in the range of 99.9% to 100.1%, leading to the standard uncertainty of purity 0.058%. KIO3 is known for its negligible hygroscopicity [31]. This was additionally tested by drying the substance at 110 °C for 4 hours. A mass decrease was not detected. The working solution was made by consecutive dilutions. The first solution –1 (KIO3_I, c=36 g kg ) was made by weighing about 1.4 grams of solid KIO3 and dissolving it in about 40 grams of water. The second solution (KIO3_II, –1 c=3 g kg ) was made by weighing about 3 grams of solution KIO3_I and adding water to bring the volume to approximately 40 grams. The working –1 –1 solution (KIO3_III, c=0.2 g kg or 1 mmol kg ) was made by weighing about 4–6 grams of KIO3_II and adding water to bring the volume up to approximately 100 grams. All these solutions were made into tightly capped bottles to avoid change of concentration of the solutions during and between the analyses.

3.3.3. Determination of the concentration

of the Na2S2O3 titrant Concentration of the titrant was determined by titrating a solution of iodine with known concentration. The iodine solution was prepared as follows. About 5 cm3 –1 of the standard KIO3_III working solution (0.7 mmol kg , see the previous paragraph) was transferred using a plastic syringe into a dried and weighed cylindrical wide-mouth 40 ml titration vessel. The vessel was weighed again. Using two 1 ml syringes approximately 0.2 cm3 of solution containing KI (puriss. 99.5%, Sigma-Aldrich, 2.1 mol dm–3) and KOH (8.7 mol dm–3) (alkaline KI solution) was added. Using a third syringe approximately 0.2 cm3 of –3 H2SO4 solution (5.3 mol dm ) was added. Under acidic conditions iodine is formed quantitatively according to the reaction 6. The iodine formed from KIO3 –1 was titrated with ca 0.0015 mol kg Na2S2O3 titrant (see reaction 5) as soon as the iodine was formed. It is not possible to use pre-titration here in order to minimize iodine evaporation: until iodate (oxidizing agent) is in the solution sodium thiosulphate (reducing agent) can not be added or else they react each other with a different stoichiometry. Titrations were done using a plastic syringe (20 cm3, Brown, needle external diameter 0.63 mm) filled with titrant and weighed. The titration end-point was determined amperometrically. Voltage of 100 mV was applied between two platinum electrodes (Metrohm Pt-Pt 6.0341.100, see the Appendix 2 for more information). Titration was completed when the current became equal to the background current (usually around

24 0.015 μA). The background current value corresponding to the equivalence point was established every day before the titrations. The random effects on the titration equivalence point are taken into account by the uncertainties of the  factors, as explained in section 3.1. The uncertainty contribution of the possible systematic effects was estimated as ± half of the drop of titrant (assuming rectangular distribution), whereby the drop mass is estimated as 0.0105 g of titrant. This leads to standard uncertainty estimate of 0.0030 g, which is a conservative estimate, because it is possible (and was used in the experiments) to dispense the titrant in amounts approximately equal to a tenth of a drop. This way the method is more precise than usual volumetric methods. The magnitude of this uncertainty estimate covers the human factor (deviation from the point where the operator considers that the equivalence has been reached), the possible uncertainty of the background current as well as the possible uncertainty of the reading of the amperometric device used for equivalence point determination. In calculations this uncertainty is divided by the respective titrant mass and is assigned as standard uncertainty to the respective F factors corresponding to the equivalence point uncertainty. After titration the syringe was weighed again to determine the consumed titrant mass. Seven parallel measurements were carried out according to the described procedure and the average result was used as the titrant concentration.

3.3.4. Sampling and sample preparation Samples were taken and prepared in 10 cm3 glass flasks with ground joint stoppers (standard ground glass stoppers). Flasks were calibrated before at different temperatures to account for the expansion/contraction of the flasks. Seven parallel samples were taken as follows: a) The flask was filled by submerging it under the water to be measured. Every care was taken to avoid air bubbles in the flask. 3 –3 3 b) 0.2 cm of MnSO4 solution (2.1 mol dm ) and 0.2 cm of the alkaline KI solution was added with previously calibrated glass syringes (250 μl, Hamilton) to the bottom of the glass flask simultaneously (an equal amount of water was forced out of the flask). Care was taken in order not to introduce air bubbles when adding those solutions. c) The flask was stoppered with care to be sure no air was introduced. The contents of the flask were mixed by inverting several times. The presence of possible air bubbles was monitored. The sample was discarded if any air bubble was seen. A brownish-orange cloud of Mn(OH)3 precipitate appeared. The precipitate was let to form until it was settled down according to reaction 1. 3 d) The solution was then acidified by adding 0.2 cm of H2SO4 solution (5.3 mol dm–3) with another syringe (250 μl, Hamilton) below the solution surface. It is very important that all the precipitate formed stays in the flask.

25 7 Under acidic conditions Mn3+ ions oxidize iodide to iodine, which eventually – forms I3 ions with the excess of KI.

The flask was stoppered again and mixed until the precipitate was dissolved. At this stage the air bubbles do not interfere anymore.

3.3.5. Titration of the sample with the Na2S2O3 titrant Before the start of the actual titration about 80–90% of the supposed amount of –1 the titrant (Na2S2O3, 0.0015 mol kg ) is added to the titration vessel from a pre- weighed plastic syringe. The formed iodine solution is transferred quantitatively to the titration vessel (to minimize evaporation of iodine) and titrated to the endpoint amperometrically as it has been discussed in section 3.3.3. This approach – so-called pre-titration – allows ca 80% of the iodine to react immediately and is a powerful tool in helping to minimize the volatilization of iodine during titration. The remaining small extent of iodine volatilization is taken into account by a correction. After reaching the end point the titration syringe was weighed again. The amount of the consumed titrant was determined from mass difference. Seven parallel titrations were carried out.

3.3.6. Determination of the correction for oxygen introduced from the reagents The concentration of DO in the reagents is low and the amount of the reagents is small. Nevertheless the amount of oxygen introduced by the reagents is on an average around 1 µg, which is significant compared to the amounts of oxygen involved in this work. Therefore this amount of oxygen has to be taken into account. In order to do this with minimal additional uncertainty it is important that the amount of oxygen in the reagents is as reproducible as possible. There are two possible approaches for achieving reproducible oxygen content of the reagents: (1) use reagents where the oxygen content has been decreased to a minimum (deoxygenated reagents) or (2) use reagents saturated with air. In principle it would be desirable to use reagents with DO content as low as possible. Initially this approach was taken. During the experiments it was discovered that the oxygen content in the reagents was highly variable. This caused high uncertainty of the correction term (even though its magnitude was small). One of the reasons might be contamination of the reagents by atmospheric oxygen during transfer to the sample bottle. Reagents saturated with air (which in turn was saturated with water vapor) were then taken into use. Although the determined magnitude of the correction term with such reagents was larger, its stability (reproducibility of parallel measurements) was significantly better. This led to ca two times lower combined standard uncertainties

26 of determined oxygen content in samples. Air-saturated reagents are immune to contamination by air oxygen. There are several ways for accounting for the effect caused by the reagents. In this work addition experiments were used. From the same sample different subsamples were collected at the same time and different amounts of the reagents were added to determine the amount of oxygen that is introduced with the reagents. Reagent solutions were added one to three times (different amounts) to consider not only the oxygen that was in the reagent solutions but also from the procedure itself (sample contamination). The concentration of DO found in the sample was plotted against times of added reagent solutions. The correction (CFO2) was found from the slope of the graph, see the Graph 3.

Graph 3. Curves from the adding tests (20.02.12).

Fourteen experiments were made for determination CFO2. Each determination was made with three points. The concentration of DO in reagents depends on atmospheric pressure. Therefore all the obtained slope values were converted to the normal (sea-level) pressure. Two of the resulting graphs were strongly non- linear (relative standard deviation of linear regression slope was above 20%) and these were left out. The remaining 12 results (obtained on 7 different days) were evaluated for agreement with the Grubbs test [38] and no disagreeing results were found. CFO2 is found as the average of the values from Table 1 (last column). Its value is 0.0940 mg kg–1 (corresponding to the normal pressure) with standard deviation 0.0068 mg kg–1. This standard deviation also accounts for the variability of the amount of added reagents. Although the mean value of CFO2 is used as correction the standard deviation of the single results (not the mean) is used as its uncertainty estimate, because this uncertainty takes into

27 account the variability of CFO2 and is not averaged during the measurements in any way. Each time the correction was used it was recalculated to the actual atmospheric pressure at the location of the measurement. Atmospheric pressure was measured by digital barometer PTB330 (Ser No G37300007, manufactured by Vaisala Oyj, Finland).

Table 1. Results of reagents adding tests.

CF Date b a ba s(b )a s(b )a C Refb Δc P (Pa) St.dev.d O2 1 0 1 0 O2 (norm) 10.10.11 0.0862 9.0116 0.0074 0.0161 9.01 0.00 99896 9% 0.087 14.10.11 0.0941 9.2034 0.0088 0.0189 9.17 –0.04 101677 9% 0.094 0.0983 9.2494 0.0048 0.0103 9.23 –0.02 102394 5% 0.097 24.10.11 0.0897 9.2707 0.0046 0.0099 9.23 –0.04 102394 5% 0.089 0.1069 9.2171 0.0152 0.0327 9.20 –0.02 102054 14% 0.106 28.11.11 0.1065 9.2131 0.0134 0.0289 9.20 –0.01 102054 13% 0.106 0.0912 9.0622 0.0077 0.0166 9.03 –0.03 100187 8% 0.092 31.11.11 0.0920 9.0629 0.0061 0.0132 9.03 –0.03 100187 7% 0.093 0.0979 9.0105 0.0159 0.0344 9.00 –0.01 100057 16% 0.099 23.01.12 0.0841 9.0305 0.0116 0.0250 9.00 –0.03 100057 14% 0.085 0.0897 12.6467 0.0052 0.0113 12.66 0.01 100677 6% 0.090 20.02.12 0.0886 12.6608 0.0005 0.0010 12.66 0.00 100677 1% 0.089 a Slope (b1) and intercept (b0) of the linear regression and their standard deviations. b reference values of DO obtained from ref 13 (in mg kg–1). c difference between the calculated reference value and b0. These values should have same magnitude while b0 corresponds to situation when reagents are not added (DO concentration in pure sample). d relative standard deviation of linear regression.

3.3.7. Determination of parasitic oxygen In order to determine the amount of oxygen introduced to the sample through the junction between the stopper and the flask neck (input quantity IntO2) seven subsamples were collected at the same time and the reagents (MnSO4 solution and alkaline KI solution) were added. Three of them were titrated on the same day. The remaining four were titrated two days later. The mass of DO found in the sample was plotted against the precipitation time. The mass of the introduced oxygen per minute was found as the slope of the Graph 4. The amount of parasitic oxygen introduced was found as ca 0.00007 mg kg–1 min–1. The precipitation time for the analysis is different and ranges from few tens of

28 minutes to slightly more than an hour, so the content of intruded oxygen can be estimated to be in the range of 0.0015 to 0.0050 mg kg–1 during the precipitation time. This effect is small compared to the overall repeatability of the measurement. The exact mechanism of this process is not known, the determination of this effect is very uncertain and the precipitation time also differs widely. Therefore, based on recommendations from ref 39 it was decided not to correct –1 for this effect but to assign the value of 0 mg kg to IntO2 and take this effect into account entirely as an uncertainty contribution of ±0.005 mg kg–1.

Graph 4. Determination of parasitic oxygen (IntO2).

3.3.8. Iodine volatilization Experiments to determine the iodine volatilization amount at different experimental conditions (stirred vs standing solution and high (ca 2.4 mmol kg–1) vs low (ca 0.5 mmol kg–1) concentration) were carried out. As it is seen from the Graph 5, the largest effect on iodine volatilization is stirring. Also the concentration of iodine in the solution influences volatilization, but this effect is not that large and it does not come out that clearly.

29 8

Graph 5. Stirring and concentration effect on iodine volatilization.

In this procedure in the case of titration of the sample it is possible to minimize the volatilization by adding about 80–90% of the expected titrant consumption into the titration vessel before transferring the iodine-containing sample solution to the titration vessel (so-called “pre-titration”). This way the main part of the iodine reacts immediately, significantly minimizing volatilization. At the same time, evaporation of iodine occurs during transfer of the iodine solution formed from the sample into the titration vessel and this has to be taken into account also. The pre-titration approach is not possible in the case of determination of the titrant concentration because there it is necessary to stir the solution containing iodate, iodide and sulphuric acid properly before starting the titration. If this is not done then thiosulphate can react directly with iodate, not with iodine and the reaction loses its stoichiometry. For both titrations the volatilization has been taken into account by introducing two corrections, nI2_vol_s and nI2_vol_t, for titration of the sample and standardizing of the titrant, respectively. For evaluating the effect of iodine volatilization on titrant standardization four parallel measurements of a solution of 5 ml with iodine concentration of 1.9 μmol g–1 were made by keeping them for different times, 1, 5 and 10 minutes while stirring at 800 rpm (PTFE stirrer bar: length 21 mm, diameter 6 mm). The results were plotted as iodine loss (in μmol) against time (see the Graph 6) and the estimates for the loss of iodine in one minute were found as the slopes of the four graphs: 0.051, 0.040, 0.048, 0.035 μmol min–1. The average iodine loss is thus 0.043 μmol min–1 with standard deviation of 0.007 μmol min–1.

Graph 6. Determination of iodine volatilization.

The titration time during standardization ranges from 30 s to 60 s. The average time of 45 s was used as the estimate of titration time. So, the iodine volatilization during the standardization nI2_vol_t=0.0325 µmol and it has two uncertainty components: repeatability of the average iodine loss and time, which is ±15 seconds according to ±0.008 µmol iodine. For evaluating the effect of iodine volatilization on titration of the sample, experiments on two different days were done, 7 replicates on both days. Every experiment consisted in titration of ca 10 ml of iodine solution with concentration of 0.5 µmol g–1 (the concentration of iodine in processed sample solutions is similar) prepared from KIO3 into the sample type of bottle that was used for sample collecting and processing. This solution was transferred into the titration vessel in a similar way as was used for titration of the samples and was titrated (using pre-titration). The difference of the amounts of initially added iodine and iodine calculated from titration data gave the amount of volatilized iodine. The average amount of volatilized iodine by titrating the sample nI2_vol_s was found as 0.0116 µmol with the standard deviation of 0.0014 µmol, which is accounted as u(nI2_vol_s) (all results are brought in Table 2).

31 Table 2. The absolute (in μmol) and relative (in %) losses of iodine during titration mimicking the titration of the sample.

Date Δn(I2) µmol Δn(I2) % 0.01036 0.20% 0.01098 0.22% 0.01167 0.23% 19.04.2012 0.01074 0.22% 0.01281 0.25% 0.01079 0.21% 0.01117 0.21% 0.01365 0.23% 0.01409 0.23% 0.01134 0.20% 27.04.2012 0.01155 0.19% 0.00866 0.14% 0.01105 0.18% 0.01284 0.21% Average 0.0116 0.21% St.dev 0.0014 0.026%

3.4. Saturation method for obtaining the reference DO values Air-saturated fresh pure (MilliQ) water (at constant humidity and temperature) was used as reference medium for validating the method. The water was aerated until equilibrium was attained. The saturation medium was created in a modified (added a second bath) thermostat CC2-K12 (Peter Huber Kältemaschinen- bau GmbH, Germany). See the Scheme 1 and the photo series in Appendix 1. The air used for saturation was taken from the air inlet situated on the roof of the building. The air flow velocity during calibration was around 1 dm3 min–1. The ordinary aquarium spray was used (at depth of 13 cm). The estimated diameter of the bubbles was between 0.8 to 1.8 mm.

Scheme 1. Thermostat CC2-K12 with additional bath, stirrer and thermometer.

The double-bath thermostat provides good temperature stability (see Table 3).

Table 3. Temperature stability test within 10 minutes before the sampling. Temperature 30°C 25 °C 20 °C 15 °C 10 °C 5 °C 29.816 24.826 19.925 15.004 10.074 5.053 29.810 24.824 19.926 15.002 10.073 5.054 29.808 24.829 19.926 14.999 10.065 5.054 29.808 24.826 19.925 14.999 10.066 5.057 29.811 24.828 19.925 15.000 10.069 5.057 29.812 24.832 19.923 14.998 10.065 5.053 29.811 24.843 19.917 14.999 10.067 5.053 29.809 24.840 19.923 14.997 10.067 5.048 29.811 24.837 19.923 15.000 10.067 5.050 29.816 24.837 19.921 15.004 10.068 5.054 St.dev 0.0028 0.0065 0.0029 0.0023 0.0031 0.0027

In this case the maximum standard deviation has been taken as the standard uncertainty (u(Tinstab)=0.0065 K). Atmospheric pressure was measured by digital barometer PTB330 (Ser No G37300007, manufactured by Vaisala Oyj, Finland,

33 9 calibrated by manufacturer 19.09.2011) with uncertainty u(pcal) = 7 Pa (k = 2). The air bubbled through the second bath was saturated with water vapor by passing it through two saturation bottles (both immersed in the same thermostat). The level of air humidity after the second saturation vessel was measured using digital hygrometer Almemo 2290–8 with sensor ALMEMO FH A646 E1C (manufacturer AHLBORN Mess- und Regelungstechnik GmbH). The humidity of the air bubbled through the water in the second bath was never lower than 95% RH. The uncertainties of all relative humidity measurements are ± 5 %RH (k = 2). The CO2 content of the air was measured during calibration by Vaisala CARBOCAP® CO2 Transmitter Series GMP 222 (SN: X0150001, manufactured by Vaisala, Finland). The evaluated uncertainty of the CO2 concentration was ± 100 ppm (k = 2). The temperature of the measurement medium was measured by reference digital thermometer Chub-E4 (model nr 1529, serial No A44623, manufacturer Hart Scientific) with two Pt100 sensors. The uncertainties of all temperature measurements are ± 0.02 °C (k = 2 calibrated by the Estonian NMI, AS Metrosert on May 2011).

3.5. Differences between gravimetric Winkler carried out in syringes and in flasks The main procedural differences between SGW and FGW are listed in Table 4. FGW is developed to decrease the measurement uncertainty, so mainly the changes in FGW procedure are made for it.

Table 4. Differences between two gravimetric Winkler method procedures.

Method SGW FGW Remarks characteristic Potassium iodate Volumetrically Uncertainty was decreased Gravimetrically by solution using a volumetric by ca 2 times consecutive dilutions preparation flask (1 dm3) Amperometric (current Uncertainty decreased from between two Pt electrodes 0.020 g (in SGW) to Titration end- Starch decreases to background 0.0032 g (in FGW) point detection current when all iodine is titrated) Open vessel increases iodine volatilization, but Capped with plastic Titration vessel Open vessel caps are impractical to use caps because of the electrode in case of FGW Because iodine Determined with Determined with separate volatilization is more Iodine separate experiment, experiment, accounted as a pronounced in FGW, volatilization accounted as an correction (with an it was taken into account as uncertainty source uncertainty) a correction

34 Table 4. Continuation Method charac- Remarks SGW FGW teristic Titrant can be added more precisely when using a Na S O titrant 2 2 3 0.0025 mol kg–1 0.0015 mol kg–1 titrant with lower concentration concentration (influence of the drop volume is smaller) 10 cm3 glass The largest uncertainty syringes with PTFE contribution in SGW was 10 cm3 glass flasks, plungers, sample uncertainty due to oxygen calibrated at different Sampling and was aspirated into dissolved in the syringe temperatures, submerged sample treatment the pre-weighed plunger, so it was necessary under the water to be syringe, the syringe to abandon the use of PTFE measured was weighed again with sample Replicate 6 7 measurements

CFO2, accounts also For decreasing the analysis C , determined oxygen, that comes from time in FGW the reagents Oxygen in the O2_reag daily with separate the procedure of adding the were saturated with air and Winkler reagents experiment reagents (average of 12 its content in the reagents adding test results) was assumed to be constant Contamination In FGW the contamination Contamination through the Sample mainly from PTFE is minimized by using junction between the contamination plunger, O , glassware only for sample 2_syringe stopper and the flask, Int , with atmospheric determined with six O2 processing determined separately, max oxygen separate 0.005 mg kg–1 experiments

35 4. RESULTS AND DISCUSSION

4.1. Validation of the methods Validation of the methods includes a number of tests: determination of parasitic oxygen from different sources, iodine volatilization in two different cases, weighing tests and in addition the test for trueness. For evaluation of trueness water saturated with air (below termed as saturation conditions) under carefully controlled conditions (air source, temperature, air pressure, air humidity) was used. Every trueness test consisted of taking six or seven samples (in SGW and FGW, respectively), measuring their DO concentration with those method and comparing the obtained average DO concentration with the reference DO values evaluated according to the standard ISO 5814 [13] by an empirical formula originally published by Benson and Krause [14]. The uncertainties of the reference values were calculated as detailed in the Appendix 3. The agreement was quantified using the En number approach [40]. The average results of 6 or 7 parallel measurements in SGW or FGW, respectively (as detailed in the experimental section) in comparison with the reference values from ref 13 are presented in Tables 5 and 6.

Table 5. Results of the SGW (in mg dm–3) under different experimental conditions.

Date 1.02.08 22.02.0825.02.08 3.03.08 31.03.08 7.04.08 9.04.08 18.04.08 Saturation 20 oC 20 oC 25 oC 5 oC 15 oC 20 oC 20 oC 20 oC conditions

CO2SGW 9.24 8.78 8.06 12.31 10.06 8.97 8.94 8.96 a U(CO2SGW) 0.09 0.08 0.10 0.13 0.13 0.10 0.14 0.10

U(CO2SGWrel) 0.97% 0.91% 1.24% 1.06% 1.29% 1.11% 1.57% 1.12%

CO2Ref 9.20 8.79 8.10 12.41 10.17 8.99 8.92 8.95 a U(CO2Ref) 0.06 0.06 0.06 0.08 0.06 0.06 0.06 0.06 b 0.04 –0.01 –0.04 –0.10 –0.11 –0.02 0.02 0.01 c En 0.4 –0.1 –0.3 –0.7 –0.7 –0.2 0.1 0.1 a Expanded uncertainty at k = 2 level. b Δ = CO2SGW – CO2Ref. c The En values are calculated and interpreted as explained in ref 40: |En| ≤ 1 means agreement, |En| > 1 means disagreement.

As it is seen from the Tables 5 and 6, the agreement between the titration methods and the saturation values in the concentration range from 7 to 13 mg dm–3 (temperature range 30 °C to 5 °C) is very good: the absolute values of En numbers [40] are below 1 in all cases. Particularly good agreement with reference value is found in case of FGW results.

36 10

Table 6. Results of the FGW in comparison with the reference values obtained from ref 13 (in mg dm–3) under different experimental conditions.

Date 15.03.12 15.03.1220.02.12 30.01.12 23.01.12 16.01.12 5.01.12 3.01.12 2.01.12 30.12.11 14.11.11 11.11.11 28.10.11 14.10.11 KCl KCl 1M, Saturation 0.01M, 5°C 25°C 20°C 15°C 30°C 25°C 15°C 20°C 10°C 5°C 20°C 20°C 25°C conditions 25°C

CO2FGW 8.298 6.172 12.680 8.538 8.999 10.052 7.286 8.176 9.941 8.876 11.241 12.968 9.189 9.180 a U(CO2FGW) 0.028 0.023 0.035 0.025 0.028 0.028 0.024 0.025 0.029 0.026 0.031 0.034 0.028 0.026

U(CO2FGWrel) 0.34% 0.38% 0.28% 0.30% 0.31% 0.28% 0.34% 0.31% 0.29% 0.29% 0.28% 0.27% 0.31% 0.29% d d CO2Ref 8.310 6.197 12.698 8.542 8.999 10.052 7.276 8.164 9.942 8.863 11.218 12.949 9.190 9.167 a e e U(CO2Ref) 0.100 0.100 0.062 0.065 0.062 0.062 0.061 0.062 0.061 0.061 0.062 0.063 0.063 0.063 b 37 Δ –0.012 –0.025 –0.017 –0.004 0.000 0.000 0.011 0.012 –0.001 0.013 0.022 0.019 –0.001 0.013 Enc –0.1 –0.2 –0.2 –0.1 0.0 0.0 0.2 0.2 0.0 0.2 0.3 0.3 0.0 0.2

a Expanded uncertainty at k = 2 level. The number of effective degrees of freedom varied from 50 to 75, depending on conditions (see ref IV for details), therefore this uncertainty roughly corresponds to 95% confidence level. b Δ = CO2FGW – CO2Ref. c The En values are calculated and interpreted as explained in ref 40: |En| ≤ 1 means agreement, |En| > 1 means disagreement. d Reference value is calculated using values from ref 41. e Uncertainty of the reference value is estimated to be larger due to different experimental conditions and due to using an additional function taking into account the salting out effect.

4.2. Measurement uncertainties Comprehensive uncertainty evaluation was made for both methods. As it is seen from Tables 5 and 6, depending on the exact measurement conditions the expanded uncertainty at k = 2 level of the methods (at saturation conditions) varies in the range of 0.08 – 0.13 and 0.023 – 0.035 mg dm–3 in SGW and FGW, respectively. The uncertainty budgets of the two developed methods together with the relative uncertainty contributions of the input quantities (expressed in %) are presented in Figures 1 and 2, respectively. The uncertainty contributions differ somewhat from measurement to measurement and the indicated contributions refer to a (rather average) particular measurement. The uncertainties of DO concentration of the two methods differ by more than three times and because of that the relative uncertainty contributions are not in all cases useful for comparison. Therefore in the discussion also the absolute uncertainty components (in k = 2 confidence level) of the input quantities are used, related directly to the dissolved oxygen concentration and expressed in mg dm–3.

M KIO3 0.0% V flask P KIO3 0.7% 3.6% t flask 0.3% m KIO3_s F m_KIO3 m 3.9%KIO3 0.0% Γm C KIO3 Na2S2O3 _ KIO3 F m_Na2S2O3_KIO3 m Γ Na2S2O3_reag 8.5% 3.9% 0.0% mreag F m_KIO3_endp C Na2S2O3 0.7% O 2 _syringe 5.1% 0.0% 0.5% F m_reag 0.0% F m_Na2S2O3_reag F I2 M O2 0.0% F m_reag_endp C Na2S2O3 0.2% 0.0% C O2_reag 1.0% 17.6% 2.1% F I2 0.0% Γ mreag_s ms F m_s 0.9% O _syringe m 2 Γ Na2S2O3_s 0.0% 47.3% F m_Na2S2O3_s ms 0.0% 6.9%

M O2 F m_s_endp 0.0% 24.9%

F I2 C O2_s 0.2% 8.78 [mg dm-3] 0.08 U , k=2

Figure 1. Uncertainty budget of the SGW in 22.02.2008.

38 m KIO3_II 0.0% m KIO3_I_transf 7.6% m KIO3_III m KIO3_II_transf 0.0% 3.8%

m KIO3_s 0.1% m M KIO3 KIO3 F m_KIO3 0.0%Γm 0.0% m KIO3_I Na2 S 2O3 _ KIO3 F m_KIO3_endp 0.0% 0.9% 1.5% C KIO3_III P KIO3 15.4% 26.9% n I2_vol 21.6%

F m_Na2S2O3_KIO3

C Na2S2O3 0% m F m _Na2S2O3_s Na 2S2O3_s 51.1% 0.1% Γ Int O2 M O2 ms 4.0% 0.0% 4.6%

p F m_s 0.0% 1.0%

F m_s_endp 6.3% CF O2 30.4% n I2_vol_s 2.4%

C O2_s 8.538 [mg dm-3] 0.025 U , k=2

Figure 2. Uncertainty budget of the FGW in 30.01.2012.

–3 The absolute uncertainty component of KIO3 solution is 0.024 mg dm and 0.013 mg dm–3 in the SGW and FGW, respectively. The decrease of the uncertainty is due to purer standard substance and gravimetrically prepared solutions. Nevertheless, because the overall uncertainty of the FGW method is significantly lower the relative uncertainty components are 8.5% and 26.9% in the SGW and FGW, respectively. Consecutive dilutions of the KIO3 solutions prepared gravimetrically in FGW were used for minimizing the uncertainty caused by weighing small amounts of solid standard substance (as was done in the case of SGW). Although this way one more uncertainty source was introduced in FGW – evaporation of water from transferred stock solutions (mKIO3_I_transf and mKIO3_II_transf) – the uncertainty component is still lower. In both methods the purity of KIO3 was one of the main contributors. The uncertainty of titrant concentration accounts for 17.6% and 51.1% of the uncertainty in the SGW and FGW, respectively. The respective absolute uncertainty components are 0.035 mg dm–3 and 0.018 mg dm–3, being ca two times different. The most important uncertainty contributions to CNa2S2O3 are distinctly different in the case of SGW and FGW. In SGW the main contributors are CKIO3, uncertainty due to titration end-point and repeatability of the titrant standardization (8.5%, 5.1% and 3.9% of the overall uncertainty, respectively). In FGW also about half of this uncertainty was caused by CKIO3, but remaining

39 half is covered by uncertainty due to iodine volatilization during the titration. In SGW this uncertainty source was small because of coating the titration vessel. The most important uncertainty contributions in SGW are uncertainty due to oxygen dissolved in the PTFE syringe plunger O2syinge (47%) and the uncertainty of titration end-point determination (25%). In the case of FGW the former is largely eliminated by the different sampling approach. The latter is minimized in FGW by amperometric end-point determination instead of starch. This influence is remarkable: the absolute uncertainty component due to end-point determination decreased about 6 times, from 0.042 mg dm–3 to 0.0064 mg dm–3. In FGW the uncertainty contributor O2syinge is eliminated by using glass flask for sample processing, but instead of this in FGW component IntO2 is introduced. This quantity accounts for sample contamination when using flasks. O2syinge is huge compared to IntO2 and that is why it is taken into account as a correction, but the IntO2 is accounted for only as uncertainty source. Uncertainty introduced by contamination of the sample is 47% and 4% of the overall uncertainty for SGW and FGW, respectively. When expressed as absolute uncertainty components, 0.058 mg dm–3 and 0.0051 mg dm–3, respectively, it can be see that the uncertainty due to contamination of the sample decreased by 11 times when moving from SGW to FGW. In SGW the DO concentration in Winkler reagent solutions was determined daily. This stage was time-consuming and it was eliminated in FGW by using reagents saturated with air. So in FGW this contributor is displaced against CFO2, which is a constant and involves determination of this parameter as well as the real change in the DO concentration and it also saves about 2 hours analysis time. These contributors correspond about 0.012 mg dm–3 and –3 0.014 mg dm of the all uncertainty, CO2_reag and CFO2, respectively, demonstrating a slight increase of the uncertainty contribution due to oxygen dissolved in Winkler reagents when moving from SGW to FGW.

4.3. Comparison with the uncertainties of other Winkler methods published in the literature The reliability of the Winkler method results is mostly discussed in terms of repeatability and agreement with other methods’ data. Table 7 summarizes the available literature data. The last column of the table indicates the meaning of the accuracy estimate. There is a large variety of the ways how accuracy was estimated.

40 Table 7. Accuracy information of DO measurement results by the Winkler method from different literature sources. Accuracies estimated as repeatabilities are given in italic.a

Accuracy Reference estimate Remarks, the meaning of the accuracy estimate (mg dm–3) Repeatability recalculated to the saturated DO Carpenter et al. [29] 0.004 concentration at 20 °C The precision or repeatability that can be achieved Carritt et al. [18] 0.07 by a good analyst during the replication of certain standardization procedures. Repeatability, 4 separate laboratories, batch standard Standard ISO 5813 [16] 0.03–0.05 deviation Standard methods for Repeatability in distilled water. In wastewater the 0.02 wastewater [42] repeatability is around 0.06 mg dm–3 Labasque et al. [19] 0.068 Within-lab reproducibility over ten consecutive days Combined standard uncertainty, re-estimated in this Fox et al. [21] 0.015–0.115 work. [II] Combined standard uncertainty, re-estimated in this Krogh [20] 0.135 work. [II] Combined standard uncertainty, re-estimated in this Whitney [22] 0.11 work. [II] Method SGW in this work. Combined standard Helm et al. [III] 0.04–0.07 uncertainty, comprehensive uncertainty analysis Repeatabilities at 1.3 – 6.96 mg L–1 dissolved O Horstkotte et al. [43] 0.02–0.15 2 levels, in-line monitoring 0.15 μmol kg–1, stated as a precision. Calculations with data presented in the article gave average Langdon [8] 0.005 relative repeatability 0.35% that corresponds on DO concentration of 9 mg dm–3 to 0.03 mg dm–3. The repeatability in measurement at mg L−1 levels is Sahoo et al. [23] 0.00014–0.11 0.11 mg L−1 with RSD 1.9% and at 10 μg L−1 level is 0.14 μg L−1, RSD 1.4% Method FGW in this work. Combined standard Helm et al. [IV] 0.012–0.018 uncertainty, comprehensive uncertainty analysis

a All repeatability and reproducibility estimates are given as the respective standard deviations.

From the point of view of practical usage of the methods the most useful accuracy characteristic is the combined measurement uncertainty taking into account all important effects – both random and systematic – that influence the measurement results. A number of authors characterize their data by repeatability [26] estimates, which by definition do not take into account any systematic effects and may give a false impression of highly accurate method. Such estimates (presented in italics in Table 7) cannot be compared with measurement uncertainties and are left out of consideration. As it is seen from Table 6 and Table 7 the FGW described in the present work has the lowest uncertainty.

41 11 4.4. Comparison of the Gravimetric Winkler method with saturation method for calibration of DO sensors Today calibration of electrochemical and optical sensors is generally done by using the saturation method. The reference values of DO saturation concentrations are usually found using the equation by Benson and Krause [13,14,15], which takes into account water temperature, air pressure and air humidity. For obtaining accurate results an accurate barometer, an accurate thermometer and a very stable thermostat are needed. Even with good equipment the saturation method is tricky to use and is prone to errors. One of the main issues is the super- or undersaturation. The smaller are the bubbles used for saturation the faster the saturation conditions are achieved. At the same time small bubbles may lead to supersaturation [52]. Use of the larger bubbles avoids supersaturation, but makes the time necessary for saturation long. The result is that if the operator is not patient enough the solution is undersaturated. Fur- thermore, it is not documented in refs [13,14,15] what was the geometry of the nozzle and the bubble size, but these are important parameters of the saturation method. If uncertainty due to the possible super- or undersaturation is carefully taken into account then the resulting uncertainty is by 2–3 times higher than the uncertainty of the gravimetric Winkler method. When measuring DO concentration with optical or amperometric sensors in water with high salinity, e.g. seawater, then calibration should be carried out in water with similar salinity. This is very difficult to do rigorously with the saturation method because the available saturation values of DO concentration in seawater are significantly less accurate than the respective values in pure water. An alternative approach is to calibrate in water and apply a salinity correction, but this again introduces a substantial uncertainty from the correction. At the same time, the dissolved salts do not hinder usage of the Winkler method.

42 CONCLUSIONS

This work presents a highly accurate primary method for determination of dissolved oxygen concentration in water based on the Winkler titration method. Careful analysis of the relevant uncertainty sources was carried out. The method was optimized for minimizing all uncertainty sources as far as practical, resulting in the most exhaustive uncertainty analysis of the Winkler method ever published. More than 20 uncertainty sources were found and their magnitudes evaluated. The most important uncertainty contributors are: oxygen introduced from the reagent solutions, iodine volatilization during the analysis and purity of the potassium iodate standard substance. Depending on measurement conditions and on the dissolved oxygen concentration, uncertainties (k = 2, expanded) of the results obtained using the developed gravimetric Winkler method are in the range of 0.023–0.035 mg dm–3 (0.27–0.38%, relative).

43 SUMMARY

Dissolved oxygen (DO) content in natural waters is a very important parameter. Recent studies show decrease in DO content in several areas of world oceans. Processes leading to this decrease are not completely understood and it is very important to be able to measure DO content very accurately for studying the dynamics of these processes. Amperometric and more recently also optical oxygen sensors are widely used in DO measurements. These sensors need calibration and therefore solutions with accurate DO concentration are necessary. Oxygen is a very unstable analyte due to its chemical, physical and biological properties. For this reason it is almost impossible to prepare oxygen solutions in ordinary way by dissolving an accurately measured amount of oxygen in water. The problem can be solved by determining DO content in the calibration solutions using some primary method (i.e. method not needing calibration) that also ensures traceability to SI units. The most reliable primary DO measurement method available is the Winkler titration method. For this method several of factors limiting its accuracy were found, including the volumetric nature of the classical Winkler method. A number of modifications of the Winkler method have been proposed that should eliminate or compensate for these disadvantages. However, before the start of this work there were no publications available that would comprehensively review all the important uncertainty sources of the Winkler method and still a lot of room existed for improving the accuracy of the Winkler method. Most of the publications give repeatability of the results only. In some cases individual uncertainty sources were separately estimated. The method proposed in this work differs from the previously proposed method by its gravimetric approach, which assures lower uncertainty. Detailed analysis of the uncertainty sources and comprehensive uncertainty estimation were carried out. Experiments for determining the different influence factors were carried out, corrections were determined and uncertainty contributions for accounting these influences were estimated. As a result a detailed uncertainty budget was compiled. This budget is very useful for optimizing the function for getting more accurate measurement results. The optimization was carried out and as a result of this the gravimetric Winkler method modification for determination of DO in water giving the results with lowest available uncertainty was developed.

44 SUMMARY IN ESTONIAN

Kõrge täpsusega gravimeetriline Winkleri meetod lahustunud hapniku määramiseks Lahustunud hapniku sisaldus looduslikes vetes on väga oluline parameeter. Viimasel ajal on täheldatud hapnikutaseme langust maailma ookeanide mitme- tes piirkondades. Protsessid, mis selleni viivad ei ole lõpuni arusaadavad ja nende lahtimõtestamiseks on väga oluline suuta hapnikusisaldusi kõrge täpsu- sega mõõta. Üsna laialdaselt mõõdetakse lahustunud hapniku sisaldust vees amperomeetriliste ja viimasel ajal ka optiliste hapnikuanalüsaatoritega. Need analüsaatorid vajavad kalibreerimist ja ei ole seega kasutatavad primaarmeeto- ditena. Kalibreerimiseks vajalike stabiilse kontsentratsiooniga hapnikulahuste valmistamine traditsioonilisel moel on hapniku keemiliste, füüsikaliste ja bioloogiliste omaduste tõttu pea võimatu. Seega, et tagada lahustunud hapniku määramisel tulemuste jälgitavus SI ühikuteni, on tarvilik primaarmeetodi olemasolu, millega saaks kalibreerimiseks kasutatavates lahustes hapniku sisaldust kõrge täpsusega mõõta. Primaarmeetodiks lahustunud hapniku määramisel on Winkleri jodomeetriline tiitrimismeetod. Sellel meetodil on leitud rida kitsaskohti kaasa arvatud see, et klassikaliselt on tegemist mahtanalüütilise meetodiga. Kirjanduses on avaldatud terve hulk Winkleri meetodi modifikat- sioone, mis peaksid selle meetodi puudusi parendama. Nende metoodikatega saadud tulemuste korrektsed, kõiki olulisi allikaid arvestavad määramatuse hinnangud aga puudusid kirjandusest enne käesoleva töö algust. Enamik kirjandusallikaid on piirdunud vaid korduvuse andmetega, mõnel juhul oli eraldi hinnatud ka üksikuid muude määramatuse allikate panuseid. Erinevalt seni pakutud Winkleri meetodi modifikatsioonidest on käesolevas töös välja töötatud metoodika gravimeetriline tagades sellega madalama mää- ramatuse kui senini saavutatud. Töö käigus välja töötatud metoodika jaoks viidi läbi detailne mõõtemääramatuse hindamine. Selle jaoks sooritati eksperimente mitmesuguste mõjuallikate kindlakstegemiseks, leiti nendele vastavad parandid ja määramatuste panused. Määramatuse hindamise tulemusena saadud määra- matuse koond sisaldab erinevate komponentide panuseid ning on võimas abi- vahend meetodi optimeerimiseks ja veelgi täpsemate tulemuste saamiseks. Seda võimalust käesolevas töös ka kasutati ning selle tulemusena arendati välja Winkleri meetodi gravimeetriline modifikatsioon, mis annab seniavaldatutest madalaima määramatusega tulemusi lahustunud hapniku määramisel vees.

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47 37. T.B. Coplen, H.S. Peiser. History of the recommended atomic-weight values from 1882 to 1997: A comparison of differences from current values to the estimated uncertainties of earlier values. Pure Appl. Chem. 1998, 70, 237–257. 38. W. Horwitz, ed. AOAC Official Methods of Analysis (1995), Supplement 1997. 39. B. Magnusson, S.L.R. Ellison, Treatment of uncorrected measurement bias in uncertainty estimation for chemical measurements, Anal. Bioanal. Chem. 2008, 390, 201–213. 40. Conformity assessment – General requirements for proficiency testing ISO/IEC 17043:2010. 41. F.J. Millero, F. Huang, T.B. Graham. Solubility of oxygen in some 1–1, 2–1, 1–2, and 2–2 electrolytes as a function of concentration at 25oC. J. Solution Chem. 2003, 32, 6, 473–487. 42. Standard Methods For the Examination of Water and Wastewater 17th edition, American Public Health Association. 1989 43. B. Horstkotte, J.C. Alonso, M. Miró, V. Cerdà. A multisyringe flow injection Winkler-based spectrophotometric analyzer for in-line monitoring of dissolved oxygen in seawater. Talanta, 2010, 80, 1341–1346. 44. C.N. Murray, J. P. Riley. The solubility of gases in distilled water and sea water— II. Oxygen. Deep-Sea Res. 1969, 16, 3, 311–320. 45. A.C. Montgomery, N. S. Thom, A. Cockburn. Determination of dissolved oxygen by the Winkler method and the solubility of oxygen in pure water and sea water. J. Appl. Chem. 1964, 14, 280–296. 46. H.L. Elmore, T. W. Hayes. Solubility of atmospheric oxygen in water. Proc. Am. Soc. Civil Engrs. 1960, 86, 41–53. 47. E.J. Green, D. E. Carritt. New tables for oxygen saturation of seawater. J. Mar. Res. 1967, 25, 140–147. 48. R.F. Weiss. The solubility of nitrogen, oxygen and argon in water and seawater. Deep-Sea Res. 1970, 17, 721–735. 49. APHA-AWWA-WPCF, Standard Methods for the Examination of Water and Wastewater, 17th ed. (1989) 50. K. Hellat, A. Mashirin, L. Nei, T. Tenno, Acta et Comment Univ. Tartuensis, 1986, 757, 184–193. 51. R.C. Landine. A Note on the Solubility of Oxygen in Water. Water and Sewage Works 1972, 118, 242. 52. G.A. Truesdale, A.L. Downing, G.F. Lowden. The solubility of oxygen in pure water and sea-water. J. Appl. Chem. 1955, 5, 53–62. 53. Аттестат на методику получения равновесных значений концентрации кислорода в воде (1982) МВССО, ЭССР (in russian), copy of this document is available from the authors on request.

48 ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to: – My supervisors doctor Lauri Jalukse and professor Ivo Leito for their unconditional help and support. – My family for being there when in needed them and Priit especially for accepting my choices even if he did not agree. – My long-term drive mate Anu for encouragement me to undertake this step. – The entire staff of the Chair of Analytical Chemistry for their help and friendly atmosphere.

49 13 APPENDIX 1

Photos of the SGW procedure

50 Photos of the FGW procedure

51 APPENDIX 2

Determination of the equivalence point Titration equivalence point was determined amperometrically by using the system shown in Scheme A1.

U mV-meter I  digital reading R 0.01 mV

Resistor Metrohm double 815Ω Pt-Pt electrode 6.0341.100

Potentiometer linear Applied voltage of 100mV

Resistor Resistor 55-250 000 Ω between two Pt electrodes 470 Regulated by potentiometer Ω

Pt Pt

2.4V battery (2 * AA type)

Scheme A1. Amperometric system for determination of equivalence point.

A voltage of 100 mV was applied between two platinum electrodes. As long as both iodine and iodide are present in solution there is non-zero current: on cathode iodine is reduced and on anode iodide is oxidized. When all the iodine has been converted to iodide the current will be equal to the background current. Near the equivalence point there is an excess of iodide in the solution and the current-limiting species is iodine. In this region the current is to a very good approximation linear with respect to the iodine concentration (see the graph A1). Therefore, by monitoring the current value it is possible to predict with very high accuracy how much titrant still needs to be added for reaching the equivalence point. This, together with the possibility of adding fractions of drops with the syringe is the reason of the low uncertainty contribution of titration end- point determination.

Graph A1. Iodine solution titration until the background current is reached.

53 14 APPENDIX 3

Measurement model in calculating the reference DO values

–3 CO2_saturation is the concentration of oxygen in air-saturated MilliQ water [mg dm ] at the measurement temperature. It is normally found using one of the various available empirical equations [15, 50]. In this work the equation A1 by Benson and Krause [14] is used. This equation is considered one of the best available and has been adopted by the standard ISO 5814 [13].

 A A A A  C  exp A  2  3  4  5 W  C  C O2_saturation  1 T  T T  T 2 T  T 3 T  T 4  O2_saturation O2_supersat (A1)  instab instab instab instab 

where T [K] is the temperature of the water and Tinstab [K] is the term taking into account the instability of the temperature in the vessel; A1, A2, A3, A4 and A5 are constants [14,15]. W is the pressure correction factor [13]:

p  p  p W  H2O CO2 (A2) pn  pH2O_100% where p [Pa] is the atmospheric pressure at measurement conditions, ∆pCO2 [Pa] is the uncertainty of carbon dioxide content in air, pn [Pa] is the atmospheric pressure at standard conditions and p [Pa] is the water vapor pressure at 100% relative humidity. It is found according to A3 [15].

 B B  p  p exp B  2  3  (A3) H2O_100% n  1 2   T (T) 

where B1, B2 and B3 are constants. The pressure p [Pa], the real content of H2O in air, is found experimentally (during aeration at calibration conditions).

The CO2_saturation value was used as the reference value for comparing the DO concentrations found with the Winkler method: CO2Ref = CO2_saturation.

Uncertainty estimation of the reference DO values

Uncertainty of CO2_saturation. Numerous tables of saturated DO concentration values have been published [13,14,15,18,44,45,46,47,48,49]. The differences between the data of different authors are generally in the order of 0.05 mg dm–3 [50]. It is assumed that these discrepancies come from the influence of two uncertainty sources: (1) Uncertainty of the reference methods of determining the DO concentration [16] used for compiling the tables of published values of saturated oxygen concentrations [13,50]. (2) Uncertainty arising from the imperfect fit of the mathematical model of oxygen saturation concentrations to the data [13,50]. This can also be regarded as the uncertainties of the constants A1 to A5.

54 All these uncertainty sources are taken into account by the term CO2_saturation. Its value is set to zero and based on the available data its uncertainty is estimated as –3 –3 ± 0.05 mg dm (k = 2) that is u(CO2_saturation) = 0.025 mg dm . Temperature T. This uncertainty source is caused by the limited accuracy of the thermometer used for temperature measurement and is taken into account as u(T). In the case of the thermometer with uncertainty u(T) = 0.01 K was used.

Temperature instability of the calibration medium instab. The uncertainty due to the non-ideal temperature stability of the thermostat is taken into account by the term Tinstab. Its value is set to zero and its uncertainty is estimated as follows: u(Tinstab) = 0.0065 K. Atmospheric pressure during calibration p. This uncertainty source is caused by the limited accuracy of the barometer used for measuring the atmospheric pressure and is taken into account as u(p). In the case of the external barometer the standard uncertainty due to calibration is 3.5 Pa. Additionally drift and reading repeatability were taken into account and the following uncertainty estimate was obtained: u(p) = 5.2 Pa. Partial pressure of water vapor pH2O. The partial water vapor pressure in air saturated with water (at minimum 95% relative humidity) was measured with uncertainty ± 5% (k = 2) at our laboratory: u(pH2O) = 111 Pa (at temperature 20.0 °C). Oxygen content in air pCO2. The partial oxygen pressure in air saturated with water depends also on the content of carbon dioxide [50,51,52]. The performed experiments (during aeration, under calibration conditions) showed that the content of carbon dioxide in air varies in the range of 0.04% to 0.07%, the lowest end of this range being the standard content of CO2 in air. The highest end of this range is possible only when the air is taken directly from the room where people are working, which is not the case with our measurements (air is taken from the ventilation inlet situated on the roof of the building). The effect of varying CO2 content is small and thus it is not practical to correct for it. It is instead included entirely in the uncertainty estimate. The value pCO2 is set to zero and its uncertainty u(pCO2) is conservatively estimated as 41 Pa (under the normal pressure 101325 Pa).

Supersaturation CO2_supersat. This component takes into account the uncertainty originating from possible supersaturation (or undersaturation). In our case the used MilliQ water was pre-saturated at level of ca 70%. At least 2.5 hours were allowed for full saturation counting from the time when the temperature of the bath was stabilized. The saturation process was monitored by optical dissolved oxygen analyzer HACH 30d with a digital resolution of 0.01 mg dm–3. The possible supersaturation depends on aeration speed (over-pressure generated by the pump), the intensity of mixing and the size of bubbles. The smaller are the bubbles the higher may be the supersaturation. Unfortunately, the exact saturation conditions, including the optimal size of the bubbles are not specified in the ISO 5813 standard [16] or in the original papers [14,15]. In this work the size of the bubbles was in the range of 0.8–1.8 mm (estimated using a ruler immersed into the bath and comparing the bubble size to the ruler using photos). The standardized procedure of obtaining accurate dissolved oxygen concentrations in water from the former Soviet Union [53] contains detailed description of the saturation conditions and the bubble size according to that standard is 3 mm. The saturation values of ref [53] are in good agreement with the ISO 5813 standard [14]. The maximum difference in the temperature range 5–30 oC is ± 0.02 mg dm–3. Truesdale et al claim [52] that bubbles with the diameter of 0.1 mm lead to a supersaturation of ca 0.6%. On the tentative assumption that the extent of supersaturation is linearly related to bubble

55 diameter it follows that when moving down from 3 mm bubbles then the supersaturation is ca 0.2% per 1 mm of bubble diameter. The smallest possible bubble diameter used in this work was 0.8 mm and this would mean ca 0.44% of supersaturation, which at 20 °C means ca 0.04 mg dm–3. In order to verify this assumption a comparison between saturation conditions differing by bubble size was made using an optical dissolved oxygen analyzer HACH 30d. The difference of 0.03 mg dm–3 was found between the dissolved oxygen concentrations when saturation with 3 mm bubbles and 0.8 mm bubbles was compared. Thus the possible supersaturation might be as high as 0.03 mg dm–3. Nevertheless it is not possible to fully rule out undersaturation and therefore the value of zero was assigned to CO2_supersat. Its standard uncertainty –3 u(CO2_supersat) is estimated from the maximum value 0.03 mg dm (assuming rectangular distribution) as 0.017 mg dm–3.

56 15

APPENDIX 4 Uncertainty evaluation for SGW in 22.02.2008: Input quantities

Constants: Determination of the Na 2S2O3 solution concentration m(tare+ m(titr syr m(titr syr M = 214.001 g/mol Nr m(tare) m(KIO3) m(titrant) KIO3 KIO3) before) after)

MO2= 31998.8 mg/mol 1 21.0640 24.0118 2.9478 70.6831 61.1625 9.5206

MNa2S2O3= 158.1077 g/mol 2 21.2989 24.2152 2.9163 70.7125 61.2976 9.4149

O2_sy ringe= 2.108 µg 3 21.5473 24.5004 2.9531 70.6996 61.1752 9.5244 4 22.4008 25.3645 2.9637 70.7006 61.1432 9.5574 Date: 5 21.4253 24.3728 2.9475 70.7063 61.1725 9.5338 22-Feb-08 6 21.4876 24.4346 2.9470 70.6886 61.1295 9.5591 Operator: arithmetic mean 2.9459 9.5184 Irja Helm, glass syringe

Preparation of the KIO3 standard solution 3 V_KIO3_solution 1.0 dm Determination of the O2 concentration in reagent solutions m(sample m(sample syr m(sample m(MnSO + m(titr syr m(titr syr Nr syr + MnSO4 m(MnSO4) m(KOHKI) 4 m(titrant) syr) KOHKI) before) after) mKIO3(t) 0.2847 g +MnSO4) +KOHKI)

57 57 PKIO3 0.9985 - 1 61.7216 64.0558 66.9806 2.3342 2.9248 5.2590 70.7043 69.7661 0.9382 Temperature of laboratory 20.0 °C 2 61.7769 64.1149 66.9890 2.3380 2.8741 5.2121 69.6652 68.7383 0.9269 3 Density of KIO3 standard solution 0.9985 kg/dm 3 61.7658 64.1048 67.0557 2.3390 2.9509 5.2899 68.6978 67.7330 0.9648

CKIO3 0.0013 mol/kg 4 61.6165 63.9547 66.8452 2.3382 2.8905 5.2287 67.7328 66.8979 0.8349 5 61.4475 63.8098 66.6491 2.3623 2.8393 5.2016 66.6808 65.7932 0.8876 6 61.2394 63.5867 66.4573 2.3473 2.8706 5.2179 65.6961 64.7937 0.9024 arithmetic mean 5.2349 0.9091

Determination of the O2 concentration in sample m(sample m(syr+ m(sample t p m(titr syr m(titr syr ref C ref C Nr syr + m(sample) sample+ m (reag) t (°C) corrected p (Pa) corrected m(titrant) O2 O2 syr) (°C) (Pa) before) after) [mg/kg] [mg/dm3] sample) reag) 1 61.7176 70.9796 9.2620 71.5058 0.5262 20.10 20.0 97850 98031.3 70.7062 66.3780 4.3282 8.805 8.790 2 61.7671 71.0305 9.2634 71.5482 0.5177 20.10 20.0 97850 98031.3 70.6929 66.3896 4.3033 8.805 8.790 3 61.7578 71.0268 9.2690 71.5459 0.5191 20.10 20.0 97850 98031.3 70.6962 66.4016 4.2946 8.805 8.790 4 61.6082 70.8472 9.2390 71.3851 0.5379 20.10 20.0 97850 98031.3 70.6530 66.3558 4.2972 8.805 8.790 5 61.4564 70.7357 9.2793 71.2528 0.5171 20.10 20.0 97850 98031.3 70.7100 66.4043 4.3057 8.805 8.790 6 61.2359 70.4961 9.2602 70.9514 0.4553 20.10 20.0 97850 98031.3 70.6984 66.3975 4.3009 8.805 8.790 arithmetic mean 9.2622 0.5122 4.305 8.805 8.790 Uncertainty evaluation for SGW in 22.02.2008: Determination of CKIO3

mKIO _ s  PKIO C  3 3   at b KIO3 M V   flask KIO3 flask Input quantities Uncertainty components of input quantities

Denotion Uncorr value u c Unit u component u component u component u component u component u component

mKIO3_s 0.2847 0.00026 g 0.00016 repeatability1 0.000029 rounding1 0.00016 repeatability2 0.000029 rounding2 0.000115 linearity 0.0000007 drift

PKIO3 0.9985 0.0009 % 0.00087 purity

MKIO3 214.00097 0.00045 g/mol 0.00005 K 0.000015 I 0.00015 O 3 Vflask 1.000 0.00038 dm 0.0002309 calibration 0.0001732 filling 0.00024 temperature

tflask 20 1.1547 °C 1.15470 temperature

Input quantities Uncertainty evaluation using the Kragten approach

Denotion Corr value Unit u c Relative mKIO3_s PKIO3 MKIO3 Vflask tflask

mKIO3_s 0.2847 g 0.00026 0.090% 0.285 0.285 0.285 0.285 0.285 58 58 PKIO3 0.9985 % 0.00087 0.087% 0.999 0.999 0.999 0.999 0.999

MKIO3 214.0010 g/mol 0.00045 0.000% 214.0 214.0 214.0 214.0 214.0 3 Vflask 1.0000 dm 0.00038 0.038% 1.0 1.0 1.0 1.0 1.0

tflask 20.0000 °C 1.15470 5.774% 20.000 20.000 20.000 20.000 20.1

CKIO3 0.0013304 mol/kg 0.0000018 0.13% 0.00133 0.00133 0.00133 0.00133 0.00133 Value 0.00000 0.00000 0.00000 0.00000 0.00000 Difference 1.4E-14 1.3E-14 7.9E-20 2.5E-15 1.0E-15 Difference squared 3.1E-14 Sum of squared differences 46% 43% 0% 8% 3% Uncertainty contribution 100% Sum of uncertainty contributions Auxiliry parameters Denotion Value Unit Function of pure water density a 4.981E-08 - Function of pure water density b 8.185E-06 - Function of pure water density c 6.106E-05 - Function of pure water density d 0.9998599 - pure water density 0.998206 kg/dm3 KIO3 solution density change 0.009105 kg/dm3/% KIO3 solution density correction 0.000259 kg/dm3 Kragten factor 10 - Uncertainty evaluation for SGW in 22.02.2008: Determination of CNa2S2O3

m C  6  C   KIO3  F  F  F  F Na 2S2O 3 KIO 3 m Na2 S 2O3 _ KIO3 mKIO3 m Na2 S 2O3 _ KIO3 mKIO3 _ endp I 2

Input quantities Uncertainty components of input quantities

Denotion Uncorr value u c Unit u component u component u component u component

CKIO3 0.0013 0.00000 mol/kg

mKIO3 2.9478 0.00028 g 0.00028 repeatability 2.9163 g 2.9531 g 2.9637 g 2.9475 g 2.9470 g

mNa2S2O3_KIO3 9.5206 g 9.4149 g 9.5244 g 9.5574 g 9.5338 g 9.5591 g

Fm_KIO3 1 0.00004 - 0.000029 rounding1 0.000029 rounding2 0.000115 linearity 0.000007 drift

Fm_Na2S2O3_KIO3 1 0.00001 - 0.000029 rounding1 0.000029 rounding2 0.000115 linearity 0.000023 drift

Fm_KIO3_endp 1 0.00103 - 0.001031 endpoint 59 59 FI2 1 0.00020 - 2.0E-04 volatility

Input quantities Uncertainty evaluation using the Kragten approach m F u KIO3 m_Na2S2O3 Denotion Corr value Unit c Relative CKIO3 m Fm_KIO3 Fm_KIO3_endp FI2 Na2S2O3 _ KIO3 _KIO3

CKIO3 0.0013 mol/kg 0.000002 0.13% 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 m KIO3 m Na2S2O3 _ KIO3 0.3095 - 0.00028 0.09% 0.3095 0.3095 0.3095 0.3095 0.3095 0.3095

Fm_KIO3 1 - 0.00004 0.00% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Fm_Na2S2O3_KIO3 1 - 0.00001 0.00% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Fm_KIO3_endp 1 - 0.0010 0.10% 1.0000 1.0000 1.0000 1.0000 1.0001 1.0000

FI2 1 - 0.0002 0.02% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

C_Na2S2O3 0.002471 mol/kg 0.000005 0.19% 0.00247 0.00247 0.00247 0.00247 0.00247 0.00247 Value 3.3E-07 2.2E-07 1.0E-08 3.2E-09 2.5E-07 5.0E-08 Difference 1.1E-13 4.9E-14 1.1E-16 1.0E-17 6.5E-14 2.5E-15 Difference squared 2.2E-13 Sum of squared differences 48% 22% 0% 0% 29% 1% Uncertainty contribution 100% Sum of uncertainty contributions Auxiliry parameters Denotion Value Unit Number of titrations 6 Kragten factor 10 - Uncertainty evaluation for SGW in 22.08.2008: Determination of CO2_reag

1 m O2_syringe C   M C  Na 2S2O3_reag  F  F  F  F  O2_reag O2 Na2S2O3 mreag mreag mNa 2S2O3 _ reag mreag _ endp I2 4 mreag Input quantities Uncertainty components of input quantities Denotion Uncorr value u c Unit u component u component u component u component MO2 31999 0.4500 mg/mol 0.15 O CNa2S2O3 0.002471 0.000005 mol/kg mNa2S2O3_reag 0.9382 0.00327 0.00327 repeatability 0.9269 g 0.9648 g 0.8349 g 0.8876 g 60 0.9024 g mreag 5.2590 g 5.2121 g 5.2899 g 5.2287 g 5.2016 g 5.2179 g O2_syringe 2.6893 0.27 µg 0.27 repeatability 1.6239 µg 2.9978 µg 1.2286 µg 2.0276 µg 2.0831 µg Fm_reag 1 0.000024 - 0.000029 rounding1 0.000029 rounding2 0.000115 linearity 0.0000126 drift Fm_Na2S2O3_reag 1 0.000135 - 0.000029 rounding1 0.000029 rounding2 0.000115 linearity 0.0000022 drift Fm_reag_endp 1 0.021592 - 0.0216 endpoint FI2 1 0.00020 - 2.0E-04 volatility

Input quantities Uncertainty evaluation using the Kragten approach m F F Denotion Corr value Unit u Relative M C Na2S2O3_reag O m F m_ m_reag_ F c O2 Na2S2O3 m 2_syringe reag m_reag I2 reag Na2S2O3_reag endp MO2 31999 mg/mol 0.45 0.00% 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8 CNa2S2O3 0.0025 mol/kg 0.000005 0.19% 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 m  Na 2S2O3_reag 0.1736 - 0.00327 1.88% 0.1736 0.1736 0.1740 0.1736 0.1736 0.1736 0.1736 0.1736 0.1736 mreag O2_syringe 2.1084 µg 0.27 12.7% 2.1084 2.1084 2.1084 2.1351 2.1084 2.1084 2.1084 2.1084 2.1084 mreag 5.2349 g 0.0000 0.00% 5.2349 5.2349 5.2349 5.2349 5.2349 5.2349 5.2349 5.2349 5.2349 Fm_reag 1 - 0.000024 0.00% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 Fm_Na2S2O3_reag 1 - 0.000135 0.01% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 Fm_reag_endp 1 - 0.021592 2.16% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0022 1.0000 FI2 1 - 0.000200 0.02% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 CO2_reag 3.02914 mg/kg 0.11 3.7% 3.0291 3.0298 3.0356 3.0240 3.0291 3.0291 3.0292 3.0366 3.0292 Value 4.8E-06 6.6E-04 6.5E-03 -5.1E-03 0.0E+00 8.1E-06 4.6E-05 7.4E-03 6.9E-05 Difference 2.3E-11 4.3E-07 4.2E-05 2.6E-05 0.0E+00 6.5E-11 2.1E-09 5.5E-05 4.7E-09 Difference squared 1.2E-04 Sum of squared differences Auxiliry parameters 0% 0% 34% 21% 0% 0% 0% 45% 0% Uncertainty contribution Denotion Value Unit 100% Sum of uncertainty contributions Number of titrations 6 Kragten factor 10 - 61 Uncertainty evaluation for SGW in 22.08.2008: Determination of CO2_s

m O 1 Na2S2O3_s mreag_s 2_syringe CO _ s   M O CNa S O m  Fm  Fm  Fm  FI CO _reag m  2 2 2 2 3 s s Na2S2O3 _ s s _ endp 2 2 s 4 ms Input quantities Uncertainty components of input quantities

Denotion Uncorr value u c Unit u component u component u component u component MO2 31999 0.45000 mg/mol 0.15 O CNa2S2O3 0.0025 0.000005 mol/kg mNa2S2O3_s 4.3282 0.00056 g 0.00056 repeatability 4.3033 g 4.2946 g 4.2972 g 4.3057 g 4.3009 g ms 9.2620 g 9.2634 g 62 9.2690 g 9.2390 g 9.2793 g 9.2602 g CO2_reag 3.0291 0.11 mg/kg mreag_s 0.5262 0.00128 g 0.00128 repeatability 0.5177 g 0.5191 g 0.5379 g 0.5171 g 0.4553 g O2_syringe 2.6893 0.26736 µg 0.27 repeatability 1.6239 µg 2.9978 µg 1.2286 µg 2.0276 µg 2.0831 µg Fm_s 1 0.00001 - 0.000029 rounding1 0.000029 rounding2 0.000115 linearity 0.000022 drift Fm_Na2S2O3_s 1 0.00003 - 0.000029 rounding1 0.000029 rounding2 0.000115 linearity 0.000010 drift Fm_s_endp 1 0.00228 - 0.00228 endpoint FI2 1 0.00020 - 2.0E-04 volatility Input quantities Uncertainty evaluation using the Kragten approach m Na2S2O3_s mreag_sample Fm_ Fm_s_ Denotion Corr value Unit u c Relative MO2 CNa2S2O3  CO2_reag  O2_syringe ms Fm_s FI2 ms msample Na2S2O3_s endp

MO2 31999 mg/mol 0.450 0.00% 31999 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8 31998.8

CNa2S2O3 0.0025 mol/kg 0.000 0.19% 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 m  Na2S2O3_s ms 0.4648 - 0.001 0.12% 0.4648 0.4648 0.4648 0.4648 0.4648 0.4648 0.4648 0.4648 0.4648 0.4648 0.4648

CO2 reag 3.029 mg/kg 0.111 3.67% 3.0291 3.0291 3.0291 3.0402 3.0291 3.0291 3.0291 3.0291 3.0291 3.0291 3.0291 mreag_s ms 0.0553 g 0.0013 2.32% 0.0553 0.0553 0.0553 0.0553 0.0554 0.0553 0.0553 0.0553 0.0553 0.0553 0.0553

O2_syringe 2.108 µg 0.267 12.68% 2.1084 2.1084 2.1084 2.1084 2.1084 2.1351 2.1084 2.1084 2.1084 2.1084 2.1084

ms 9.262 g 0.000 0.00% 9.2622 9.2622 9.2622 9.2622 9.2622 9.2622 9.2622 9.2622 9.2622 9.2622 9.2622

Fm_s 1 - 0.000 0.00% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Fm_Na2S2O3_s 1 - 0.000 0.00% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Fm_s_endp 1 - 0.002 0.23% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0002 1.0000

FI2 1 - 0.000 0.02% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

CO2_s 8.79 mg/kg 0.042 0.48% 8.7909 8.7927 8.7920 8.7903 8.7905 8.7880 8.7909 8.7909 8.7909 8.7930 8.7911 Value 3 CO2_s 8.78 mg/dm 0.042 0.48% 0.0000 1.8E-03 1.1E-03 -6.1E-04 -4E-04 -2.9E-03 0E+00 1.2E-05 2.6E-05 2.1E-03 1.8E-04 Dif f erence 0.0000 3.1E-06 1.2E-06 3.8E-07 1.5E-07 8.3E-06 0E+00 1.5E-10 6.8E-10 4.4E-06 3.4E-08 Dif f erence squared 1.8E-05 Sum of squared dif f erences 0% 18% 7% 2% 1% 47% 0% 0% 0% 25% 0% Uncertainty contribution 63 100% Sum of uncertainty contributions Auxiliry parameters Denotion Value Unit Number of titrations 6 a 5E-08 - Function of pure water density b 8.2E-06 - Function of pure water density c 6.1E-05 - Function of pure water density d 0.99986 - Function of pure water density temperature of water 20.0 °C density of pure water 0.9982 kg/dm3 correction of air saturated water density -3.2E-06 kg/dm3 density of air saturated water 0.9982 kg/dm3 Kragten factor 10 - APPENDIX 5

Uncertainty evaluation for FGW in 30.01.2012: Input quantities

Constants: Preparation of the KIO3 standard solution M (KIO 3)= 214.00097 g/mol 7-Oct-11 M (O 2)= 31998.8 mg/mol Primary solution KIO3 I M(Na 2S2O3)= 158.108 g/mol m(flask)= 24.27969 g

m(flask+KIO3_s)= 25.67851 g m(solution) 38.74661 g

Date: m(KIO3_s)= 1.39882 g c(solution)=36101.827 mg/kg 30-Jan-2012 m(flask+KIO3I)= 63.02630 g

Operator: 9-Jan-12

Irja Helm Secondary solution KIO3 II m(flask)= 27.42392 g

p_Vaisala= 104289 Pa m(flask+KIO3I)= 31.06630 g m(solution) 37.06656 g

t_Chub= 24.90 °C m(KIO3 I)= 3.64237 g c(solution)=3547.5731 mg/kg

m(flask+KIO3II)= 64.49048 g

27-Jan-12 3 CO2Ref= 8.542 [mg/dm ] Working solution KIO3 III 3 U (CO2Ref) = 0.065 [mg/dm ] m(flask)= 97.7426 g ∆=-0.004[mg/dm3] m(flask+KIO3II)= 102.8880 g m(solution) 96.59347 g m(KIO3 II)= 5.14533 g c(solution)=188.97185 mg/kg m(flask+KIO3III)= 194.3361 g

Determination of the Na2S2O3 solution concentration

Nr m(tare) (g) m(tare + KIO3) (g) m(KIO3) (g) m(titr syr before) (g) m(titr syr after) (g) m(titrant) (g) 1 20.60535 25.47930 4.87395 32.97503 15.81398 17.16105 2 21.62533 26.22042 4.59509 32.56234 16.39622 16.16612 3 20.12579 24.99128 4.86549 32.73514 15.61546 17.11968 4 21.26223 26.08841 4.82618 32.36815 15.39320 16.97495 5 20.49135 25.35827 4.86692 32.77649 15.64416 17.13233 6 20.26203 25.14634 4.88431 32.78205 15.59120 17.19085 7 20.50111 25.32389 4.82278 33.84083 16.87373 16.96710 arithmetic mean 4.81925 16.95887

Determination of the O2 concentration in sample

ρ= 0.997074411 "+" 7.73831E-06 "=" 0.997082149 g/cm3 Nr V(s.bottle) (cm3) V(sample) (cm3) m(sample) (g) m(titr syr before) (g) m(titr syr after) (g) m(titrant) (g) 1 11.82361 11.41237 11.37907 32.71434 24.52099 8.19335 2 11.77924 11.36801 11.33484 32.56797 24.42122 8.14675 3 11.89705 11.48581 11.45230 32.66569 24.42856 8.23713 4 11.87858 11.46735 11.43389 32.95339 24.73213 8.22126 6 11.88738 11.47615 11.44266 32.45531 24.22320 8.23211 7 11.84125 11.43002 11.39667 32.84362 24.64559 8.19803 8 11.73808 11.32684 11.29379 32.81941 24.68239 8.13702 arithmetic mean 11.39046 32.71710 24.52201 8.19509

Input quantities: rep_low 0.000043 g rep_high 0.000057 g rounding_low 0.0000029 g rounding_high 0.0000289 g drift 0.00000080 calibration 0.00000042

u(evaporation H2O) 0.00147537 g u(warming effect) 0.00045611 g 3 V(MnSO4_H2O) 0.205981334 cm 3 s(V_H2O_1) 0.0009898 cm 3 V(KOHKI_H2O) 0.205252695 cm 3 s(V_H2O_2) 0.0004596 cm Mass of the drop 0.011 g

n_I2vol_t 0.0000325 mmol

st.dev.n_I2vol_t 0.0000074 mmol u(± titration time) 0.0000081233 mmol cal 5°C 0.000032 cal 25°C 0.000338

n_I2vol_s 0.0000116 mmol

st.dev.n_I2vol_s 0.0000014 mmol

IntO2 0.00256 mg/kg

CFO2 0.094014806 mg/kg

u(CFO2) 0.006833671 mg/kg

64 17

Uncertainty evaluation for FGW in 30.01.2012: Determination of CKIO3_III  g  mg m g 1000 1000 m g m g  P   KIO3 _ s     KIO3 _ I _transf KIO3 _ II _transf KIO mol kg g 3 C      KIO3III   kg  mg   M m g m g m g  KIO3   KIO3 _ I KIO3 _ II KIO3 _ III mol Input quantities Uncertainty components of input quantities

Denotion Uncorr value u c Unit u component u component u component u component u component u component u component

m(KIO3)s 1.399 0.000061 g 0.000043 repeatability1 0.000003 rounding1 0.000043 repeatability2 0.000003 rounding2 0.00000112 drift 0.00000058 calibration

P_KIO3 1.000 0.000577 - 0.000577 purity

M_KIO3 214000.97 0.453018 mg/mol 0.05 K 0.015 I 0.15 O

m(KIO3I_tr ansf) 3.642 0.001477 g 0.000043 repeatability1 0.000003 rounding1 0.000043 repeatability2 0.000003 rounding2 0.00000291 drift 0.00000152 calibration 0.00148 evaporation

m(KIO3II_tr ansf) 5.145 0.001478 g 0.000057 repeatability1 0.000029 rounding1 0.000057 repeatability2 0.000029 rounding2 0.00000412 drift 0.00000214 calibration 0.00148 evaporation

m(KIO3I) 38.747 0.000070 g 0.000043 repeatability1 0.000003 rounding1 0.000043 repeatability2 0.000003 rounding2 0.00003100 drift 0.00001614 calibration

m(KIO3II) 37.067 0.000096 g 0.000057 repeatability1 0.000029 rounding1 0.000057 repeatability2 0.000029 rounding2 0.00002965 drift 0.00001544 calibration

m(KIO3III) 96.593 0.000125 g 0.000057 repeatability1 0.000029 rounding1 0.000057 repeatability2 0.000029 rounding2 0.00007727 drift 0.00004025 calibration

Input quantities Uncertainty evaluation using the Kragten approach

Denotion Corr value Unit u c Relative m(KIO3)s P_KIO3 M_KIO3 m(KIO3I_tr ansf)m(KIO3II_tr ansf)m(KIO3I) m(KIO3II) m(KIO3III) 65 m(KIO3)s 1.3988 g 0.00006 0.0044% 1.399 1.3988 1.3988 1.399 1.399 1.399 1.399 1.399

P_KIO3 1.00000 - 0.00058 0.0577% 1.00000 1.00006 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000

M_KIO3 214000.97 mg/mol 0.45302 0.0002% 214000.97 214000.97 214001.02 214000.97 214000.97 214000.97 214000.97 214000.97

m(KIO3I_tr ansf) 3.6424 g 0.00148 0.0405% 3.642 3.6424 3.6424 3.643 3.642 3.642 3.642 3.642

m(KIO3II_tr ansf) 5.1453 g 0.00148 0.0287% 5.145 5.1453 5.1453 5.145 5.145 5.145 5.145 5.145

m(KIO3I) 38.7466 g 0.00007 0.0002% 38.747 38.7466 38.7466 38.747 38.747 38.747 38.747 38.747

m(KIO3II) 37.0666 g 0.00010 0.0003% 37.067 37.0666 37.0666 37.067 37.067 37.067 37.067 37.067

m(KIO3III) 96.5935 g 0.00013 0.0001% 96.593 96.5935 96.5935 96.593 96.593 96.593 96.593 96.593

C_KIO3 0.0008830 0.0000007 0.076% 0.0008830 0.0008831 0.0008830 0.0008831 0.0008831 0.0008830 0.0008830 0.0008830 Value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Difference 1.5E-17 2.6E-15 3.5E-20 1.3E-15 6.4E-16 2.6E-20 5.2E-20 1.3E-20 Difference squared Auxiliry parameters 4.5E-15 Sum of squared differences Denotion Value Unit 0% 57% 0% 28% 14% 0% 0% 0% Uncertainty contribution Number of titrations 7- 4.5E-15 Sum of uncertainty contributions Kragten factor 10 - Uncertainty evaluation for FGW in 30.01.2012: Determination of CNa2S2O3

m 2 n [mmol] mol mol KIO3 I 2 _ vol _ t CNa S O [ ]  6CKIO [ ]m  Fm  Fm  Fm  2 2 3 kg 3 kg Na2S2O3 _ KIO3 KIO3 Na2S2O3 _ KIO3 KIO3 _ endp m [g] Na2 S2O3 _ KIO3 Input quantities Uncertainty components of input quantities

Denotion Uncorr value correction u c Unit u component u component u component u component u component

CKIO3 0.00088304 0.0000006737 mol/kg

mKIO3 4.87395000 0.0000400270 g 0.00004 repeatability 4.59509000 g 4.86549000 g 4.82618000 g 4.86692000 g 4.88431000 g 4.82278000 g

mNa2S2O3_KIO3 17.16105000 g 16.16612000 g 17.11968000 g 16.97495000 g 17.13233000 g 66 17.19085000 g 16.96710000 g

Fm_Na2S2O3_KIO3 1.00000000 0.0000269024 - 0.000003 rounding1 0.000003 rounding2 0.000007066 calibration 0.0000071 drift 0.000456107 warming efect

Fm_KIO3 1.00000000 0.0000635368 - 0.000003 rounding1 0.000003 rounding2 0.000002008 calibration 0.0000039 drift 0.000306142 evaporation

Fm_KIO3_endp 1.00000000 0.0001787318 - 0.000179 endpoint

nI2_vol_t 0.00003249 0.0000087238 mmol 0.0000074 eksp.st.h. 0.0000047 ±15 sek

Input quantities Uncertainty evaluation using the Kragten approach m F F CKIO3 KIO3 m_Na2S2O3_ m_KIO3 Γm Denotion Corr value Unit u c Relative Na2S2O3 _ KIO3 Fm_KIO3 KIO3 _endp nI2_vol_t CKIO3 0.0009 mol/kg 0.000001 0.08% 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009 m KIO3 m 0.28417350 0.00004003 0.01% 0.2842 0.2842 0.2842 0.2842 0.2842 0.2842 Na2S2O3 _ KIO3 -

Fm_Na2S2O3_KIO3 1.00000 - 0.00003 0.00% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Fm_KIO3 1 - 0.00006 0.01% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Fm_KIO3_endp 1 - 0.0002 0.02% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

nI2_vol_t 0.000032 mmol 0.0000 26.85% 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 C_Na2S2O3 0.0015018 mol/kg 0.0000016 0.11% 0.00150 0.00150 0.00150 0.00150 0.00150 0.00150 Value 1.1E-07 2.1E-08 4.1E-09 9.6E-09 2.7E-08 -1.0E-07 Difference 1.3E-14 4.5E-16 1.6E-17 9.2E-17 7.2E-16 1.1E-14 Difference squared 2.5E-14 Sum of squared differences Auxiliry parameters 53% 2% 0% 0% 3% 42% Uncertainty contribution Denotion Value Unit 100% Sum of uncertainty contributions Number of titrations 7 Kragten factor 10 - Uncertainty evaluation for FGW in 30.01.2012: Determination of CO2_s

 mg  kg  mg 1  mol m 2 nI _ vol _ s [mmol] mg mg P[Pa]  C  [ ]M [ ] C [ ]  Na2S2O3_s  2   F  F  F  Int [ ]  CF   O2 _ s 3 3 O2 Na2S2O3 ms ms mNa S O _ s ms _ endp O2 O2   dm  dm  mol 4  kg  2 2 3 kg kg 101325[Pa]     ms [g]     Input quantities Uncertainty components of input quantities

Denotion Uncorr value u c Unit u component u component u component u component u component u component u component u component

MO2 31998.80 0.45000 mg/mol 0.15 O

CNa2S2O3 0.0015 0.000002 mol/kg

mNa2S2O3_s 8.1934 0.00023 g 0.00023 repeatability 8.1468 g 8.2371 g 8.2213 g 8.2321 g 8.1980 g 8.1370 g

ms 11.3791 0.00003 g 11.3348 g 11.4523 g 11.4339 g 11.4427 g 11.3967 g 67 11.2938 g

CFO2 0.09401 0.006833671 mg/kg 0.00683 eksp.st.dev P 104289 3.5 Pa 3.50 Certificate

Fm_s 1 0.000150160 - 0.00034 cal25°C 0.000032 cal5°C 0.00000025 rounding1 0.00000025 rounding2 0.00000080 drift 0.0000047 calibration 0.0015 cal MnSO4 0.00071 cal KOHKI

Fm_Na2S2O3_s 1 0.000055666 - 0.000003 rounding1 0.0000029 rounding2 0.0000066 drift 0.0000034 calibration 0.000456 warming efect

Fm_s_endp 1 0.000369866 - 0.00037 endpoint

nI2_vol_s 0.000012 0.000001412 mmol 0.00000 st.dev

IntO2 0 0.002563435 mg/kg 0.002563

Input quantities Uncertainty evaluation using the Kragten approach C m F Na2S2O Na2S2O3_s m Corr value Unit u c Relative MO2  CFO2 PFm_s Fm_s_endp nI2_vol_s IntO2 Denotion 3 ms _Na2S2O3_s

MO2 31999 mg/mol 0.450 0.00% 31999 31999 31999 31999 31999 31999 31999 31999 31999 31999

CNa2S2O3 0.0015 mol/kg 0.000 0.11% 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0 m  Na 2S2O3_s ms 0.719471 - 0.0002266 0.03% 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7

CFO2 0.0940 mg/kg 0.0068 7.27% 0.0940 0.0940 0.0940 0.0947 0.0940 0.0940 0.0940 0.0940 0.0940 0.1 P 104289 Pa 3.500 0.00% 104289 104289 104289 104289 104289 104289 104289 104289 104289 104289

Fm_s 1 - 0.000 0.02% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0

Fm_Na2S2O3_s 1 - 0.000 0.01% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0

Fm_s_endp 1 - 0.000 0.04% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0

nI2_vol_s 0.000012 mmol 0.000 12.23% 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0

IntO2 0 mg/kg 0.003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0

CO2_s 8.563 mg/kg 0.013 0.15% 8.5631 8.5640 8.5634 8.5624 8.5631 8.5632 8.5631 8.5634 8.5633 8.5634 Value 3 CO2_s 8.538 mg/dm 0.013 0.15% 0.0000 0.0009 0.0003 -0.0007 0.0000 0.0001 0.0000 0.0003 0.0002 0.0003 Difference 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Difference squared 1.6E-06 Sum of squared differences 68 0.0% 51.1% 4.6% 30.4% 0.0% 1.0% 0.1% 6.3% 2.4% 4.0% Uncertainty contribution 100% Sum of uncertainty contributions Auxiliry parameters Denotion Value Unit Number of titrations 7 a 4.98E-08 - Function of pure water density b 8.18E-06 - Function of pure water density c 6.11E-05 - Function of pure water density d 0.99986 - Function of pure water density temperature of water 24.9 °C density of pure water 0.9971 kg/dm3 corr of air saturated water density -2.9E-06 kg/dm3 density of air saturated water 0.9971 kg/dm3 Kragten factor 10 -

PUBLICATIONS

I I. Helm, L. Jalukse, I. Leito, Measurement Uncertainty Estimation in Amperometric Sensors: A Tutorial Review. Sensors, 2010, 10, 4430–4455.

Reproduced with permission from Measurement Uncertainty Estimation in Amperometric Sensors. Copyright 2010, Open assess, Sensors. Sensors 2010, 10, 4430-4455; doi:10.3390/s100504430 OPEN ACCESS sensors ISSN 1424-8220 www.mdpi.com/journal/sensors

Review Measurement Uncertainty Estimation in Amperometric Sensors: A Tutorial Review

Irja Helm, Lauri Jalukse and Ivo Leito *

Institute of Chemistry, University of Tartu, 14a Ravila str. 50411 Tartu, Estonia; E-Mails: [email protected] (L.J.); [email protected] (I.H.)

* Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +372-5-184-176.

Received: 26 February 2010; in revised form: 29 March 2010 / Accepted: 10 April 2010 / Published: 30 April 2010

Abstract: This tutorial focuses on measurement uncertainty estimation in amperometric sensors (both for liquid and gas-phase measurements). The main uncertainty sources are reviewed and their contributions are discussed with relation to the principles of operation of the sensors, measurement conditions and properties of the measured samples. The discussion is illustrated by case studies based on the two major approaches for uncertainty evaluation–the ISO GUM modeling approach and the Nordtest approach. This tutorial is expected to be of interest to workers in different fields of science who use measurements with amperometric sensors and need to evaluate the uncertainty of the obtained results but are new to the concept of measurement uncertainty. The tutorial is also expected to be educative in order to make measurement results more accurate.

Keywords: amperometric sensors; measurement uncertainty; uncertainty sources

1. Introduction

Amperometric sensors are applied widely to the concentration measurements of different analytes, e.g., gas components in the gas phase or analytes dissolved in a liquid medium. They offer good sensitivity [1,2] and wide linear range [3]. They can be low-cost and can be mass produced via microfabrication technology [4]. They are simple to use and are widely used in different areas of chemical analysis such as environmental monitoring, surveillance, security, industrial safety and medical and health applications. Numerous substances can be determined with amperometric sensors [1,5] (see Table 1 for an overview).

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Uncertainty estimation of measurement results (including chemical analysis results [6]) has nowadays become a standard requirement [7,8]. Results without an uncertainty estimate cannot be considered complete [9]. At the same time, due to the nature of chemical measurements estimation of their uncertainty is often complicated [7]. This has resulted in a still continuing mismatch between the requirements imposed on laboratories and their ability to meet them. The aim of this tutorial is to give an overview of the main uncertainty sources that influence measurements with amperometric sensors, briefly look at two major approaches for uncertainty estimation and to illustrate practical uncertainty evaluation with two case studies. Our emphasis is on depth and usefulness for potential readers rather than on a (formally) exhaustive coverage of literature, therefore the literature references are selective rather than extensive. This tutorial is expected to be of interest to workers in different fields of science who use measurements with amperometric sensors and need to evaluate the uncertainty of the obtained results. We focus on low-temperature membrane amperometric sensors based on chemical reactions. High-temperature amperometric sensors as well as biosensors are outside the scope of this review.

2. Design and Principle of Operation of Amperometric Sensors

Numerous reviews have been published on design and operation of amperometric sensors [1,5,10-12] and only a brief introduction will be given here. The fundamental process for sensing an analyte by an amperometric sensor can be described in four steps: (1) the analyte diffuses to the sensing electrode. In order to achieve selectivity and/or diffusion-limited working mode this diffusion may proceed through a membrane or some other diffusion barrier. (2) The analyte is adsorbed on the sensing electrode. (3) The electrochemical reaction occurs. (4) The reaction products desorb from the sensing electrode and diffuse away [13,14]. Amperometric sensors are based on electrochemical cells consisting of working electrode, counter-electrode and reference electrode that are in connection through an electrolyte phase. By the design the sensors can be broadly divided into three groups: Clark type, SPE and GDE, see Scheme 1 (see [1] for more information). On the working electrode the electrochemical reaction involving the analyte is carried out. The response (analytical signal) of the sensor is the current between the working electrode and counter-electrode. The working conditions of the sensor are usually chosen such that the sensor works in the diffusion-limited mode [1,5,10] and the current is independent of the working electrode potential. In this mode the mass-transfer rate of the analyte is slow and the Faradaic current is controlled by diffusion rather than the kinetics of the electrode reaction [5,15]. This assures a linear dependence of the current on concentration of the analyte [1,14]. The diffusion barrier is usually formed by the membrane (Clark, GDE) or is created artificially by a mechanical barrier (SPE) [14]. If the limitation is on the kinetics of the reaction then the response of the sensor is non-linear and the sensor will be more susceptible to ageing [1]. The porous PTFE-membrane of the GDE-devices serves to restrict the transport of the analyte to the electrode, but a further artificial barrier in the form of a covering plate with holes of controlled dimensions is usually still needed to obtain a well defined diffusion control and stable signal. This diffusion barrier also reduces the effects of drafts in the atmosphere being sampled [1].

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Scheme 1. The most frequently used amperometric sensor designs–Clark's, GDE and SPE sensors (reprinted from [1] with permission from Elsevier).

In the SPE-membrane based sensors, the electrode surface directly faces the sample gas or liquid and therefore essentially no diffusion barrier is present [1,2]. This makes the sensitivity and response time of the SPE sensors better than those of the Clark or GDE sensors [16]. The virtual absence of diffusion layer also greatly reduces the temperature-dependence of the response of a SPE electrode [16]. The negligible diffusion barrier also has a downside. If diffusion is very fast then there is the danger that the sensor will not be operating in the diffusion-limited mode any more resulting in loss of linearity [17]. Therefore in SPE sensors an artificial diffusion barrier is sometimes added. SPE sensors also have a stronger dependence of the signal on the gas flow rate [1,14] and are therefore usually used in systems with a forced and constant gas flow. The electrolyte phase carries the cell current by enabling the transport of charge carriers in the form of ions and often provides co-reactants to electrode and allows the removal of ionic products from the reaction site. Note, that counter and reference electrodes may be combined into a single electrode [1,5]. Each sensor can have a unique design and a different set of materials and geometries for membranes, electrolytes, and electrodes in order to take advantage of chemical properties of a specific target analyte and survive under various operating conditions [5]. A critical issue in design of amperometric sensors is achieving selectivity, i.e., situation that the sensor current depends on analyte concentration but is insensitive towards possible interferents in the solution. In early amperometric measurements selectivity was achieved by the choice of working electrode material and the potential of the working electrode. A major breakthrough in this field was achieved in 1953, when Leland C. Clark developed the practically usable membrane oxygen sensor for measuring oxygen tension in the cardiovascular system in vitro and in vivo [18]. The choice of membrane material became the third important tool for achieving selectivity. With this advancement actually the amperometric sensors were born. After patenting the method in 1959, electrochemical membrane covered amperometric sensors have become a common method in situ measurement of oxygen and the design is often called ”Clark type”. By appropriate selection of the membrane material (PTFE, PFA, FEP, PE, PP, silicone, cellophane etc.) and specific properties, one can control the analytical characteristics of the sensor, permitting the analysis of several analytes over a wide range of concentration [5]. Modern Clark electrodes are often fitted with a porous PTFE membrane. Because of the hydrophobicity of the material, the pores are not Sensors 2010, 10 4433 wetted by the aqueous solution and are impermeable for ions and polar organic compounds but allow the transport of dissolved non-polar gases to the electrode [1]. Out of the gases normally dissolved in the aqueous environment only oxygen can undergo reduction at the working electrode. This way the selectivity of the dissolved oxygen sensor is ensured. Several diffusion layers are formed in the classic Clark sensor: the electrolyte layer, the membrane and a stagnant layer [5,14]. The thinner are the layers the higher the sensitivity and the faster the response. The electrolyte can be an aqueous or a non-aqueous solution or a so-called solid-phase electrolyte (SPE), which in most cases is a conductive polymer. These are good because of their high boiling point and often very high ionic conductivity. A typical solid polymer electrolyte is Nafion, a hydrated copolymer of poly(tetrafluoroethylene) (PTFE) and polysulfonyl fluoride vinyl ether, which contains sulfonic acid groups. It has more positive features, such as high structural stability and resistance to acids and strong oxidants. The only limitation for field use was the issue of the water in the Nafion freezing at low temperatures. [5]. The second breakthrough in amperometric sensor design–introduction of nanostructured materials – has taken place during the turn of the century [3,19-21]. It is clear that sensor's sensitivity depends on the surface area on which the electrochemical reaction takes place. The limiting current is proportional to the electrochemically active surface area, i.e., the three-phase boundary (TPB: interface between the gas, the electrode and the electrolyte) area, because the electrochemical reaction takes place only in this area [22]. Nanostructures can dramatically increase the three-phase boundary area, followed by an enhancement of the sensors sensitivity [5]. A further improvement of the sensitivity from ppm to ppb gas concentration levels can be obtained using the new membrane–electrode assembly composed of a PTFE membrane and nanocomposite materials of carbon nanotubes and PTFE [5]. In contrast to the Clark electrode the sensors of this type are not affected by evaporation of water because the porous electrode is directly in contact with the bulk of the electrolyte solution. The mass transfer of the analyte from the sample to the working electrode can be faster, resulting in shorter response times and higher currents that leads to higher sensitivity [5]. Newer design concepts have also been proposed, so that new breakthroughs are to be expected [23-25]

3. General Principle of Amperometric Measurement in Gas Phase and in Liquid Phase

Amperometric sensors measure the chemical potential of the analyte in the gas phase (termed as fugacity) and/or in the liquid phase (termed as activity) [26]. Thermodynamically, gas-liquid phase equilibrium is described by the Henry's law as: f  K  a (1) where  is the fugacity of the analyte in the gas phase, K is an equilibrium coefficient for a particular analyte and liquid, called Henry's constant [15,27] and a is the activity of the analyte in the liquid phase. For low-pressure systems the fugacity of the analyte in the gas phase can be assumed to be equal to its partial pressure and the liquid-phase activity of the analyte can be expressed as product of activity coefficient and concentration of analyte, thus: p  K  C (2) Sensors 2010, 10 4434

where, p is the partial pressure of the analyte,  is the activity coefficient of the analyte and C is the concentration of the analyte. According to this equation the solubility of the analyte is proportional to its partial pressure above the liquid phase. The gases that have low boiling points and lack the

reactivity towards water (H2, O2, CO, etc.) have low solubility in water and the

temperature-dependence of solubility is linear. Gases that react with water (NH3, SO2, CO2, etc.) have higher solubilities. It is often assumed that the activity coefficient is equal to 1.0 or at least constant. However, in real samples this assumption often breaks down [28]. Especially important from practical point of view are different salt solutions, such as e.g., sewage [28] and seawater [26,29]. Using Fick’s first law and Faraday’s law the following general expression for the steady state current of an amperometric sensor can be written [15,17]: n  F I  3  p (3) Rk   Ri i1 where I is the sensor output current, n is number of electrons involved in electrochemical reaction, F is

the Faraday constant, Rk is the kinetic resistance of the electrochemical reaction and Ri is the analyte diffusion layer resistance of a layer i. This generic equation holds for Clark, GDE and with some reservations also for SPE sensors. Albantov and Levin regard the diffusion layers mathematically as a set of resistors sequentially connected. The resistivity of a layer i to diffusion is described by the following equation for membrane-covered sensors [15]:

i Ri  (4) Si  Di  Ai

where, i is the thickness of the diffusion layer i, Si is analyte solubility in the diffusion layer i and Di is analyte diffusion coefficient in the diffusion layer i, A is the diffusion layer area (projected area of the electroactive surface in Clark type sensors [10]). The construction parameters of the sensor, such as surface area of the vacuum-deposited metal layer, width of the measurement cell, thickness of the metal layer, membrane thickness, membrane character (number of ionic groups in the total mass of polymer), the way of analyte supply to the working electrode surface (axial or radial) and composition of the internal electrolyte impose have an impact on the sensor signal. In reference [14] a comprehensive mathematical model is given, which describes the effects of these variables. Equation 3 is the general measurement model of the amperometric sensors. In the classical Clark sensors in the gas phase usually two diffusion layers are assumed [30] and in the liquid phase three diffusion layers [15,31]. In the GDE and SPE sensors the diffusion limitation can be achieved using mechanical barriers and a single diffusion layer is used in eq (3) [32].

4. Literature Survey: Overview

Because of the nature of amperometric measurement described in the previous section it is clear that it is affected by numerous uncertainty sources. In the literature there is no shortage of reports that describe amperometric sensors of different design and address their characteristics, such as response time, detection limit, linearity, repeatability and sensitivity of sensors [14,16,22,33-43]. There are also works that discuss accuracy [38,44] and drift [34,36,37]. But there are only a handful of papers that

20 Sensors 2010, 10 4435 describe combined uncertainty (i.e., uncertainty taking into account all relevant uncertainty sources) estimation of amperometric measurement results and analyze the relevant uncertainty sources. Most of them are devoted to amperometric oxygen sensors [31,45-48]. Jalukse and Leito have carried out in-depth analysis and modeling of amperometric dissolved oxygen sensors. They identified 16 separate uncertainty sources [31] and found that the relative expanded uncertainties (k = 2) obtained by experts under laboratory conditions varied between 1% and 9%. More recently Nei has stated that uncertainties in amperometric dissolved oxygen measurement at field laboratory level tend to be larger (between 5% and 20%) [46]. Table 1 gives the overview of the articles found that address at least three uncertainty sources in amperometric sensors. The uncertainty sources will be reviewed in detail in the next section. The general observation from the literature survey is that, apart from certain articles on dissolved oxygen concentration measurement, uncertainty of measurement results obtained with amperometric sensors is rarely discussed in the literature. Most authors examine certain characteristics that are relevant to uncertainty but cannot be easily combined into the combined standard uncertainty estimate of the result uc (see below for terminology of uncertainty estimation).

5. Literature Survey: Sources of Uncertainty

Based on the generalization of the literature survey and the experience from our laboratory we discuss below the main uncertainty sources relevant to amperometric sensors.

5.1. Temperature (Compensation)

The rate of the diffusion or permeation (below diffusion) processes is influences by temperature. Temperature directly influences the following: widths of the diffusion layers, diffusion coefficients of the analytes in the different layers [29,62-65]. This is the reason why amperometric sensors are normally equipped with accurate temperature measurement capability and the results are in most cases corrected for taking into account the difference between measurement and calibration temperatures. In most cases measurement and calibration are carried out at temperatures that differ from each other (at least by few degrees). This temperature difference has to be taken into account. Temperature effects cause uncertainty in amperometric measurement via two factors: (1) limited accuracy of temperature measurement (during calibration and measurement) and (2) limited accuracy of compensation for temperature difference between calibration and measurement [31]. The latter may in turn be due to inaccuracy of the model underlying the temperature compensation or the inaccuracy of the value(s) of the parameter(s) involved in the compensation [31]. Sensors 2010, 10 4436

Table 1. Uncertainty sources of amperometric sensors discussed in the literature. Analyte Phase Response time Linearitya Repeatability Drift Interferences Ref. Nominal Range: 0–2 ppm, <5% signal O Gas <20 sb [49] 2 linearity: linear loss/year Range: 0–25%, linearity: ± 0.1% of ± 0.25% O2 O Gas 20 sc [50] 2 ± 1% of full scale range per week General purpose: 180 sc <1% per O Gas 0.05–60 mg dm3 [51] 2 Fast Response: 30 sc month

c Nominal Range: 0–10,000 <2% signal CO; H2S; NO; H2 Gas <70 s 2% of signal [52] ppm, linearity: linear loss/month HCN; C2H4 Ppm level: 20–50 s H Gas 0.2–2% ± 10% d [53] 2 % level: 5–20 s Nominal Range: 0–20 <2% signal CO; H S; NO ; SO Gas 15 sc ppm, Output linearity: 2% of signal 2 2 [54] 2 loss/month HCN; Cl ; HCl linear 2 No interference Calibration from Br , O Liquid <90 sc 0.005–2 ppm 1.0% interval 2 2 [55] 3 chloramines, Cl , months 2 ClO2 or H2O2 Nominal Range: 0–100 <2% signal NO Gas 15 sc ppm, Output linearity: 2% of signal H S; HCl; NO [56] loss/month 2 2 linear Measuring range: 0–1000 <10% per 6 NH Gas <90 sc ppm, H S; SO [57] 3 months 2 2 Linearity: <5% full scale

0.002–1.25 Ca 1.4% per CH3OH; HCHO; HCHO Liquid Tens of seconds -1 [58] mg mL hour HOCH2CH2OH H2S Liquid <100 ms 2–300 μM 2.5% <5% per day SO2; CH3CH2SH [36] Sensors 2010, 10 4437

Table 1. Cont. CO Gas 7 s 0.70–56 µg mL-1 5.3% (n = 5) [35] 4·10-7–1·10-3 SO Liquid 4 s ± 3% H S; NO [16] 2 mol dm-3 2 8·10-9–2·10-4 SO Gas ± 3% H S; NO [16] 2 1 s mol dm-3 2 c e f SO2 Gas 189 s 5–500 ppm None [41] ± 1 ppmg H S Gas Ca. 10 s 0–100 ppm [59] 2 Good long- PH Gas 4.6 sc 0–100 ppm ± 3%g [60] 3 term stability a Linearity data has been presented the way it was given in the original paper. b T95 c T90 d Reproducibility, the stability of the sensor was monitored for a period of three weeks and found to be stable within ±10% of the concentration value. e The linear equation was y = –0.07x – 2.66 with a correlation coefficient of 0.9946. f Other copresent gases, such as CO, NO, NH3 and CO2, did not cause interference under these conditions. g Reproducibility

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This component is also influenced by changes in properties of diffusion layers: for example: deformation, ageing and contamination of the membrane in the case of membrane-based electrodes. Different sensor designs are affected somewhat differently by temperature. In the Clark and GDE type sensors temperature affects the permeability of the membrane (activation energy of diffusion through membrane). At the same time in the SPE sensors the analyte does not need to diffuse through the membrane. The temperature dependence of permeability is determined by measurement of sensor current at different temperatures at constant (and known) analyte concentration. The temperature dependence can then be either used empirically [52,54,56,57,66] or converted into activation energies of diffusion through the diffusion layers [10,31]. The importance of this uncertainty source is widely acknowledged, but rigorous evaluation of magnitude of this uncertainty is generally not done (except in reference [31]).

5.2. Drift

Drift is defined by VIM [67] as continuous or incremental change over time in indication, due to changes in metrological properties of a measuring instrument. Instrumental drift is related neither to a change in a quantity being measured nor to a change of any recognized influence quantity. In amperometric sensors all changes during sensor use, which lead to changes of the sensor properties compared to the time of calibration cause drift. Possible causes of drift are unstable reference potential, caused by contamination, poisoning or consumption (depletion) of the reference or counter-electrode, local changes of electrolyte concentration and/or pH, contamination or poisoning of the working electrode (changed catalytic activity) [10,29,68]. One of the most important of them is change of the diffusion layer that limits the mass transfer [31]. Changes in the properties of the working electrode do not affect the sensor as long as mass transfer remains the rate-limiting step (Clark and GDE type sensors). However, in more severe cases the sensor may begin to work in a mixed kinetics mode, leading to drift of the parameters and loss of linearity. The factors causing drift are known to change with age and periodically over time. Some factors can be predicted while others are more or less random. In order to evaluate the uncertainty due to drift the sensor signal has to be monitored in time at constant analyte concentration. This can be done either continuously or periodically. Keeping the measurement conditions constant is very important.

5.3. Stirring Speed or Flow Rate

Stirring speed or solution (or gas stream) flow rate (below termed flow rate) influences the result, because it affects the thickness of the outer diffusion layer. This happens because of analyte consumption by the sensor at the boundary layer between the sample and the membrane [15,29,31]. If the measurement is carried out in the gas phase then the dependence of the sensor signal on the flow rate strongly depends on the sensor type and design. The higher is the porosity of the contact between the sensor and the measured solution (i.e., membrane in the case of Clark and GDE sensors and working electrode in the case of SPE sensors) the higher is the sensitivity of the sensor signal towards flow rate [1,14]. At low values of gas or liquid flow rate the signal dependence on the flow rate is almost linear. Above a certain value the linearity is lost and if the flow rate is further increased then the influence of flow rate on sensor signal becomes negligible. This is because the stagnant layer thickness decreases with increasing volumetric flow rate and stops playing a significant role in the overall

21 Sensors 2010, 10 4439 diffusion resistance [14]. When measuring in solution then a stagnant solution layer always forms on the membrane surface [15]. This layer decreases the signal, compared to the respective signal in the gas phase (with equal activity of the analyte) [31]. If calibration and measurement are carried out at different flow rates then this effect has to be corrected for or taken into account as an uncertainty source (see Figure 1, difference of diffusion layer compared to measurement) [31]. The thickness of this stagnant layer strongly depends on the flow rate [29]. If the flow rate is the same during calibration and measurement (e.g., if both are carried out in the same measurement cell) then the flow rate uncertainty component need not be taken into account. The effect of flow rate on the sensor response can be evaluated by carrying out measurements at constant temperature and constant analyte concentration and varying the flow rate.

5.4. Repeatability

Repeatability is measurement precision under repeatability conditions (set of conditions including the same measurement procedure, same operator, same measuring system, same operating conditions and same location, and replicated measurements over a short period of time) of measurement [67]. It is commonly expressed as standard deviation sr of the values obtained from repeated measurements. In the literature many repeatability estimates for different sensors can be found [16,22,33-37]. Sensitivity of the sensor is closely related to repeatability. High sensitivity maximizes signal to noise ratio and thus improves repeatability [69]. In other words, the greater the sensitivity the better is normally the capability of the sensor to distinguish between the signal and the background noise [29]. The stability of the sensor signal and thus the repeatability can be influenced by several parameters, for example fluctuations of measurement temperature, flow rate [31] or reference potential). Repeatability is usually dependent on the magnitude of the signal itself and is often roughly proportional to it. This, however, needs to be experimentally confirmed for a particular sensor and repeatability should therefore be investigated at different concentration levels. Repeatability is also influenced by the flow rate [31]. Therefore, if measurements are carried out at different flow rates then it is necessary to evaluate the dependence of repeatability on stirring speed. An important parameter related to repeatability is within-laboratory reproducibility (also known as intermediate precision) sR. It characterizes long-term measurement precision within a laboratory [67,70]. By its nature reproducibility is a compound parameter, accounting for repeatability, as well as all other effects that may have different magnitudes on different days. This involves changes in the sensor due to ageing (drift os sensor characteristics), uncertainty sources related to calibration, etc. Only effects that retain their magnitude over a long time period remain outside of within-lab reproducibility. Within-lab reproducibility is a very useful characteristic because it is relatively easy to determine it experimentally and it is one of the two cornerstones of the validation-data-based uncertainty estimation approach (see below). Literature data on reproducibility of amperometric measurements are scarce [59,60] and in addition it may be possible that in fact repeatability is what is meant in references [59] and [60].

5.5. Response Time

Sensor response time is one of the basic quality indexes for evaluating the performance of electrochemical sensors [32]. It is a parameter describing dynamic properties of the sensor with respect Sensors 2010, 10 4440 to changes of the analyte concentration [14]. Response time of amperometric sensors has been investigated extensively both experimentally [16,22,35,36,38,41-43,59,72] and via theoretical simulations [32,73]. The diffusion process, which controls the response time, can be modeled using Fick’s second law

[74,32]. The response time of the sensor is commonly specified by the so called T90. This value indicates the time required to reach 90% of the sensor's stationary current corresponding to the analyte concentration [32,43]. Other values referring to different percents of the stationary current, such as T63,

T95, etc, are also used [14,49,51,75]. Contributing factors include diffusion through the diffusion barriers, membrane(s), electrolyte, and also kinetics of the electrode reaction (where appropriate), as well as some aspects of the electronic circuit [14,32,43]. In the case of GDE and Clarke type sensors the diffusion of analyte through membrane is the most significant factors of these [10]. Since mass transport by diffusion through the membrane is the slowest step in the overall process, dramatically shortened response times can be obtained by using thinner membranes [29]. To model this effect, diffusion transport must be understood and characterized. This is done by measurement of the sensor output signal in time, first without and then with and finally again without the analyte [29,73,75]. From these data the response times are evaluated. It is also possible to estimate how much the signal at a specific time will be different from the signal at the steady state. This information can be used for uncertainty estimation. This uncertainty source can be eliminated almost completely by taking reading when stationary current has been achieved [31].

5.6. Linearity

Linearity of response of amperometric sensors has been extensively discussed in the literature [14,16,33-36,38-40,41,59,52,53]. As the mass-transfer rate of the analyte is slow compared to electron transfer, the current is controlled by diffusion rather than the kinetics of the electrode reaction, and this assures a linear dependence of the current over a wide range of concentration [5]. Linearity refers to the analyte concentration range, in which the sensor signal is proportional to concentration. Measurement range is connected with linearity and is defined as the range between the lowest and the highest concentration, which can be determined with assumed accuracy and precision [14]. Accurately prepared calibration mixtures are very important for linearity testing. In the case of gas-phase measurements gas mixtures of controlled composition can be used. Such mixtures are commercially available or can be prepared in the laboratory [32]. In the liquid phase the standard addition method can be used. If accurate preparation of calibration mixtures is difficult then an accurate independent reference method can be used if available. If the linear range of the sensor is established then the sensor should be used in the linear range only. If deviations from linearity occur then these should be corrected for or taken into account by additional uncertainty components [76]. Linearity also depends on the realizable analyte concentrations in the measurement medium. For example solubility of many gases in water is limited and in many cases even at saturation level the responses are still in the linear range. At the same time solubility of e.g., ethanol in water is unlimited and non-linearity can be a problem at higher concentrations. Linearity is assessed at constant conditions varying the analyte concentration in the solution or in the gas phase. Uncertainty due to possible non-linearity can be accounted for by the generic approach as described in reference [76]. The Sensors 2010, 10 4441 possible non-linearity component of uncertainty is the larger the more the concentrations during calibration and measurement differ.

5.7. Zero Current

Zero current (also termed as background current) arises from numerous sources. The most common of them is the oxidation or reduction of electrochemically active impurities and other side reactions [29]. The impurities may be present in the analyzed solution, but as well in the sensor materials. It can be especially important if too high a polarizing voltage is applied. Thus, the concept of zero current is closely related to selectivity [24]. High zero current can also be caused by the analyte from the previous measurements dissolved in the insulating body of the sensor (or in the electrolyte). This is especially noticeable in high-concentration environment. Analyte "stored" this way may slowly diffuse out during future use when the sensor is in an environment where analyte concentration is low [29]. This is similar to the sample carryover effect, frequently observed with different trace analysis techniques. If the zero current is high then it should be taken into account either in the calibration model (preferably) or as a component of uncertainty. Neither of the two approaches is easy, if the zero current varies and depends on the composition of previous samples. In the former case there will still be an additional uncertainty associated with the inaccuracy of zero current determination. Zero current is determined at the temperature of measurement and zero concentration of the analyte. Under these conditions zero current is the stationary current of the sensor. In the literature only few authors have addressed zero current [22,31,36].

5.8. Rounding of the Digital Reading

Modern instruments display results in the digital form, rounding the result and thus introducing uncertainty due to rounding. Whether or not this uncertainty component is of importance is highly dependent on measurement conditions. In most cases its effect is small, but in certain cases can make op to 60% of the uncertainty [31]. Uncertainty due to rounding is easy to take into account: its magnitude is ± 0.5 of the last digit of the reading, with rectangular distribution [77].

5.9. Analyte Concentration in Calibration Medium

There is always an uncertainty associated with the analyte concentration in the calibration medium. This uncertainty is transferred to the uncertainty of all measurement results obtained with the sensor, regardless accurate the sensor otherwise is. If reference mixtures are used for calibration then there is usually an accompanying document that contains also the uncertainties of the analyte concentrations. If the calibration mixture is prepared in-house then the uncertainty of analyte concentration is mostly due to gravimetric and/or volumetric measurements and can be estimated using the standard uncertainty estimation approaches [77]. With certain analytes there are additional complications that arise: the analyte may be volatile, prone to decomposition or adsorption, etc. These effects significantly complicate preparation of calibration mixtures and evaluating the uncertainty. In some cases calibration mixtures can be prepared only in situ. For example, there is up to now no standard solution Sensors 2010, 10 4442

of dissolved oxygen available [31,45]. Standard substance purity should also be accounted for, which can be difficult, if the impurities do not act as inert compounds but influence the response [78].

5.10. Activity of the Analyte and Matrix Effect

Amperometric sensors measure actually not analyte concentration, but activity [29]. Calibrating the sensors in concentration terms implicitly introduces the assumption that the activity coefficient of the analyte is the same during calibration and measurement. This assumption breaks down e.g., when there is a high concentration of salts in the measured medium. In salt-rich water the active concentration of water decreases and this leads to increase of the activity coefficients of most neutral compounds,

notably gases (salting-out effect). For example, investigations of the solubility of H2S in pure water and NaCl brine solutions at different ionic strengths show significant influence on the activity

coefficient of molecular H2S [36]. If a calibration made in pure water is used to calculate the concentration of the analyte in real sample with high ionic strength (e.g., sea water) then significant uncertainty is introduced by the difference between the activity coefficient of the analyte in the calibration solutions and the sample during measurement. For example, if in a stream of natural water the dissolved oxygen activity coefficient is 1.075 and the dissolved oxygen concentration as measured by the Winkler method [79] is 4.7 mg dm-3 then the reading of an amperometric sensor calibrated in water with negligible ionic strength will be approximately 5.0 mg dm-3 [28]. This effect either has to be corrected for or introduced as an additional uncertainty component. This issue has been studied e.g., with dissolved oxygen measurement [28] and it is possible to calculate the activity coefficient of oxygen if the ionic strength is known [29,Error! Reference source not found.,81]. The activity coefficients found this way are approximate, because conductivity does not directly show the ionic strength of the solution.

5.11. Interferences from Other Compounds (Insufficient Selectivity)

The usual assumption in sensor use is that the sensor response is influenced only by the analyte and not by other compounds in the sample matrix. In reality there are often interfering compounds (interferents) that either (1) behave as the analyte or (2) disturb the operation of the sensor in some way. There are some possibilities to enhance sensor selectivity by sensor design. One of them is choice of the membrane (applicable to GDE and Clark type sensors). Appropriately chosen membrane can efficiently limit the access of interfering substances to the electrode [82]. The second possibility is tuning the composition and pH of the electrolyte solution [2]. The third possibility is to vary the working potential [29] of the sensor. The fourth possibility is to apply filters that trap and eliminate interfering substances [1]. The fifth possibility is to use an auxiliary electrode that works at a lower potential than the working electrode and electrochemically removes the interfering substances [1]. As a general rule lower potential of the working electrode is preferable, because it excludes interference by substances of higher oxidation potential. Nevertheless, selectivity certainly remains an issue with amperometric sensors and is often one of the main uncertainty components in analysis with amperometric sensors. In some drastic cases the sensitivity of the sensor can actually be higher towards an interferent that towards the analyte. For example, this holds in the case of certain ethanol sensors that are more sensitive towards methanol than towards ethanol [33].

22 Sensors 2010, 10 4443

In spite of its importance, selectivity has been discussed scarcely in the papers devoted to amperometric sensors. The reason might be that it is extremely difficult to model it, express it numerically or take it into account as an uncertainty source [83]. This is the reason, why most of the discussion on selectivity [16,13,23,24,33,34,38,40-42] remains qualitative: the majority of authors discuss selectivity in yes/no terms only. In a small number of papers also quantitative estimates are given [82,84]. For example, the effect of water on the Au-Nafion® on and Au-ADP SPE electrodes for determination of ethanol and acetaldehyde was investigated. It was found that the signal dramatically increases with humidity content up to approximately 80% r. h., after which further increase does not vary the response considerably. The presence of H2O in the gas thus can cause strong interference and has to be either controlled or compensated for. [2] If data are available on sensor selectivity with respect to the potential interferents and if the concentration ranges of the interferents in the samples can be estimated then the uncertainty due to the possible presence of the interferents can be estimated. Alternatively, if it is possible to remove the analyte from the sample and measure the zero current (which will mostly be due to the interferents) then it will be possible to correct the results for the interference. This can be done if the background current is steady and the interfering substances do not contaminate the system [29]. When the background current is large and is not steady, then the only real solution is to remove the interference either before or during measurement using chemical treatment or with some separation device.

6. Literature Survey: Conclusions

The literature survey reveals that the main uncertainty sources relevant to amperometric measurement are well known. As a generalization the following "fishbone" diagram of uncertainty sources inherent to amperometric measurements can be presented:

Figure 1. Uncertainty sources in amperometric measurement.

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All of the uncertainty sources indicated in Figure 1 have been at least in some context dealt with in the literature. The level of coverage of the uncertainty sources differs very strongly. For example, repeatability as an uncertainty source is almost always included while the activation energy of diffusion is examined only in few works. A potentially very important uncertainty source is interference from other compounds in the matrix. Interference is often mentioned and discussed but rarely handled as an uncertainty source. Uncertainty sources in amperometric measurements of different analytes are broadly the same. Nevertheless, their magnitudes are strongly dependent on the analyte, the matrix, sensor design and measurement conditions [31]. Therefore it is not to be expected that uncertainty estimation at a reasonable level of rigor can be carried out based purely on literature data.

7. Approaches for Uncertainty Estimation in Amperometric Measurement

Most of the available approaches for measurement uncertainty estimation evaluate the uncertainty due to different uncertainty sources and combine these into the combined standard uncertainty uc – uncertainty estimate taking into account all significant uncertainty sources and expressed at the level of standard deviation [7,9,70]. For reporting the result usually a higher coverage level is desired than the one provided by uc (roughly 68% if the result is Normally distributed) and thus uncertainty is usually reported as expanded uncertainty U:

U = k · uc (5) where k is the coverage factor. Often k = 2, which means that the coverage level is roughly 95%, if the result is normally distributed. The approaches differ in two aspects: (1) how detailed is the examination of the uncertainty sources and (2) how the estimates of the uncertainty sources are combined into uc. We look at two widespread approaches for uncertainty estimation: 1. Full-fledged modeling approach as proposed in Reference [9]. The use of this approach implies compiling a measurement model for the sensor, in-depth analysis of the uncertainty sources and experiments for quantifying the uncertainty components. This means that the uncertainty is broken down into a number of sources and they are combined using the measurement model. If the output quantity Y is found as a function F of input quantities X1 .. Xn as:

Y = F(X1, X2 ... Xn) (6) then the combined standard uncertainty is found as:

2 2 2  Y   Y   Y  (7) uC (y)   u(x1 )   u(x2 )  .....  u(xn ) X 1  X 2  X n  where u(xi) is the standard uncertainty estimate of Xi. All these standard uncertainty contributions have to be evaluated. 2. Approach based on validation and quality control data. This approach was originally proposed in the handbook published by Nordtest [70] and has later been revisited in reference [7]. The advantages of the approach are that there is no need for a measurement model and in-depth analysis of uncertainty sources. Instead, use can be made of validation data, control charts, reference measurements [71] and participation in interlaboratory comparisons–all of which are rather accessible even to routine analysis Sensors 2010, 10 4445

laboratories. The different uncertainty sources are accounted for by two principal components–u(RW) accounting for all the random factors (at lab level) contributing to the uncertainty and u(bias) accounting for all the systematic factors (at lab level) contributing to the uncertainty. These two are combined as follows:

2 2 uc  u(Rw )  u(bias) (8)

Reference [70] envisages the ways to estimate these two components by using control charts [85]

(for u(RW)), analysis of certified reference materials or participation to interlaboratory comparisons (for u(bias)). The uncertainty component accounting for possible bias is found as follows [86]:

2 2 u(bias)  RMSbias  u(Cref ) (9) where RMSbias is the root mean square of differences found as: 2  2 ... 2 RMS  1 2 n (10) bias n where i are the differences between the results of the procedure and Cref and u(Cref) is the standard uncertainty of Cref. Contrary to the model-based approach the uncertainty estimate obtained with the Nordtest approach does not characterize a single measurement result but rather gives an average uncertainty value obtained in a laboratory using a given measurement procedure [7]. This estimate is appropriate for the measurement conditions under which the uncertainty components u(Rw) and u(bias) were evaluated. Further comments on the approaches are given in the case studies presented below.

7.1. Case study 1: Model-Based Measurement Uncertainty Estimation

Model-based measurement uncertainty estimation [9] closely follows the operation principle of the sensor, expressed by the measurement model. An adequately compiled model allows taking into account all significant uncertainty sources [77]. The uncertainty estimate obtained with the model-based approach are directly relevant to a particular measurement situation and allows to take into account all the aspects of the measurement, such as temperature, calibration conditions, sensor design, etc. [31]. The outcome of uncertainty estimation with this approach is not only the uncertainty estimate but also the uncertainty budget, which allows seeing where most of the uncertainty comes from and thus provides valuable information on improving the measurement. This is certainly a big advantage of this approach. At the same time, in order to get a realistic uncertainty estimate, all the individual uncertainty components have to be discovered and also quantified. This requires careful investigation of the measurement procedure and high level of competence. We present here a case study of uncertainty estimation of amperometric dissolved oxygen measurement. It was originally published in reference [31] and full details can be found there. This case study is useful for demonstrating how much measurement conditions can affect uncertainty. The WTW OXI340i analyzer with a CellOx 325 sensor was used for measurements. The calibration and measurement conditions correspond to cases 1 and 4 in reference [31] and have been described in detail there. Case 1 represents a laboratory measurement under nearly ideal conditions. The sensor membrane and electrolyte have been freshly changed. Calibration has been carried out in water immediately before measurement. The stirring speed is the same during measurement and calibration Sensors 2010, 10 4446

and is quite high: 30 cm s−1. Case 4 represents a typical measurement situation in a laboratory doing field work. Sensor's membrane is 0.5 months old. Calibration was carried out in laboratory at 20 °C (stirring speed 20 cm s−1) 5 days before measurement. The measurement is performed under outdoor conditions with different water temperatures. The estimated stirring speed during measurement is 10 cm s−1 (this is a suitable estimate of the flow speed in the case of slow river flow or moving the sensor up and down during measurement). In both cases saturated oxygen concentrations are examined at various temperatures. The results are presented in Table 2.

Table 2. The expanded uncertainties (k = 2) of WTW OXI340i with a CellOx 325 sensor for laboratory and field conditions by model-based measurement uncertainty estimation.

U U relative U U relative tmeas Cmeas (mg/L) (%) (mg/L) (%) (°C) (mg/L) Case 1 Case 4 laboratory conditions field conditions 20 0 0.10 - 0.10 - 5 12.71 0.24 1.9% 0.66 5.2% 15 10.01 0.10 1.0% 0.50 5.0% 20 9.01 0.07 0.8% 0.44 4.9% 25 8.18 0.08 0.9% 0.41 5.0%

The uncertainty budgets for both cases at temperature 5 and 20 °C are presented in Table 3.

Table 3. Uncertainty budgets for cases 1 and 4 at temperatures of 5 and 20 °C.

a Inputs Calibration environment: water

Case 1 Case 4 Case 1 Case 4 Measurement conditions -3 Cmeas (mg dm ) 12.71 12.71 9.01 9.01 o a tmeas ( C) 5 5 20 20 -1 stirring speed_meas (cm s ) 30 30 30 30 o a tcal ( C) 20 20 20 20

u(pcal) (Pa) 150 150 150 150 -1 stirring speed_cal (cm s ) 30 20 30 20

day_newcal-meas (day) 0 5 0 5

day_oldcal-meas (day) 0 0 0 0 month (month) 0 0.5 0 0.5

a Input Parameters (xi) Uncertainty contributions (indexes) of the

input parameters xi

tcal 0% 0% 0% 0%

Tinstab 0% 0% 1% 0%

J0 2% 0% 0% 0%

Jcal_output 2% 1% 12% 1%

pcal 3% 0% 15% 0%

Csat_cal 9% 1% 47% 1%

pCO2 0% 0% 1% 0%

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Table 3. Cont.

pH2O_cal 2% 0% 9% 0%

Cread_cal 0% 0% 0% 0%

tmeas 3% 0% 0% 0%

J_meas_output 2% 3% 12% 4%

Cread_meas 0% 0% 1% 0%

lsme_drift 0% 2% 4% 2%

Esme_drift 0% 0% 0% 0%

Jstir 0% 81% 0% 91%

Esme_membrane 77% 10% 0% 0%

 Expanded uncertainties (k = 2) of Cmeas

U(Cmeas) 0.24 0.66 0.07 0.44

U(Cmeas), relative 1.9% 5.2% 0.8% 4.9% a The definitions of all the quantities and parameters are given in reference [31].

At all temperatures (except in the case with zero oxygen concentration) the uncertainty is significantly lower under laboratory conditions, because calibration was carried out immediately before measurement and the stirring speed is equal during calibration and measurement and the sensor membrane has been freshly changed. As can be easily seen from Table 3, under different measurement conditions different uncertainty sources have the most significant contributions. At 20 °C in Case 1 the contribution of the calibration solution concentration uncertainty is near 50%, meaning that these measurement conditions allow to obtain accuracy approaching the highest possible with that sensor–calibration solution concentration is a factor extraneous to the sensor. At 5 °C in Case 1 the uncertainty is mainly due to the quite strong temperature correction –the activation energy of permeation of oxygen through the membrane Esme_membrane is the main uncertainty source. In Case 4 at both temperatures the main part of uncertainty comes from the uncertainty of the stirring speed. The reason is that this particular sensor has a very thin membrane with high O2 permeability and under field conditions the stirring speed can only be vaguely estimated. In order to use this approach successfully the uncertainty contributions due to all these (and other) factors have to be estimated reliably. Detailed discussion on these (and some more, corresponding to different concentrations) uncertainty budgets can be found in reference [31].

7.2. Case study 2: Measurement Uncertainty Estimation Based on the Nordtest [70] Approach

The same instrument was used as in Case study 1. However, due to the nature of the Nordtest approach–pooling of the data over a long time period–the sensor properties–age of the membrane and time that has passed from the last calibration –cannot be as well defined as in the case of the ISO GUM modeling approach. The approach rather evaluates an average uncertainty of the measurement procedure as applied under the normal working conditions of a particular laboratory.

The component taking into account random effects u(Rw) was estimated from a control chart made at saturation concentration at temperature 20 °C and from these data u(Rw) = 0.089 mg/L. In order to be applicable also to concentrations lower than saturation we use this estimate as relative standard uncertainty urel(Rw) = 0.98%. Due to the working principle of amperometric dissolved oxygen Sensors 2010, 10 4448 measurement it can be assumed that this relative uncertainty estimate is in broad terms constant over the different concentrations [31]. The u(bias) component can be estimated from the results of interlaboratory comparison measurements from references 87 and 88 as well as from reference measurements with air-saturated water at different temperatures. The bias estimates obtained are presented in Table 4:

Table 4. Bias estimates obtained from the reference measurements and interlaboratory comparisons.

a b a tmeas (°C) 16.01.2006 7.03.2006 9.06.2006 0 mg/L 0.04 0.20 0.04 5 −0.35 −0.56 0.01 15 −0.28 −0.18 0.07 20 −0.32 −0.11 −0.18 25 −0.31 −0.03 −0.08 a Reference measurements. b Interlaboratory comparisons.

The uncertainty estimates obtained from these data using eqs 8–10 are given in Table 5. The uncertainty of the reference value at the saturation conditions was 0.15 mg/L (k = 2). The uncertainty of the reference value of zero solution was 0.01 mg/l (k = 2) [88].

Table 5. The uncertainties of WTW OXI340i with a CellOx 325 sensor by the Nordtest approach.

tmeas Cmeas RMSbias u(bias) U U (°C) (mg dm-3) (mg dm-3) (mg dm-3) (mg dm-3) (%) 20 0 0.12 0.12 0.24 5 12.71 0.38 0.39 0.82 6.4 15 10.01 0.20 0.21 0.46 4.6 20 9.01 0.22 0.23 0.50 5.5 25 8.18 0.19 0.20 0.43 5.3

In this case both control charts and interlaboratory comparisons were carried out at saturation concentrations. Therefore these uncertainty estimates are more suitable for higher concentrations.

7.3. Comparison of the Model- and Nordtest Based Uncertainty Estimation Approaches

Comparison of the uncertainty estimates obtained with both approaches is presented in Figure 2. As seen from the figure the uncertainties obtained using the Nordtest approach and the ISO GUM approach under the non-ideal conditions (Case 4) agree well. This is remarkable, given the completely different foundations of the data used for uncertainty evaluation. It is fair to say that in practice this level of agreement between the ISO GUM modeling and Nordtest approaches is not always found. The uncertainty under nearly ideal laboratory conditions is expectedly significantly lower – up to five times–than in the remaining two cases. Sensors 2010, 10 4449

Figure 2. Expanded uncertainties for all conditions using two estimation approaches.

0.90 Nordtest, U 0.80 Case 1 Model-based, U Case 4 Model-based, U 0.70 ) -3 0.60

0.50

0.40

0.30

Uncertainty (mg dm (mg Uncertainty 0.20

0.10

0.00 0 12.71 10.01 9.01 8.18 t=20°Ct=5°C t=15°C t=20°C t=25°C Measurement concentration (mg dm-3)

The ISO GUM approach allows evaluating uncertainty for a particular measurement result taking account the particular measurement conditions. In contrast, the Nordtest approach allows evaluating an averaged uncertainty, which takes into account the average state of the equipment and working practices over a long period of time. Mathematically the Nordtest approach is simpler, but availability of data for a sufficiently long period of time is necessary. The most important issue with the Nordtest approach is estimation of the bias. It may often be difficult to find reference values of sufficiently high quality for that. The most accessible reference values for laboratories are generally results of Interlaboratory comparison measurements. However, their reference values can be of low quality, especially if consensus values based on participant results are used. For example, in 1981 an interlaboratory comparison measurement of dissolved oxygen concentration was carried out [89] at two concentrations 1.20 and 5.86 mg dm-3. The mean absolute difference of the participant results from the reference values was 0.6 mg dm-3. Also, 11 laboratories out of 14 obtained higher results than the first reference value and all laboratories obtained results higher than the second reference value.

8. Practical Notes on Achieving Accuracy When Measuring with Amperometric Sensors

The lowest uncertainty is obtained when the analyte concentration is near the calibration concentration(s), measurement is carried out during a short time after calibration, measurement and calibration are carried out in the same medium and the flow rate and temperature are the same during measurement and calibration. It must be made sure that the stationary current has indeed been reached. Strong interferences should be eliminated if present and salinity correction carried out (if relevant). When measuring low analyte concentrations the zero current has to be either corrected for or taken into account as uncertainty source. If so done the main uncertainty sources are those associated with analyte concentration in calibration solutions and repeatability/stability of the sensor (in the medium concentration range) or zero current (in the low concentration range).

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9. Conclusions

A large number of different factors cause uncertainty in analysis using amperometric sensors. All of them have been addressed in the literature and estimates of the uncertainty invoked by them can be found in the literature. However, different uncertainty sources differ vastly by their coverage and only a handful of papers describe calculation of combined standard uncertainty that takes into account all relevant uncertainty sources. Uncertainty estimation by the modeling approach, which explicitly takes into account all major uncertainty sources and combines them using a measurement model, needs a high level of knowledge about the measurement procedure. The alternative–Nordtest approach–is less demanding on the detail of knowledge but needs ample validation data. The approaches yield uncertainties that refer to different situations–the particular measurement under question and the measurement procedure in routine use at the laboratory, respectively. The case studies demonstrate that even with the same sensor the relative contribution of the different uncertainty sources can be very different depending on the sample, condition of the sensor and measurement conditions.

Acknowledgments

This work was supported by the Estonian Science Foundation grant 7449 and by the targeted financing project SF0180061s08 from the Estonian Ministry of Education and Science.

References and Notes

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© 2010 by the authors; licensee MDPI, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/). II

L. Jalukse, I. Helm, O. Saks, I. Leito, On the accuracy of micro Winkler titration procedures: a case study Accredit. Qual. Assur. 2008, 13, 575–579.

Reproduced with kind permission of Springer Science and Business Media from Accreditation and Quality Assurance, 2008, vol 13 L. Jalukse, I. Helm, O. Saks and I. Leito. On the accuracy of micro Winkler titration procedures: a case study. Pages 575–579. Accred Qual Assur (2008) 13:575–579 DOI 10.1007/s00769-008-0419-1

PRACTITIONER’S REPORT

On the accuracy of micro Winkler titration procedures: a case study

Lauri Jalukse Æ Irja Helm Æ Olev Saks Æ Ivo Leito

Received: 12 April 2008 / Accepted: 28 May 2008 / Published online: 1 July 2008 Ó Springer-Verlag 2008

Abstract Accuracy data (expressed as precision and Introduction trueness) presented by the authors of three different micro modifications of the Winkler titration procedure for dis- Dissolved oxygen concentration is one of the most impor- solved oxygen concentration determination are critically tant parameters of water and is of great practical interest. evaluated. Tentative uncertainty estimates are extracted Several methods are available for the determination of from the data based on the single-laboratory validation dissolved oxygen concentration [1, 2], among which, the approach (originally published in the Nordtest Technical Winkler iodometric titration method (from here on termed Report 537) and they lead to expanded uncertainty (k = 2) the Winkler procedure) [3] occupies a special position, estimates in the range from 0.13 to 0.27 mg l-1 for the because it is the only available method that does not need three procedures. It is demonstrated that, in all cases, the calibration with the analyte—oxygen. The Winkler proce- authors have presented the accuracy and/or precision esti- dure has been elaborated by different authors with great mates of the procedures in a way that can lead to too care, and a number of publications [2–5] and an ISO stan- optimistic conclusions about the uncertainty of their pro- dard [6] are devoted to it. Accurate determination of cedures. This case study demonstrates the usefulness and dissolved oxygen concentration by the Winkler procedure is flexibility of the single-laboratory validation approach to a demanding task that requires skill and is affected by uncertainty estimation, even in the case of insufficient data, numerous uncertainty sources. Several of these are specific and can be of interest to laboratory workers dealing with to the Winkler procedure: contamination of the sample by measurement procedures from the literature. It is also atmospheric oxygen, oxygen dissolved in the reagents used, expected to be of interest to university instructors of ana- iodine volatilization, etc. The analysis of literature data lytical chemistry and metrology in chemistry as a real-life allowed us to obtain the precision/accuracy of the classical example of the critical evaluation of the literature data. Winkler procedure performed by highly skilled operator as ‘‘standard deviation ± 0.1 mg l-1’’ [4, 5, 7]. This standard Keywords Winkler method Titration deviation combines both random and systematic effects, Dissolved oxygen Measurement uncertainty and can be regarded as an estimate of the combined standard Nordtest method uncertainty. Replicate determinations, with 10 degrees of freedom, of dissolved oxygen in air-saturated water (concentration range 8.5–9 mg l-1), carried out in four separate laboratories, gave within-batch (repeatability) standard deviations of between 0.03 and 0.05 mg l-1 [6]. Compari- Electronic supplementary material The online version of this -1 article (doi:10.1007/s00769-008-0419-1) contains supplementary son of these values with the above estimate of 0.1 mg l material, which is available to authorized users. implies that bias and long-term effects dominate the Win- kler procedure and amount to 0.095 to 0.085 mg l-1, & L. Jalukse I. Helm O. Saks I. Leito ( ) respectively. These effects are, e.g., systematic effects on Institute of Chemistry, University of Tartu, 2 Jakobi Str., 51014 Tartu, Estonia the end-point, concentration of the standard KIO3 solution, e-mail: [email protected] concentration of the sodium thiosulfate solution, etc. 123

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Perhaps the most important data that have historically 19], with the goal of obtaining combined uncertainty esti- been obtained using the Winkler procedure are the con- mates for them. All three procedures are from the first half centrations of dissolved oxygen in air-saturated water [8]. of the 20th century, but, interestingly, we found no newer These are routinely used for the calibration of amperometric publications of micro Winkler procedures. The purpose of dissolved oxygen sensors, which are currently the most this paper is threefold: widespread dissolved oxygen measurement devices. This 1. To clarify the situation with the uncertainty of the means that the Winkler procedure is one of the procedures above-mentioned micro Winkler procedures and to that lie in the basis of all electrometric dissolved oxygen demonstrate that the uncertainty of the published concentration measurements [1, 9, 10]. The other procedure procedures is, in fact, higher than that implied by the is gasometric measurement, which, differently from the estimates of the authors. Winkler procedure, does not provide chemical selectivity. 2. To provide a case study on the use of the single- The first concentrations of dissolved oxygen in water sat- laboratory validation approach to uncertainty estima- urated with air were published by Winkler at the end of the tion based on the literature data, in particular, such 19th century [3, 11]. During the first half of the 20th cen- data that come from the ‘‘pre-uncertainty era.’’ tury, the most widely used saturation concentration values 3. To encourage the analytical community to critically were those from the so-called Fox tables [12, 13]. Fox used assess accuracy/uncertainty estimates of procedures gasometry for the determination of the saturation concen- published in the literature. trations. Later works demonstrated that the values obtained by Fox were positively biased [14]: by 0.13 mg dm-3 at 5 °C and by 0.30 mg dm-3 at 20 °C. The main reason for this was the use of dry air for saturation [14]. During the Methodology period 1950–1980, intense investigations of the solubility of oxygen in water were carried out, in particular, with the Extracting data for estimating uncertainties, which would Winkler procedure [7]. The currently most used saturation account for all relevant uncertainty sources, from the ori- values of Benson and Krause [8, 15] have been obtained by ginal publications [16–19] is not an easy task. All three combining data from different sources. works were published a long time ago and the reliability of The classical Winkler procedure uses water samples of the results was not evaluated by combined uncertainty 100–150 ml and titrant volumes up to 100 ml. For many estimates (obtained according to the ISO GUM principles applications (especially if analysis has to be carried out [21]), but, rather, by estimating accuracy via trueness and outside laboratory), the method is too clumsy and not precision. This approach has traditionally been (and still is) suitable. Therefore, a number of modifications of the very popular among analytical chemists. classical Winkler procedure—micro Winkler proce- The data available in the original publications do not dures—have been developed, which allow water samples permit us to carry out uncertainty estimation using the from 1 to 10 ml and titrant volumes of a few ml to be modeling approach. At the same time, the availability of used [16–19]. reproducibility and bias (from the comparison of obtained In our work on dissolved oxygen concentration mea- values with those from other procedures or with pub- surement [9, 20], we became interested in setting up an lished reference values) data enables us to use the so accurate micro Winkler procedure at our laboratory. In this called ‘‘single-laboratory validation approach’’ for connection, we were interested to know what level of uncertainty estimation. This approach was originally uncertainty is achievable using the micro modifications of published in the Nordtest uncertainty handbook [22] and the Winkler procedure. It is known that several uncertainty reviewed in the recent EUROLAB uncertainty report sources become significantly more influential with micro [21]. The combined standard uncertainty u is expressed procedures (contamination of the sample by atmospheric c as: oxygen, volume measurement, etc.). This implies that the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uncertainty of the micro Winkler procedures should be at 2 2 uc ¼ uRðÞw þ uðÞbias ð1Þ least as high as with the classical Winkler procedure, and probably higher. We were, therefore, surprised to learn where u(Rw) is the within-laboratory long-term from the original publications [16–19] that the data reproducibility standard deviation and u(bias) is the reported for the micro Winkler procedure implied very standard uncertainty due to laboratory bias. The bias high accuracy, significantly higher than in the case of the uncertainty is found by the comparison of the results of the classical Winkler procedure. procedure to some reference value Cref (certified reference This situation prompted us to undertake the uncertainty material, different measurement procedure, etc. [22]) and is analysis of three published micro Winkler procedures [16– calculated as: 123 Accred Qual Assur (2008) 13:575–579 577 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi estimate of the within-lab reproducibility u(Rw) and u bias RMS2 uC 2 2 ðÞ¼ bias þ ðÞref ð Þ neglecting the uncertainty of the classical Winkler proce-

dure (i.e., assuming that u(bias) = RMSbias)—we can where RMSbias is the root mean square of differences, obtain a tentative estimate of the uncertainty of the pro- calculated as: -1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cedure as uc = 0.067 mg l , which, most probably, is D2 þ D2 þ ...þ D2 underestimated (due to the two simplifications). RMS ¼ 1 2 n ð3Þ bias n Krogh [17, 18] presents a micro Winkler procedure performed with syringe pipettes. The author correctly states where Di are the differences between the results of the that, in order to obtain accurate results, it is of utmost procedure and Cref, and u(Cref) is the standard uncertainty importance to eliminate (or take into account) the diffusion of Cref. All calculations are available in the electronic of oxygen into the sample and oxygen dissolved in the supplementary material (ESM). reagents. The accuracy of the procedure for sample vol- The EUROLAB report [21] describes a total of four umes 7–15 ml was reported as ‘‘results obtained on the approaches for uncertainty estimation. In addition to the same water by the author have varied by ±0.007 cm3 l-1’’ above-mentioned modeling and single-laboratory valida- [17, 18]. This corresponds to ±0.01 mg l-1. Variability for tion approach, there are two more approaches described: ‘‘the same water,’’ based on the previous examples, no the interlaboratory and the proficiency testing approaches. doubt, indicates that this variability means repeatability. The latter two, however, provide uncertainty estimates of No coverage factor is given, but we assume k = 2. This lower quality than the first two and there are also no suit- estimate could also be interpreted as a repeatability limit, able data for their application. Because the modeling meaning k = 2.8. However, as seen below, the bias com- approach cannot be applied due to the lack of data, the ponent is, in this case, so much larger than the repeatability above-described single-laboratory validation approach component that the value of k here is actually of no sig- remains the only reasonable choice. nificance. At the end of the investigation, it is stated that a deviation of 1% from the values of the Fox tables [17, 18] is systematically obtained and that this difference ‘‘has to Analysis of the published micro Winkler procedures be added to the titration results,’’ meaning that the values are systematically too low by 1%. It is known now [8, 10, Our goal is to demonstrate that the uncertainties of the 14] that the values of the Fox tables are systematically reported procedures are higher than what could be per- higher than the true saturation values. The average relative ceived from the accuracy statements of the authors. discrepancy in the temperature range 5–25 °C is 2.5% (see Therefore, this is one of the rare cases where we should the ESM). This means that the results obtained in [17, 18] under- rather than overestimate the uncertainty of the are, actually, on average, 1.5% too high. From these data, reported procedures. Thus, the uncertainties of all proce- we can extract the following tentative uncertainty contri- dures discussed below are at least as high as the estimate butions (for the saturation level, ca 9 mg l-1, for which -1 obtained by us and, most probably, are higher. most of the results are reported) u(Rw) = 0.005 mg l and In Fox and Wingfield [16], a portable apparatus is u(bias) = 0.015 9 9mgl-1 = 0.135 mg l-1, leading to -1 described that allows one to perform dissolved oxygen uc = 0.135 mg l . According to the author’s information, determinations with as little as 1–2 ml of sample. Dis- the bias component is relative, meaning that, at the -1 -1 solved oxygen content in the reagents is taken into account. 5mgl level, uc = 0.075 mg l . Again, both of these uc The authors do not report a full uncertainty of the results, values are most likely underestimated, since the same but they present parallel analysis data for different dis- simplifications as in the previous case are made. solved oxygen concentrations, from which, repeatability In Whitney [19], a syringe pipette procedure is descri- can be calculated as the pooled standard deviation bed that is claimed to be more accurate than the classical 3 -1 sr = 0.014 cm l (the results are reported with this unit Winkler procedure. No precision data are given, but the in [16]), which is 0.019 mg l-1. Although the dissolved procedure is compared with the classical Winkler proce- oxygen concentrations of the solutions range from 1 to dure and with the procedure of Fox and Wingfield [16]. 8cm3 l-1, pooling is justified because the spread of the The author states that the results of his procedure agree parallel results is very similar at different concentrations. with those of Fox and Wingfield [16] over the whole range The authors also report data for parallel determinations and with those of the classical Winkler procedure at con- 3 -1 with their procedure and the classical Winkler procedure. centrations above 4 cm l . Calculating the RMSbias,we This allows us to estimate the bias of their procedure as get two bias estimates: 0.109 cm3 l-1 with respect to the 3 -1 -1 3 -1 RMSbias = 0.045 cm l , i.e., 0.064 mg l . By intro- classical Winkler procedure and 0.041 cm l with ducing two simplifications—taking the repeatability as an respect to the procedure of Fox and Wingfield [16]. Pooling 123 578 Accred Qual Assur (2008) 13:575–579

Table 1 Results of the uncertainty analysis Reference Accuracya information as given by the Remarks u (k = 2) estimated authors of the original publications in this work (mg l-1)

[16] ‘‘The method... is accurate to 2%, even at Concentration range 1.4–11.5 mg l-1. 0.13b low oxygen concentrations’’ The accuracy estimate corresponds depending on the concentration to 0.03–0.23 mg l-1 [17, 18] 1. ‘‘Results obtained on the same water by Saturation conditions (concentration 0.27b the author have varied ca 9 mg l-1) 3 -1 by ±0.007 cm l ’’ 1. This corresponds to a 2. ‘‘A comparison of the absolute values... repeatability of ±0.01 mg l-1 with Fox’s tables revealed a systematic 2. This corresponds to a bias of discrepancy of 1%’’ 0.09 mg l-1 [19] 1. The author states that the results of his 1. This corresponds to 5.7 mg l-1 0.22b method ‘‘agree with those of Fox and 2. This can be interpreted as having Wingﬁeld [16] over the whole range k = 2 expanded uncertainty less and with those of the classical Winkler than 0.2 mg l-1 method at concentrations above 4cm3 l-1’’ 2. The method is ‘‘... more accurate than the ordinary method of analysis’’ a Accuracy is, in line with Eq. 1, considered to be inﬂuenced both by precision (within-laboratory long-term reproducibility) and bias (the numerical estimate of the trueness of the procedure) b These uncertainty estimates are tentative and are underestimated due to the lack of data in the original publications

these two estimates, we obtain 0.077 cm3 l-1, i.e., data that we used for uncertainty estimation. And as for 0.110 mg l-1. Since there are no data on the precision of uncertainty—they simply did not report uncertainty esti- the procedure, we use this as an estimate of uc, although it mates the way in which we use them now. Nevertheless, is, again, most probably underestimated. the way that they interpreted their data and stated the The results of the analysis are presented in Table 1.Itis accuracy/precision of their procedures can easily lead the seen that the uncertainty estimates are not very different readers to a false perception of significantly lower uncer- from each other. Given the simplifications involved in the tainty than is actually the case. Table 1 clearly reveals this uncertainty evaluation, we estimate the real standard for [17, 18, 19]. For [16], the 2% limit holds at saturation uncertainties of all of these procedures to be in the range of concentration, but already at half-saturation (around 0.10 to 0.15 mg l-1, and the respective expanded (k = 2) 4.5 mg l-1), the relative expanded uncertainty is 2.9% (the -1 -1 uncertainties as ±0.2–0.3 mg l . This is similar to the data used for pooling the RMSbias decreased to 3.5 mg l , estimate published for the classical Winkler procedure: thus, 4.5 mg l-1 is within range). 0.1 mg l-1 [2]. A common feature is the heavy dominance of u(bias) in Conclusions the uncertainty: in the first two cases, we could have actually neglected the precision term altogether. This The critical evaluation of the three micro Winkler proce- dominance would, perhaps, be less pronounced if, instead dures led to a combined standard uncertainty estimate of of repeatability, reproducibility could be used, but obtain- -1 around 0.10–0.15 mg l for all three procedures. It was ing this estimate with an unstable analyte like dissolved demonstrated that, in all cases, the authors of the original oxygen is complicated. procedures have presented the accuracy and/or precision It is important to note two things. Firstly, because all estimates of the procedures in a way that can lead to too three groups reporting the analyzed procedures were truly optimistic conclusions about uncertainty. This case study experts in the field, the obtained uncertainty estimate is demonstrates the usefulness and flexibility of the single- relevant to expert laboratories and not to an ordinary lab- laboratory validation approach [21, 22] to uncertainty oratory. Secondly, we, by no means, want to accuse the estimation, even in the case of insufficient data. authors of [16–19] neither in cheating or manipulating of their data nor in underestimating uncertainty. We are sure Acknowledgments This work was supported by the Estonian Sci- that they carried out excellent work and it is actually their ence Foundation, grant no. 7449.

123 Accred Qual Assur (2008) 13:575–579 579

References 12. Fox CJJ (1907) Publ Circ Cons Explor Mer 41:1–23 13. Fox CJJ (1909) Trans Faraday Soc 5:68–87. doi:10.1039/ 1. Hitchman ML (1978) Measurement of dissolved oxygen. Wiley, tf9090500068 New York, pp 71–123 14. Richards FA, Corwin N (1956) Limnol Oceanogr 1:263–267 2. Mancy KH, Jaffe T (1966) Analysis of dissolved oxygen in 15. Benson BB, Krause D Jr, Peterson MA (1979) J Solution Chem natural and waste waters. US Department of Health, Education, 8:655–690. doi:10.1007/BF01033696 and Welfare, Public Health Service, Robert A. Taft Sanitary 16. Fox HM, Wingfield CA (1938) J Experim Biol 15:437–445 Engineering Center, Cincinnati, Ohio 17. Krogh A (1935) J Industr Eng Chem 7:131–133 3. Winkler LW (1888) Ber Dtsch Chemischen Ges 21:2843–2855. 18. Krogh A (1935) J Industr Eng Chem 7:130–131 doi:10.1002/cber.188802102122 19. Whitney RJ (1938) J Exp Biol 15:564–570 4. Carpenter JH (1965) Limnol Oceanogr 10:135–140 20. Jalukse L, Vabson V, Leito I (2006) Accredit Qual Assur 10:562– 5. Carritt DE, Carpenter JH (1966) J Mar Res 24:286–318 564. doi:10.1007/s00769-005-0058-8 6. International Organization for Standardization (ISO) (1983) 21. European Federation of National Associations ofMeasurement, Water quality—determination of dissolved oxygen—Iodometric Testing and Analytical Laboratories (EUROLAB) (2007) Mea- method, ISO 5813. ISO, Geneva, Switzerland surement uncertainty revisited: alternative approaches to 7. Mortimer CH (1981) Mitt Int Ver Limnol 22:1–23 uncertainty evaluation. EUROLAB technical report no. 1/2007. 8. Benson BB, Krause D Jr (1980) Limnol Oceanogr 25:662–671 EUROLAB, Paris, France. Available online at: http://www. 9. Jalukse L, Leito I (2007) Meas Sci Technol 18:1877–1886. doi: eurolab.org/docs/technical%20report/ 10.1088/0957-0233/18/7/013 Technical_Report_Measurement_Uncertainty_2007.pdf 10. International Organization for Standardization (ISO) (1990) 22. Magnusson B, Naÿkki T, Hovind H, Krysell M (2004) Handbook Water quality—determination of dissolved oxygen—electro- for calculation of measurement uncertainty in environmental chemical probe method. ISO, Geneva, Switzerland laboratories: edition 2. Nordtest technical report TR 537. Nord- 11. Winkler LW (1891) Ber Dtsch Chemischen Ges 24:3602–3610. test, Espoo, Finland. Available online at: http://www. doi:10.1002/cber.189102402237 nordicinnovation.net/nordtestfiler/tec537.pdf

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I. Helm, L. Jalukse, M. Vilbaste, I. Leito, Micro-Winkler titration method for dissolved oxygen concentration measurement. Anal. Chim. Acta, 2009, 648, 167–173.

Reprinted from Analytica Chimica Acta, Vol. 648, I. Helm, L. Jalukse, M. Vilbaste and I. Leito, Micro-Winkler titration method for dissolved oxygen concentration measurement. Pages 167–173. Copyright 2012 with permission from Elsevier. Analytica Chimica Acta 648 (2009) 167–173

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Analytica Chimica Acta

journal homepage: www.elsevier.com/locate/aca

Micro-Winkler titration method for dissolved oxygen concentration measurement

Irja Helm, Lauri Jalukse, Martin Vilbaste, Ivo Leito ∗

Institute of Chemistry, University of Tartu, Jakobi 2, 51014 Tartu, Estonia

article info abstract

Article history: In this report a gravimetric micro-Winkler titration method for determination of dissolved oxygen con- Received 25 March 2009 centration in water is presented. Mathematical model of the method taking into account all influence Received in revised form 29 June 2009 factors is derived and an uncertainty analysis is carried out to determine the uncertainty contributions of Accepted 30 June 2009 all influence factors. The method is highly accurate: the relative expanded uncertainties (k = 2) are around Available online 4 July 2009 1% in the case of small (9–10 g) water samples. The uncertainty analysis carried out in characterizing the uncertainty of the method is the most comprehensive published for a micro-Winkler method, result- Keywords: ing in experimentally obtained estimates for all uncertainty sources of practical significance (around 20 Micro-Winkler titration Gravimetric titration uncertainty sources altogether). Primary method © 2009 Elsevier B.V. All rights reserved. Dissolved oxygen Measurement uncertainty Uncertainty budget

1. Introduction Although often perceived as a simple method, the physical and chemical processes on which the amperometric method is based Dissolved oxygen (DO) is one of the most important substances are complex [6] and a large number of factors are involved in present in water. Insufficient concentration of DO in natural waters determining the result and its uncertainty. Among them are the sat- leads to perishing of higher living organisms. High DO concen- uration concentration itself, temperature, air composition, possible tration is also very important for the efficiency of wastewater supersaturation, atmospheric pressure and humidity, stirring of the treatment plants. On the other hand oxygen is a strong oxidant and solution, stability of current, zero current value, drift, difference even a low DO concentration in, e.g. central heating systems may between calibration and measurement temperature (temperature lead to premature repairs of the pipelines. compensation), condition of the sensor membrane, etc. [6]. The It is thus very important to be able to accurately measure DO measurement uncertainty under expert laboratory conditions is in concentration in water. The main methods of DO concentration the range of ca ±0.1–0.2 mg dm−3 (k = 2) and under field conditions measurement are the Winkler iodometric titration method (WM) ca ±0.2–0.4 mg dm−3 [6]. The corresponding relative uncertainties [1,2], the amperometric sensor method [3] and now also the optical (at saturation conditions at 25 ◦C) are in the ranges of 1.2–2.4% and sensor method (based on luminescence quenching) [4,5]. 2.4–4.8%, respectively. Due to the speed and ease of use the amperometric method is The published DO concentrations in water saturated with air the most widespread in routine analysis. At the same time it is a [7] have been determined gasometry and WM [1]. Gasometry lacks relative measurement method and needs calibration with the ana- chemical selectivity and therefore the WM can be considered the lyte and this means that these methods are not primary methods. only truly primary method for DO determination. The WM method DO is an unstable analyte and preparation and storage of calibra- is based on the following. Two solutions are added to the oxygen- tion solutions is very difficult. Calibration is thus normally carried containing sample: one containing KI and KOH and the other out in water saturated with air. Luminescence method is also a containing MnSO4. Oxygen reacts under alkaline conditions with quick and simple method, very sensitive at low dissolved oxygen Mn2+ ions forming manganese(III) hydroxide [8,9]: concentrations, but it is also a relative measurement method.

2+ − 4Mn + O2 + 8OH + 2H2O → 4Mn(OH)3↓ (1)

∗ 3+ Corresponding author. Tel.: +372 7 375 259; fax: +372 7 375 264. The solution is then acidiﬁed. Under acidic conditions Mn ions − E-mail address: [email protected] (I. Leito). oxidize iodide to iodine, which eventually forms I3 ions with the

28 168 I. Helm et al. / Analytica Chimica Acta 648 (2009) 167–173 excess of KI [8,9]: 2. Experimental

+ → 3+ + 2− + 2Mn(OH)3(s) 3H2SO4 2Mn 3SO4 3H2O (2) In this section the developed gravimetric analysis method is described in detail, the calculation formulas are given, the sources of 2Mn3+ + 2I− → 2Mn2+ + I (3) 2 uncertainty and ways used for their estimation are listed. The proce- − − dure of analysis is described in Electronic Supplementary Material I2 + I → I3 (4) (ESM) with a series of photos. The volumetric method developed for − The concentration of the formed I3 ions is determined by comparison with the gravimetric method is described in the ESM. titration with sodium thiosulfate solution, which is standardized using potassium iodate. Winkler method is the primary method of 2.1. Determination of the concentration of the Na2S2O3 titrant DO concentration measurement: the obtained DO concentration is 3 traceable to the mass measurement of the standard substance KIO3. Iodine solution was prepared as follows. 2 cm of the standard −1 Thus using the Winkler method it is possible to calibrate and test KIO3 solution (0.0013 mol kg ) was transferred using a plastic amperometric sensors with DO concentrations below saturation. syringe through plastic septum into a dried and weighed sample This method also offers possibility of obtaining accurate DO concen- bottle. The bottle was weighed again. Using another syringe 0.1 cm3 tration values for carrying out in situ interlaboratory comparison of solution containing KI (2.1 mol dm−3) and KOH (8.7 mol dm−3) measurements [10]. (alkaline KI solution) was added. Using a third syringe ca 0.1 cm3 of −3 Although DO determination by the classical WM, if executed by H2SO4 solution (2.7 mol dm ) was added carefully, until the color a skilled operator and with care, offers lower uncertainty and is of the solution did not change anymore. Under acidic conditions less dependent on measurement conditions than the amperomet- iodine is formed according to the following reaction: ric measurement, it is a demanding task that requires skill and is + + → + + affected by numerous uncertainty sources. Several of these sources KIO3 5KI 3H2SO4 3I2 3K2SO4 3H2O (5) are specific to WM: contamination of the sample by atmospheric The care in adding H2SO4 solution is necessary in order to avoid oxygen, oxygen dissolved in the reagents used, iodine volatiliza- over-acidification of the solution because under strongly acidic con- tion, etc. We recently carried out an analysis of literature data and ditions additional iodine may form via oxidation of iodide by air obtained the precision/accuracy of the classical WM performed by oxygen: highly skilled operator as “standard deviation 0.1 mg dm−3” [11]. − + This standard deviation combines both random and systematic 4I + 4H + O2 → 2I2 + 2H2O (6) effects and can be regarded as an estimate of the combined standard The iodine formed from KIO was titrated immediately (to avoid uncertainty of the WM in skilled hands. Results of interlaboratory 3 loss of iodine by evaporation) with ca 0.0025 mol dm−3 Na S O comparisons as well as experience of practitioners suggest that the 2 2 3 solution: uncertainty under usual laboratory conditions is higher by a factor − 2− − 2− of 3–4 [12]. I3 + 2S2O3 → 3I + S4O6 (7) Different modifications of the original Winkler method have been proposed [8,13,14]. An important group of the modified meth- It has been stressed [19] that loss of iodine may be an important ods are micro-methods [15–17] where sample volume is in the source of uncertainty. This uncertainty has been estimated by us range of 1–10 cm3 (samples of 100–150 cm3 are used with the by additional experiments and has been taken into account as an classical Winkler method). Several uncertainty sources become sig- uncertainty source (see the ESM for details). nificantly more influential with micro-methods (sample volume Titration was carried out using a glass syringe filled with titrant around or below 10 cm3). It is thus reasonable to expect that uncer- and weighed. After titration the syringe was weighed again to deter- tainty of the micro-modifications of the WM tends to be higher mine the titrant mass. Six parallel measurements were carried out that that of the classical WM, unless features are introduced that according to the described procedure and the average result was enhance accuracy. In our recent literature survey [11] we attempted used as the titrant concentration. to convert the accuracy and precision data from the original papers on micro WM-s [15–17] into uncertainty estimates compliant with 2.2. Sample preparation the contemporary uncertainty paradigm [18]. It was not possible to do that entirely satisfactorily because of lack of information, but a Samples were prepared in 10 cm3 glass syringes with poly- k = 2 expanded uncertainty range of 0.2–0.3 mg dm−3 could reason- tetrafluoroethylene (PTFE) plungers (Hamilton 1010LT 10.0 cm3 ably describe these published procedures. The survey also indicated Syringe, Luer Tip) (see the ESM for details). Masses of all syringes that all of these modifications were volumetric. Mass measure- were determined beforehand. ment, especially with small solution amounts and if syringes are Six parallel samples were taken as follows: used, is more accurate than volume measurement. This led us to the idea to use mass measurement instead of volume measurement a) The syringe and the needle were rinsed with sample solution. for increasing the accuracy of the micro-Winkler method. b) Air bubbles were eliminated by gently tapping the syringe. DO In this report we present a gravimetric modification of the concentration decreases when doing this, therefore the syringe Winkler micro-titration method, which uses inexpensive commer- was emptied again so that only its dead volume was filled. cially available syringes and a conventional analytical balance. We c) The syringe was rinsed again avoiding air bubbles. The concen- demonstrate by validation the suitability of the method for deter- tration of oxygen in air per volume unit is more than 30 times mination of DO concentrations in the range of 2.9–12.4 mg dm−3 in higher than in water saturated with oxygen. Therefore avoiding water samples of 9–10 g. The expanded uncertainty of the method air bubbles is extremely important. is in the range of ±0.08–0.14 mg dm−3 (k = 2). Thus this is a highly d) 9.4 cm3 of the sample was aspirated into the syringe. accurate (in terms of correctly estimated measurement uncertainty e) The tip of the needle was poked into a rubber septum. [11]) primary method for determination of DO concentration in small samples. We demonstrate that the uncertainty of the devel- When six syringes were filled with samples and weighed the oped gravimetric method is more than two times lower than in the reagents were added. Ca 0.2 cm3 of the alkaline KI solution and ca 3 −3 case of a similar volumetric method. 0.2 cm of MnSO4 solution (2.1 mol dm ) was aspirated into each I. Helm et al. / Analytica Chimica Acta 648 (2009) 167–173 169

syringe. The needle tip was again sealed, the sample was intensely of KI. The titrant concentration was found according to Eq. (9).

mixed (turning the syringe about ten times upside down until all the m C = · C · KIO3 · Fm · Fm Na2S2O3 6 KIO3 m KIO Na S O KIO syringe was ﬁlled with the ﬂoating Mn(OH)3 precipitate) and the Na2S2O3 KIO3 3 2 2 3 3 Mn(OH)3 precipitate was let to form during 45 ± 10 min (accord- ·Fm · FI (9) ing to Eq. (1)). The syringe was weighed again to determine the KIO3 endp 2 net amount of the added reagents. This is necessary because the where C is the titrant concentration [mol kg−1], m [g] reagents also contain DO, which is taken into account. After 45 min Na2S2O3 KIO3 is the mass of the KIO solution taken for titration, m ca 0.2 cm3 of H SO solution was aspirated into the syringe. Iodine 3 Na2S2O3 KIO3 2 4 [g] is the mass of the Na S O titrant used for titrating the iodine is formed according to reactions (2), (3) and (4). At this stage the air 2 2 3 liberated from KIO3. Fm [–] and Fm [–] are factors bubbles do not interfere anymore. KIO3 Na2S2O3 KIO3 taking into account the uncertainties of these solutions weighing. Fm [–] is the factor taking into account the uncertainty of 2.3. Titration of the sample with the Na S O titrant KIO3 endp 2 2 3 F determining the titration end-point, I2 [–] is the factor taking into account evaporation of iodine from the solution. These factors have The formed iodine solution is transferred through a plastic sep- unity values and uncertainties corresponding to the relative uncer- tum to the sample bottle. Simultaneously titrant is added from a tainties of the effects they account for. Value of mX is calculated pre-weighed glass syringe (to avoid possible evaporation of iodine). mY here and below by the general Eq. (10) and it is the average (of six The sample syringe was rinsed twice with distilled water and the parallel determinations) ratio of the amounts of X and Y solutions, rinsing water was added to the sample bottle. The solution was used in the analysis. titrated with Na2S2O3 using a syringe until the solution was pale yellow. Then ca 0.2 cm3 of 1% starch solution was added and titra- mX i/mY i mX i tion was continued until the formed blue color disappeared. The m = (10) Y 6 titration syringe was weighed again. The amount of the consumed C titrant was determined from mass difference. Six parallel titrations The concentration of parasitic DO in the reagents O2 reag − were carried out. [mg kg 1] was found as follows:

1 m C = · M · C · Na S O reag · F · F 2.4. Determination of parasitic oxygen O reag O Na S O m 2 2 3 mreag m 2 4 2 2 2 3 reag Na2S2O3 reag O 2 syringe Due to the small sample volume the possible sources of parasitic ·Fm · F − (11) reag endp I2 m oxygen have to be considered. The two main sources of parasitic reag oxygen are the reagents and the PTFE plunger of the glass syringe. where M [mg mol−1] is the molar mass of oxygen, m The concentration of DO in the reagents is lower than in the O2 Na2S2O3 reag [g] is the amount of titrant consumed for titration, m [g] is the sample and the amount of the reagents is small. Nevertheless the reag overall mass of the solutions of the alkaline KI and MnSO and amount of oxygen introduced by the reagents can be around 1.5 ␮g 4 O [␮g] is the mass of oxygen introduced by the syringe and thus has to be taken into account. The overall amount of oxy- 2 syringe plunger. gen introduced by the MnSO4 and the alkaline KI solutions was F 3 Fmreag [–] and m [–] are factors taking into account the determined daily by aspirating into the glass syringe ca 2 cm of Na2S2O3 reag 3 uncertainties of these solutions weighing. Fmreag endp [–] is the fac- the solution of KI and KOH, ca 2 cm of MnSO4 and the titration was carried out as described above. tor taking into account the uncertainty of determining the titration All polymeric materials can dissolve oxygen. In this work the end-point. These factors have unity values and uncertainties cor- oxygen dissolved in the PTFE plunger is important. In order to responding to the relative uncertainties of the effects they account determine the amount of oxygen introduced from the plunger the for. DO concentration of different quantities of the same sample were The DO concentration in the sample was found according to Eq. (12): titrated. The mass of DO found in the sample was plotted against the sample mass. The mass of the parasitic oxygen introduced from 1 m the plunger was found as the intercept of the graph. The amount of C = · MO · CNa S O · m Na2S2O3 sample · Fm O2 sample 4 2 2 2 3 sample sample parasitic oxygen introduced from the plunger was found as 2.11 ␮g ␮ with standard uncertainty of 0.27 g. The Mn(OH)3 precipitate was ·Fm · Fm · F − C Na S O sample sample endp I2 O2 reag let to form during 45 ± 10 min in this experiment (see the ESM for 2 2 3 O details). m 2 syringe ·m reag sample − (12) sample m sample 2.5. Mathematical model of the gravimetric method where C [mg dm−3] is the DO concentration in the sam- O2 sample −3 Potassium iodate (KIO3) was used as standard titrimetric sub- ple, [kg dm ] is the density of water saturated with air (see the stance. The stock solution concentration was found according to ESM for details), m [g] is the mass of Na S O solu- Na2S2O3 sample 2 2 3 Eq. (8). tion consumed for sample titration, msample [g] is the sample mass, m · P mreag sample [g] is the overall mass of the added reagent solutions. KIO3 s KIO3 F CKIO = (8) Fmsample [–] and m [–] are factors taking into account 3 M · V · Na2S2O3 sample KIO3 flask KIO3 the uncertainties of these solutions weighing. Fmsample endp [–] is C −1 the factor taking into account the uncertainty of determining the where KIO3 [mol kg ] is the concentration of the KIO3 solution, m P titration end-point. These factors have unity values and uncertain- KIO3 s [g] is the mass of the KIO3, KIO3 [–] is the purity of KIO3, M −1 3 ties corresponding to the relative uncertainties of the effects they KIO3 [g mol ] is molar mass of KIO3, Vflask [dm ] is the volume of −3 account for. the flask, KIO3 [kg dm ] is the density of 0.02847% KIO3 solution (additional information is found in the ESM). Uncertainty estimation has been carried out according to the Concentration of the Na2S2O3 titrant was found by titrating ISO GUM modelling approach [20] using the Kragten spreadsheet iodine liberated from the KIO3 standard substance in acidic solution method [21]. 170 I. Helm et al. / Analytica Chimica Acta 648 (2009) 167–173

2.6. Quantifying the uncertainty components of the gravimetric same and are linearity and drift of the balance and rounding of method the digital reading (see Section 2.6.1). These components are taken Fm Fm into account by KIO3 and Na2S2O3 KIO3 , respectively (see Eq. (9)). The uncertainty estimation of MW gravimetric analysis was car- Repeatability is accounted for separately, by the uncertainty of the m ratio of the masses m KIO3 (see below). ried out on the basis of ISO GUM [20]. Measurements have been Na S O KIO ◦ 2 2 3 3 carried out in saturation conditions at 20 C on the 22nd of February 2.6.2.2.3. Uncertainty of the titration end-point. Random effects 2008. The calculations of measurement uncertainty are available in on the titration end-point are taken into account by the mean ratio the ESM. m m KIO3 and Na2S2O3 KIO3 (according to Eq. (10)). Possible systematic effects are taken into account by the factor Fm (see Eq. (9)). KIO3 endp 2.6.1. Uncertainty of concentration of KIO3 solution The end-point was determined using a visual indicator. The uncer- 2.6.1.1. Specifying the measurand and defining the mathematical tainty of end-point determination was estimated as ±1 drop. Mass model. Potassium iodate (below KIO3) solution with concentra- of one drop with the used syringe was 0.017 g and thus the stan- tion of ca 0.0013 mol kg−1 was prepared in a 1000 cm3 volumetric dard uncertainty was u = 0.01 g. The average titrant consumption flask. 0.2847 g of KIO3 (purity 99.7%) was weighed on a Mettler per titration was 9.5 g giving the relative standard uncertainty as Toledo B204-S analytical balance (resolution 0.0001 g). The calibra- 0.001. ± 3 m m tion uncertainty of the volumetric flask was 0.4 cm (information 2.6.2.2.4. Repeatability of KIO3 and Na2S2O3 KIO3 . Repeatabili- −1 from producer). Concentration of the KIO3 solution CKIO [mol kg ] ties of masses are taken into account by the standard deviation of 3 m was found using Eq. (8). See the ESM for details. the mean ratio m KIO3 (according to Eq. (10)). Six repetitions Na2S2O3 KIO3 were made. The mean ratio is 0.3095 and its standard deviation 2.6.1.2. Identification and evaluation of the uncertainty sources. is 0.00028 giving the relative standard uncertainty of the ratio as m 0.0009. 2.6.1.2.1. Mass of KIO3, KIO3 s. Uncertainty of weighing F solid KIO3 has the following components: repeatabil- 2.6.2.2.5. Evaporation of iodine before and during titration I2 . ity, u(repeatability) = 0.00016 g; rounding of the digital Titration of iodine was carried out in closed bottles and was per- reading, u(rounding) = 0.000029 g; linearity of the bal- formed quickly to minimize loss of iodine by evaporation. Some ance, u(linearity) = 0.000115 g; and drift of the balance, loss of iodine nevertheless can take place and the uncertainty due F u(drift) = 0.00024 g. The uncertainty contributions of these to this is taken into account by the factor I2 in the model (see Eq. components have been found taking into account that KIO3 mass (9)). Dedicated experiments were carried out in order to evaluate was found as difference of masses of KIO3 with tare and the empty its uncertainty (see the ESM for details) giving the relative standard tare. See ESM for more details. uncertainty as 0.00020. P 2.6.1.2.2. Purity of KIO3 standard substance, KIO3 . The certificate of KIO has purity specified as min 99.7%. Assuming rectangular C 3 2.6.2.3. Finding combined uncertainty of Na2S2O3 concentration. distribution we get 99.85% as the average purity and ±0.15% as the C = Under our conditions the following was obtained: Na2S2O3 uncertainty, giving the relative standard uncertainty as 0.00087. 0.002471 ± 0.000010mol kg−1, k = 2. The largest uncertainty con- M 2.6.1.2.3. Molecular mass of KIO3, KIO3 . Molecular mass and tributors are the concentration of the KIO3 solution (48%) and M = its uncertainty were found from atomic masses [22]: KIO3 uncertainty due to the end-point determination (28%). . −1 u M = . −1 214 00097 g mol and ( KIO3 ) 0 00045 g mol . 2.6.1.2.4. Volume of the KIO3 solution, Vflask. Uncertainty com- 2.6.3. Uncertainty of DO concentration in the reagents ponents of the 1 dm3 volumetric flask volume are: uncertainty of (uncertainty of the blank) the nominal volume as specified by the manufacturer (no cali- 2.6.3.1. Defining the measurand and the model. The measurand is ± 3 3 C −1 bration was done at our laboratory): 0.4 cm (u(cal) = 0.23 cm ); the concentration of DO in the reagents O2 reag [mg kg ] and the uncertainty due to the imprecision of filling of the flask: ±10 drops model is Eq. (11). or ±0.3 cm3, u(filling) = 0.17 cm3; uncertainty due to the temperature effect on solution density: u(temperature) = 0.24 cm3. The 2.6.3.2. Identification and evaluation of the uncertainty sources. C standard uncertainty of the KIO3 solution volume was found as 2.6.3.2.1. Concentration of the Na2S2O3 titrant Na2S2O3 . This 3 u(Vflask) = 0.38 cm . concentration and its uncertainty have been evaluated in Section 2.6.2: 0.002471 ± 0.000010mol kg−1, k =2. 2.6.3.2.2. Molar mass of oxygen M . The molar mass and its 2.6.1.3. Combined uncertainty of the KIO3 solution concentration. O2 −1 M = C = . ± . uncertainty were found based on data from literature [22]: O2 KIO3 0 0013304 0 0000036 mol kg , k = 2. The largest uncer- . −1 u M = . tainty contributions are due to weighing (47%) and purity of KIO3 31 9988 g mol and ( O2 ) 0 0003. (42%). 2.6.3.2.3. Uncertainty of the net mass of reagent solutions mreag m and titrant mass Na2S2O3 reag. Uncertainty of these masses has the following components: Linearity and drift of the balance, rounding 2.6.2. Uncertainty of Na2S2O3 concentration 2.6.2.1. Defining the measurand and the model. Concentration of the of the digital reading (see Section 2.6.1). These uncertainty components are taken into account by the factors F (see Eq. (11)). Na2S2O3 solution was determined by titration of iodine formed mreag Repeatability of weighing is taken into account separately, by the from KIO3 by titration with Na2S2O3 solution. According to Eqs. (5) mreag and (7) six moles of Na S O is used for titration of iodine corre- standard deviation of the mean ratio of these masses m . 2 2 3 Na2S2O3 reag sponding to one mole of KIO3. Six repetitions were performed and 2.6.3.2.4. Uncertainty of the titration end-point. Possible sys- m m ratios KIO3 and Na2S2O3 KIO3 were found (see Eq. (9)). Concentra- tematic effect in finding titration end-point is taken into account C −1 tion of Na2S2O3 solution Na2S2O3 [mol kg ] is the measurand. by Fmreag end (see Eq. (11)). This uncertainty has been estimated as ±2 drops. Mass of one drop is 0.017 g leading to the standard uncer- 2.6.2.2. Identification and evaluation of the uncertainty sources. tainty of 0.02 g. Average titrant consumption for the blank titration 2.6.2.2.1. Concentration of the KIO3 solution CKIO . Uncertainty was 0.9 g, giving the relative standard uncertainty as 0.022. 3 m has been evaluated in Section 2.6.1. 2.6.3.2.5. Repeatability of Na2S2O3 reag and mreag. Repeatability 2.6.2.2.2. Mass of KIO3 solution mKIO and mass of Na2S2O3 titrant of the masses was taken into account by the standard deviation of 3 m m . Uncertainty components for these masses are the the mean ratio m reag (according to Eq. (10)). The mean ratio Na2S2O3 KIO3 Na2S2O3 reag I. Helm et al. / Analytica Chimica Acta 648 (2009) 167–173 171

mreag m is 0.1736 and its standard deviation is 0.0033 giving the plunger (O2 syringe) and end-point detection (Fmsample endp) con- Na2S2O3 reag the relative standard uncertainty of the ratio as 0.019. tributing 47% and 25%, respectively of the uncertainty, see Fig. 1. F Calculation of volumetric method is found in the ESM. 2.6.3.2.6. Evaporation of iodine before and during titration I2 . See Section 2.6.2. 2.6.3.2.7. Oxygen from the PTFE plunger, O2 syringe. Uncertainty due to oxygen diffusion into the solution from the PTFE plunger of 3. Results and discussion the syringe was taken into account by the parameter O2 syringe (see Eq. (11)). Dedicated experiments were carried out (see the ESM 3.1. Accuracy (measurement uncertainty) of the gravimetric for details) and it was found that the mean (six repetitions) oxy- method gen intake from the plunger is 2.11 ␮g and its standard deviation is 0.27 ␮g. The uncertainty budget of the developed gravimetric micro- Winkler method and of the volumetric method developed for reference are presented in Figs. 1 and 2, respectively. The 2.6.3.3. Combined uncertainty of DO concentration in the reagents. −1 uncertainty contributions differ slightly from measurement to CO reag = 3.03 ± 0.22 mol kg , k = 2. The largest uncertainty con- 2 measurement and the indicated contributions refer to one particu- tribution is by determination of titration end-point (45%), followed lar measurement. by the repeatability of the six parallel measurements (34%). The uncertainty of KIO3 standard solution concentration accounts for 8.5% and 1.6% of the uncertainty in the gravimetric 2.6.4. Uncertainty of DO concentration in the sample and volumetric method, respectively. In both methods the purity 2.6.4.1. Defining the measurand and the model. The measurand is − of KIO and weighing of KIO mass were the main contributors to the concentration of DO in the sample C [mg kg 1] found 3 3 O2 sample uncertainty. according to Eq. (12). C In contrast the largest uncertainty contributions to Na2S2O3 are distinctly different in the case of gravimetric and volumetric 2.6.4.2. Identification and evaluation of the uncertainty sources. methods. In the gravimetric method the main contributor is C C KIO3 2.6.4.2.1. Concentration of the Na2S2O3 titrant, Na2S2O3 . This C = (8.5% of the overall uncertainty). In the volumetric method the uncertainty has been evaluated in Section 2.6.2: Na2S2O3 − uncertainty of C is dominated by the volume-related uncer- 0.00247 ± 0.00001mol kg 1, k =2. Na2S2O3 FV tainties (accounted for by KIO3 ) and repeatability of titration 2.6.4.2.2. Mass of sample solution msample and mass of Na2S2O3 V KIO V 3 (23% and 11%, respectively). titrant m . Uncertainty of these masses has the follow- Na S O KIO Na2S2O3 sample 2 2 3 3 ing components: linearity and drift of the balance, rounding of the The contribution of the uncertainty due to the oxygen dissolved digital reading (see Section 2.6.1). These uncertainty components in the reagents is small: around 2% of the overall uncertainty in both are taken into account by the factors F and Fm methods. msample Na2S2O3 sample (see Eq. (12)). Repeatability of weighing is taken into account sep- The largest uncertainty contributions in the gravimetric method arately, by standard deviation of the mean ratio of these masses are uncertainty due to oxygen dissolved in the syringe plunger (47%) m m sample (see below). and uncertainty of end-point determination (25%). The main uncer- Na2S2O3 sample 2.6.4.2.3. Uncertainty of the titration end-point. Possible sys- tainty contributions of the volumetric method are due to taking the tematic effect in finding titration end-point is taken into account by reading (from syringe) during the two titrations involved, jointly F F F F ± contributing ( V KIO , V Na S O sample, V Na S O KIO , V sample) Fmsample end (see Eq. (12)). This uncertainty has been estimated as 1 3 2 2 3 2 2 3 3 drop. Mass of one drop is 0.017 g leading to the standard uncertainty more than 50% of the uncertainty. All other uncertainty contribu- of 0.01 g. Average titrant consumption for the sample titration was tions are masked by these contributions and are at few per cent 4.3 g, giving the relative standard uncertainty as 0.0023. level. The dominance of the uncertainty sources related to vol- 2.6.4.2.4. Repeatability of m and m . Repeata- ume measurement clearly indicates the superiority of gravimetric Na2S2O3 sample sample bility of the masses was taken into account by the standard titration. m 3 sample The uncertainty of the volumetric Winkler method with 9.4 cm uncertainty of the mean ratio m (according to Eq. (10)). − Na2S2O3 sample sample at saturation level is ±0.19 mg dm 3 (expanded uncertainty The mean ratio is 0.4648 and the standard deviation of the mean at k = 2 level). The uncertainty of the gravimetric micro-Winkler is 0.00056 giving the relative standard uncertainty of the ratio as method in water at saturation level is more than two times lower: 0.0012. ±0.08 mg dm−3. M 2.6.4.2.5. Molar mass of oxygen, O2 . See Section 2.6.3. C 2.6.4.2.6. Concentration of oxygen in the reagent solutions O2 reag. −1 This has been evaluated in Section 2.6.3 as 3.03 ± 0.22 mol kg , 3.2. Validation of the method k =2. 2.6.4.2.7. Repeatability uncertainty of mreag sample and msample. Both methods were validated by measuring DO concentration This uncertainty is taken into account as repeatability of the mean in water saturated with air. The concentrations of DO in water sat- m ratio of these masses m reag sample . The mean ratio of the masses of sample urated with air were taken from the standard ISO 5814 [23]. Water the reagents and the sample (according to Eq. (10)) is 0.0553 and was saturated with air at 5–25 ◦C using the procedure described the standard deviation of the mean is 0.0013 giving the relative earlier [7]. The results are given in Table 1. standard uncertainty of the ratio as 0.023. The uncertainty takes into account the uncertainty of the tab- F 2.6.4.2.8. Evaporation of iodine before and during titration I2 . ulated value as well as the additional uncertainty due to the See Section 2.6.2. imperfections of the saturation conditions. The agreement between 2.6.4.2.9. Oxygen from the PTFE plunger, O2 syringe. See Section the reference value and the obtained results is very good: the abso- 2.6.3. lute En values [24] are well below 1 in all cases. At the same time the results of the table indicate that the results of both methods are 2.6.4.3. Combined uncertainty of DO concentration in the sam- slightly (within uncertainty) biased. This bias may originate from ple. The gravimetric MW analysis gave the following results: the correction taking into account the oxygen diffusing into the 8.78 ± 0.08 mg dm−3, k = 2 (0.96%, relative). The largest uncertainty syringe from the plunger: the negative bias indicates that this effect contribution was due to the correction of oxygen introduced from may be slightly “overcorrected”.

29 172 I. Helm et al. / Analytica Chimica Acta 648 (2009) 167–173

Fig. 1. Uncertainty budget of the gravimetric micro-Winkler method.

Fig. 2. Uncertainty budget of the volumetric micro-Winkler method (see the ESM for the deﬁnitions of the symbols).

Table 1 Results of the gravimetric and volumetric micro-Winkler methods (in mg dm−3) under different experimental conditions.

Date 1.02.08 22.02.08 25.02.08 3.03.08 31.03.08 7.04.08 9.04.08 18.04.08

Saturation temperature 20 ◦C20◦C25◦C5◦C15◦C20◦C20◦C20◦C Reference value 9.20 ± 0.06 8.79 ± 0.06 8.10 ± 0.06 12.41 ± 0.08 10.17 ± 0.06 8.99 ± 0.06 8.92 ± 0.06 8.95 ± 0.06 C a O2 saturation Gravimetric 9.24 ± 0.09 8.78 ± 0.08 8.06 ± 0.10 12.31 ± 0.13 10.06 ± 0.13 8.97 ± 0.10 8.94 ± 0.14 8.96 ± 0.10 micro-Winkler C a O2 sample b 0.04 −0.01 −0.04 −0.10 −0.11 −0.02 0.02 0.01 c En 0.4 −0.1 −0.3 −0.7 −0.7 −0.2 0.1 0.1 Volumetric 8.72 ± 0.19 8.02 ± 0.18 12.30 ± 0.24 10.14 ± 0.26 micro-Winkler C a O2 sample b −0.07 −0.08 −0.11 −0.03 c En −0.4 −0.4 −0.4 −0.1

a All values are given with k = 2 uncertainties. b = C − C O2 sample O2 saturation. c The En values are calculated and interpreted as explained in ref [24]: |En|≤1 means agreement, |En| > 1 means disagreement. I. Helm et al. / Analytica Chimica Acta 648 (2009) 167–173 173

The gravimetric method was validated also by measuring DO [2] ISO 5813, Water quality - Determination of dissolved oxygen - Iodometric concentration in water saturated with mixture of air and nitro- method, 1983. [3] M.L. Hitchman, in: P.J. Elving, J.D. Winefordner, I.M. Kolthoff (Eds.), Measure- gen. The obtained concentrations with estimated uncertainty were ment of Dissolved Oxygen (Chemical Analysis, ch 5), Wiley, New York, 1978, pp. −3 −3 2.90 ± 0.10 mg dm (k = 2) and 5.10 ± 0.12 mg dm (k = 2). These 71–123. results were compared with amperometric method (WTW Oxi340i [4] I. Kilmant, O.S. Wolfbeis, Anal. Chem. 67 (1995) 3160. [5] A. Mills, M. Thomas, Analyst 122 (1997) 63. with CellOx 325 sensor). Uncertainties were calculated [6] and con- [6] L. Jalukse, I. Leito, Meas. Sci. Technol. 18 (2007) 1877. −3 centration of dissolved oxygen was found as 2.85 ± 0.12 mg dm [7] C.H. Mortimer, Mitt. Int. Ver. Limnol. 22 (1981) 1. (k = 2) and 5.07 ± 0.18 mg dm−3 (k = 2), respectively. The calculated [8] D.E. Carritt, J.H. Carpenter, J. Marine Res. 24 (1966) 286. E values [24] are 0.3 and 0.1, respectively, indicating good agree- [9] M.E. Johll, D. Poister, J. Ferguson, Chem. Educ. 7 (2002) 146. n [10] L. Jalukse, V. Vabson, I. Leito, Accredit. Qual. Assur. 10 (2006) 562. ment. [11] L. Jalukse, I. Helm, O. Saks, I. Leito, Accredit. Qual. Assur. 13 (2008) 575. [12] R.J. Wilcock, C.D. Stevenson, C.A. Roberts, Water Res. 15 (1981) 321. 4. Conclusions [13] T. Labasque, C. Chaumery, A. Aminot, G. Kergoat, Mar. Chem. 88 (2004) 53. [14] K.H. Mancy, T. Jaffe, Analysis of Dissolved Oxygen in Natural and Waste Waters, As a result of this work an accurate gravimetric micro-Winkler U.S. Department of Health, Education, and Welfare, Public Health Service, method for determination of DO concentration has been developed. Robert A. Taft Sanitary Engineering Center, Cincinnati, Ohio, 1966, p. 94. [15] A. Krogh, J. Ind. Eng. Chem. (Anal. Ed.) 7 (1935) 131. The method is highly accurate: its expanded uncertainty is in the [16] A. Krogh, J. Ind. Eng. Chem. (Anal. Ed.) 7 (1935) 130. − range of 0.08–0.14 mg dm 3. [17] R.J. Whitney, J. Exp. Biol. 15 (1938) 564. [18] Measurement uncertainty revisited: Alternative approaches to uncertainty evaluation (2007) EUROLAB Technical report No 1/2007, EUROLAB, Acknowledgment Paris, France (available from the Internet: http://www.eurolab.org/docs/ technical%20report/Technical Report Measurement Uncertainty 2007.pdf). This work was supported by the Estonian Science Foundation [19] J.H. Carpenter, Limnol. Oceanogr. 10 (1965) 135. [20] ISO Guide to the Expression of Uncertainty in Measurement (GUM). BIPM, IEC, grant 7449. IFCC, ISO, IUPAC, IUPAP, OIML, Geneva, 1993. [21] J. Kragten, Analyst 119 (1994) 2161. Appendix A. Supplementary material [22] T.B. Coplen, H.S. Peiser, Pure Appl. Chem. 70 (1998) 237. [23] ISO 5814, Water quality - Determination of dissolved oxygen - Electrochemical probe method, 1990. Supplementary material associated with this article can be [24] ISO Guide 43-1 Proﬁciency Testing by Interlaboratory Comparisons. Part found, in the online version, at doi:10.1016/j.aca.2009.06.067. 1: Development and Operation of Proﬁciency Testing Schemes. ISO/IEC 1997.

References

[1] L.W. Winkler, Berichte der Deutschen Chemischen Gesellschaft 21 (1888) 2843.

I. Helm, L. Jalukse, I. Leito, A new primary method for determination of dissolved oxygen: gravimetric Winkler method. Analytica Chimica Acta, 2012, 741, 21–31.

Reprinted from Analytica Chimica Acta, Vol. 741, I. Helm, L. Jalukse, I. Leito, A new primary method for determination of dissolved oxygen: gravimetric Winkler method. Pages 21–31. Copyright 2012 with permission from Elsevier.

Analytica Chimica Acta 741 (2012) 21–31

Contents lists available at SciVerse ScienceDirect

Analytica Chimica Acta

j ournal homepage: www.elsevier.com/locate/aca

A highly accurate method for determination of dissolved oxygen: Gravimetric

Winkler method

∗

Irja Helm, Lauri Jalukse, Ivo Leito

University of Tartu, Institute of Chemistry, 14a Ravila str., 50411 Tartu, Estonia

h i g h l i g h t s g r a p h i c a l a b s t r a c t

Probably the most accurate method

available for dissolved oxygen con-

centration measurement was developed.

Careful analysis of uncertainty

sources was carried out and the

method was optimized for minimiz-

ing all uncertainty sources as far as practical.

This development enables more

accurate calibration of dissolved

oxygen sensors for routine analysis

than has been possible before.

a r t i c l e i n f o a b s t r a c t

Article history: A high-accuracy Winkler titration method has been developed for determination of dissolved oxygen

Received 8 May 2012

concentration. Careful analysis of uncertainty sources relevant to the Winkler method was carried out

Received in revised form 25 June 2012

and the method was optimized for minimizing all uncertainty sources as far as practical. The most

Accepted 29 June 2012

important improvements were: gravimetric measurement of all solutions, pre-titration to minimize

Available online 6 July 2012

the effect of iodine volatilization, accurate amperometric end point detection and careful accounting

for dissolved oxygen in the reagents. As a result, the developed method is possibly the most accu-

Keywords:

rate method of determination of dissolved oxygen available. Depending on measurement conditions

Dissolved oxygen

and on the dissolved oxygen concentration the combined standard uncertainties of the method are

Winkler method

−3

Uncertainty in the range of 0.012–0.018 mg dm corresponding to the k = 2 expanded uncertainty in the range of

−3

Primary method 0.023–0.035 mg dm (0.27–0.38%, relative). This development enables more accurate calibration of elec-

trochemical and optical dissolved oxygen sensors for routine analysis than has been possible before.

1. Introduction environment in general. Besides dissolved CO2, DO concentration

is an important parameter shaping our climate. It is increasingly

Dissolved oxygen (DO) is one of the most important dissolved evident that the concentration of DO in oceans is decreasing [2–5].

gases in water. Sufﬁcient concentration of DO is critical for the Even small changes in DO content can have serious consequences

survival of most aquatic plants and animals [1] as well as in for many marine organisms, because DO concentration inﬂuences

wastewater treatment. DO concentration is a key parameter char- the cycling of nitrogen and other redox-sensitive elements [2].

acterizing natural and wastewaters and for assessing the state of Decrease of DO concentration leads to formation of hypoxic regions

in coastal seas, in sediments, or in the open ocean, which are inhab-

itable for most marine organisms [2]. DO concentration is related to

the changes in the ocean circulation and to the uptake of CO2 (incl

∗ anthropogenic) by the ocean [6]. All these changes in turn have

Corresponding author. Tel.: +372 5 184 176; fax: +372 7 375 261.

E-mail address: [email protected] (I. Leito). relation to the climate change.

22 I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31

Accurate measurements of DO concentration are very important factors that inﬂuence the results and it is difﬁcult to realize it in

for studying these processes, understanding their role and predict- a highly accurate way. An independent primary method, such as

ing climate changes. These processes are spread over the entire WM, would be free from these shortcomings.

vast area of the world’s oceans and at the same time are slow and Winkler method is known for a long time, it has been extensively

need to be monitored over long periods of time. This invokes seri- studied and numerous modiﬁcations have been proposed. The data

ous requirements for the measurement methods used to monitor on accuracy of the Winkler methods described in the literature have

DO. On one hand, the results obtained at different times need to be been summarized in Section 5.2. There have been very few stud-

comparable to each other. This means that the sensors used for such ies that report combined uncertainties taking into account both

measurements need to be highly stable and reproducible [7]. The random and systematic factors inﬂuencing the measurement. Usu-

performance of oxygen sensors – amperometric and (especially) ally repeatability and/or reproducibility data are presented that do

optical – has dramatically improved in recent years [8]. not enable complete characterization of the accuracy of the meth-

On the other hand, measurements made in different locations of ods and tend to leave too optimistic impression of the methods.

the oceans have to be comparable to each other. The latter require- Very illuminating in this respect are the results of an interlabora-

ment means that the sensors have to be rigorously calibrated so tory comparison study [17] where the between-lab reproducibility

−3

that the results produced with them are traceable to the SI (Inter- standard deviation is as large as 0.37 mg dm [17].

national System of Units). The sensors need to be calibrated with From these data we conclude that there is a lot of room

solutions of accurately known oxygen concentration in order to cor- for improvement of the Winkler method. Thus the aim of this

rect for sensor drift, temperature, salinity and pressure inﬂuences investigation was to contribute to signiﬁcant reduction of mea-

[9,10]. Oxygen is an unstable analyte thus signiﬁcantly complicat- surement uncertainty of measurement with sensors by proposing

ing sensor calibration. an improved calibration approach for sensors based on a high-

It has been established that if every care is taken to achieve as accuracy Winkler titration procedure.

accurate as possible results then the accuracy of DO measurements We present a realization of the Winkler method with the high-

by amperometric sensors is limited by calibration [9] and speciﬁ- est possible accuracy and present a careful analysis of the method

cally by the accuracy of the reference DO concentration(s) that can for its uncertainty sources. To the best of our knowledge this is the

be obtained. This is similar with optical sensors: their lower intrin- most comprehensive uncertainty analysis of the Winkler method

sic uncertainty may make the relative contribution of calibration that has been published to date. This work prepares the ground for

reference values even larger. putting the DO measurements as such onto a more reliable metro-

The issues with sensors, among them issues with calibration, logical basis enabling lower uncertainties and allowing detection

have caused a negative perception about the data using sensors of trends and relationships that may remain obscured with the

in the oceanography community and because of this the recent current level of accuracy achievable for DO determination.

issue of the World Ocean Atlas [11] was compiled with taking into

account only DO concentrations obtained with chemical titration

2. Experimental

methods (ﬁrst of all the Winkler method) and rejecting all sensor-

based data. Similar decision was taken in a recent study of DO

In this section the developed method is described in detail, the

decline rates in coastal ocean [5]. It is nevertheless clear that there

calculation formulas are given, the sources of uncertainty and ways

is need for large amounts of data, so that the slow and clumsy titra-

used for their estimation are listed. Additional details are found

tion method cannot satisfy this need. It is necessary to be able to

in the Electronic supplementary material (ESM) with a series of

collect data automatically and in large amounts. It is thus expected photos.

that eventually sensors will be “back in business”.

There are two ways to prepare DO calibration solutions with

2.1. Materials

known concentrations: (1) saturating water with air at ﬁxed

temperature and air pressure and using the known saturation con-

The water used for all operations was produced with a Millipore

centrations [12–14] and (2) preparing a DO solution and using some

Milli-Q Advantage A10 setup (resistivity 18.2 M cm). In present

primary measurement method for measuring DO concentration.

work the following reagents were used: potassium iodide (KI)

The premier method for this is the Winkler titration method (WM)

puriss. p.a., reag. ISO, reag. Ph. Eur., 99.5% (Sigma–Aldrich); sodium

[15]. WM was ﬁrst described by Winkler [16] more than hundred

thiosulfate solution, FIXANAL (Fluka); potassium iodate (declared

years ago. Also gasometry is an old method for DO determina-

purity: 99.997% on trace metals basis, Sigma–Aldrich); sulphuric

tions, but it is a partly physical method requiring quite speciﬁc and

acid, puriss. p.a., reag. ISO, reag. Ph. Eur., 95–97% (Sigma–Aldrich);

complex experimental setup and is therefore not routinely used

nowadays. manganese(II)sulfate monohydrate (MnSO4 H2O) puriss. p.a., ACS

reagent, reag. Ph. Eur., 99.0–101.0%; potassium hydroxide (KOH)

DO measurement practitioners currently almost exclusively

puriss. p.a., reag. Ph. Eur., 85% (Sigma–Aldrich).

use the saturation method for calibration of DO measurement

instruments. This method gives quite accurate results when all

assumptions made are correct. DO values obtained with the sat- 2.2. Instrumentation

uration method are also used in this work for comparison with the

WM values. Nevertheless, it uses ambient air – a highly changing Weighing was done on a Precisa XR205SM-DR balance. The

medium – as its reference, thereby relying on the assumption that balance was regularly adjusted using the internal adjustment (cali-

the oxygen content of the Earth’s atmosphere is constant, which bration) weight. This adjustment was additionally checked using 5

is not entirely true [3]. The oxygen content of air depends on air independent reference weights in 9 different combinations result-

humidity and CO2 content, which both can change over a wide ing in masses ranging from 0.01 g to 200 g (and traceable to the SI

range of values. Also, this method needs careful accounting for air via the Estonian national mass standard). The obtained differences

pressure, humidity and water temperature. It is customary to use of the readings from the masses of the weights were too small to

published values of DO concentrations in air-saturated water at dif- justify correction, however they were taken into account in eval-

ferent temperatures. At the same time, different published values uation of mass measurement uncertainty. Air buoyancy correction

−3 ◦

are in disagreement by up to 0.11 mg dm at 20 C at even up to was not taken into account because it essentially cancels out (for

−3 ◦

0.19 mg dm at 40 C [14]. Thus the saturation method has many reasons explained in the supplementary material of Ref. [18]).

I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31 23

Samples were taken and prepared in 10 cm glass ﬂasks with

ground joint stoppers (standard ground glass stoppers). Flasks

were calibrated before at different temperatures to account for the

expansion/contraction of the ﬂasks (see additional information in

ESM).

For adding reagent solutions into the sample solution previously

calibrated glass syringes with tight plungers (250 ␮L, Hamilton)

were used. In other cases plastic syringes were used. Titrations

were carried out amperometrically, using a 20 cm plastic syringe

(Brown, needle external diameter 0.63 mm).

For endpoint determination an amperometric setup described

in the ESM was used.

2.3. Procedures

All solutions where accurate concentration was important were

prepared by weighing. The amounts of the solutions were measured

by weighing.

All amounts of reagents, which directly inﬂuenced the result,

were measured by weighing.

2.3.1. Preparing of standard working solutions of KIO3

Standard solutions were prepared gravimetrically using the

highest purity standard substance KIO3 available (see Sections Graph 1. Iodine solution titration until the background current is reached.

2.1 and 3.3 for purity and its uncertainty). The working solu-

tion was made by consecutive dilutions. The ﬁrst solution (KIO I,

3 see the ESM for more information). Voltage of 100 mV was applied

−1

c = 36 g kg ) was made by weighing about 1.4 g of solid KIO and

3 between the platinum electrodes Titration was completed when

dissolving it in about 40 g of water. The second solution (KIO II,

3 the current became equal to the background current (see Graph 1

−1

c = 3 g kg ) was made by weighing about 3 g of solution KIO I

3 for illustration). The background current value corresponding to the

and adding water to bring the volume to approximately 40 mL. The

equivalence point was established every day before the titrations.

−1 −1

working solution (KIO III, c = 0.2 g kg or 1 mmol kg ) was made ␮

3 The background current ranged on different days from 0.012 A to

by weighing about 4–6 g of KIO II and adding water to bring the ␮

3 0.018 A, but was essentially constant within a given day.

volume up to approximately 100 mL. All these solutions were made

One drop of the titrant from the syringe needle weighs about

into tightly capped bottles to avoid change of concentration of the

0.0105 g. This is very little compared to the usual drop from a

solutions during and between the analyses.

burette. There was also a possibility of adding just a fraction of a

drop of the titrant. This way the method is more precise than usual

2.3.2. Determination of the concentration of the Na2S2O3 titrant volumetric methods.

Concentration of the titrant was determined by titrating an After titration the syringe was weighed again to determine the

iodine solution with known concentration. The iodine solution was consumed titrant mass. Seven parallel measurements were carried

prepared as follows. About 5 cm of the standard KIO3 III working out according to the described procedure and the average result

−1

solution (0.7 mmol kg , see the previous paragraph) was trans- was used as the titrant concentration.

ferred using a plastic syringe into a dried and weighed cylindrical

wide-mouth 40 mL titration vessel (see photo in the ESM). The ves-

2.3.3. Sampling and sample preparation

sel was weighed again. Using a 1 mL syringe approximately 0.2 cm

Seven parallel samples were taken as follows:

−3 −3

of solution containing KI (2.1 mol dm ) and KOH (8.7 mol dm )

(alkaline KI solution) was added. Using a third syringe approxi-

a) The ﬂask was ﬁlled by submerging it under the water to be mea-

3 −3

mately 0.2 cm of H2SO4 solution (5.3 mol dm ) was added. Under

sured. Every care was taken to avoid air bubbles in the ﬂask. The

acidic conditions iodine is formed quantitatively according to the

concentration of oxygen in air per volume unit is more than 30

following reaction:

times higher than in water saturated with air. Therefore avoiding

air bubbles is extremely important.

KIO + 5KI + 3H SO → 3I + 3K SO + 3H O (1)

3 2 4 2 2 4 2 3 −3 3

b) 0.2 cm MnSO4 solution (2.1 mol dm ) and 0.2 cm of the alka-

The iodine formed from KIO3 was titrated with ca line KI solution were added to the bottom of the glass ﬂask

−1

0.0015 mol kg Na2S2O3 titrant as soon as the iodine was simultaneously (an equal amount of water was forced out of

formed: the ﬂask). Care was taken in order not to introduce air bubbles

− 2− − 2− when adding those solutions.

I3 + 2S2O3 → 3I + S4O6 (2)

c) The ﬂask was stoppered with care to be sure no air was intro-

duced. The contents of the ﬂask were mixed by inverting several

It is not possible to use pre-titration (see Section 2.3.4) here in

times. The presence of possible air bubbles was monitored. The

order to minimize iodine evaporation, because of the Eq. (9): until

sample was discarded if any air bubble was seen. A brownish-

iodate (oxidizing agent) is in the solution we cannot add sodium

orange cloud of Mn(OH) precipitate appeared. The precipitate

thiosulphate (reducing agent) or else they react each other with 3

was let to form until it was settled down according to Eq. (3):

a different stoichiometry [19]. Titration was carried out gravimet-

rically to lessen the uncertainty caused by volumetric operations 2+ −

4Mn + O2 + 8OH + 2H2O → 4Mn(OH)3↓ (3)

[20]. It was done using a plastic syringe ﬁlled with titrant and

weighed. The titration end point was determined amperometri- d) The solution was then acidiﬁed by adding 0.2 cm of H2SO4

−3

cally using two platinum electrodes (Metrohm Pt–Pt 6.0341.100, solution (5.3 mol dm ) with another glass syringe below the

24 I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31

solution surface. It is very important that all the precipitate

formed stays in the ﬂask. Under acidic conditions Mn ions oxi-

−

dize iodide to iodine, which eventually forms I3 ions with the

excess of KI [21,22]:

3+ 2−

2Mn(OH)3(s) + 3H2SO4 → 2Mn + 3SO4 + 3H2O (4)

3+ − 2+

2Mn + 2I → 2Mn + I2 (5)

+ − −

I2 I → I3 (6)

The ﬂask was stoppered again and mixed until the precipitate

was dissolved. At this stage the air bubbles do not interfere any-

more.

Graph 2. Curves from the adding tests (20.02.12).

2.3.4. Titration of the sample with the Na2S2O3 titrant

Before the start of the actual titration about 80–90% of the sup-

−1

posed amount of the titrant (Na2S2O3, 0.0015 mol kg ) is added to From the same sample different subsamples were collected at

the titration vessel from a pre-weighed plastic syringe. The formed the same time and different amounts of the reagents were added

iodine solution is transferred quantitatively to the titration vessel to determine the amount of oxygen that is introduced with the

(to minimize evaporation of iodine) and titrated to the end-point reagents. Reagent solutions were added one to three times (dif-

amperometrically as it has been discussed in Section 2.3.2. This ferent amounts) to consider not only the oxygen that was in the

approach – so-called pre-titration (a kind of an initial titration) – reagent solutions but also from the procedure itself (sample con-

allows ca 80% of the iodine to react immediately and is a powerful tamination). The concentration of DO found in the sample was

tool in helping to minimize the volatilization of iodine during titra- plotted against times of added reagent solutions. The correction

tion. The remaining small extent of iodine volatilization is taken CF

( O2 ) was found from the slope of the resulting graph (Graph 2).

into account by a correction. Fourteen experiments were made for determination CFO2. Each

After reaching the end point the titration syringe was weighed determination was made with three points. The concentration of

again. The amount of the consumed titrant was determined from DO in reagents depends on atmospheric pressure. Therefore we

mass difference. Seven parallel titrations were carried out. converted all the obtained slope values to the normal (sea-level)

pressure. Two of the resulting graphs were strongly non-linear (rel-

ative standard deviation of linear regression slope was above 20%)

2.3.5. Determination of the correction for oxygen introduced from

and these were left out. The remaining 12 results (obtained on 7

the reagents

different days) were evaluated for agreement with the Grubbs test

Due to the small sample volume the possible sources of parasitic

[23] and no disagreeing results were found (see the ESM for full

oxygen have to be determined and their inﬂuence minimized. The

data). The results were averaged arriving at the averaged correction

two main sources of parasitic oxygen are the reagents and (with

−1

value of 0.0940 mg kg (corresponding to the normal pressure)

possible additional effect from the adding procedure) and invasion

−1

with standard deviation 0.0068 mg kg . This standard deviation

of oxygen through the junction between the stopper and the ﬂask

neck. also accounts for the variability of the amount of added reagents.

Each time the correction was used it was recalculated to the actual

The concentration of DO in the reagents is low and the amount

atmospheric pressure at the location of the measurement.

of the reagents is small. Nevertheless the amount of oxygen intro-

duced by the reagents is on an average around 1 ␮g and thus has to

be taken into account. In order to estimate the possible amount of 2.3.6. Determination of parasitic oxygen (IntO2)

oxygen carried into the sample by the reagents the latter were satu- In order to determine the amount of oxygen introduced to the

rated with air for assuring their constant oxygen content. There are sample through the junction between the stopper and the ﬂask

several ways for accounting for the effect caused by the reagents. neck seven subsamples were collected at the same time and the

In this work we have used addition experiments. reagents (MnSO4 solution and alkaline KI solution) were added.

It is important to keep the oxygen content in the reagents under Three of them were titrated on the same day. The remaining four

control and take it into account in calculations as a correction term were titrated two days later. The mass of DO found in the sam-

in the model. There are two possible approaches for this: (1) use ple was plotted against the precipitation time. The mass of the

reagents where the oxygen content has been decreased to a min- introduced oxygen per minute was found as the slope of the graph

imum (deoxygenated reagents) or (2) use reagents saturated with (Graph 3). The amount of parasitic oxygen introduced was found as

−1 −1

air. In principle it would be desirable to use reagents with DO ca 0.00007 mg kg min . The precipitation time for the analysis

content as low as possible. Initially we took this approach. Dur- is different and ranges from few tens of minutes to slightly more

ing the experiments we discovered that the oxygen content in the than an hour, so the content of intruded O2 can be estimated to

−1

reagents was highly variable. This caused high uncertainty of the be in the range of 0.0015–0.0050 mg kg during the precipitation

correction term (even though its magnitude was small). One of the time. This effect is small compared to the overall repeatability of the

reasons might be contamination of the reagents by atmospheric measurement, our understanding of the actual mechanism of this

oxygen during transfer to the sample bottle. We then shifted to process is limited, the determination of this effect is very uncertain

reagents saturated with air (which in turn was saturated with water and the precipitation time also differs widely. Therefore we decided

vapor) and although the determined magnitude of the correction not to correct for this effect but take it entirely into account as an

−1

term was larger, its stability (spread of parallel measurements) and uncertainty, expressed as 0.005 mg kg .

uncertainty were signiﬁcantly better leading to ca two times lower

combined standard uncertainties of determined oxygen content in 2.3.7. Iodine volatilization

samples. Air-saturated reagents are immune to contamination by It has been stressed [21,24] that loss of iodine may be an impor-

air oxygen. tant source of uncertainty in Winkler titration, however, concrete

I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31 25

sample solutions is similar) in our usual sample bottle. This solution

was transferred into the titration vessel in a similar way as was used

for titration of the samples and was titrated (using pre-titration).

The difference of the amounts of initially added iodine and iodine

calculated from titration data gave the amount of volatilized iodine.

The average amount of volatilized iodine was found as 0.0116 ␮mol

with the standard deviation of 0.0014 ␮mol. This amount is taken

into account as nI2 vol s – iodine volatilization by titrating the sam-

ple.

Additional details are available in the ESM.

2.4. Measurement model of the gravimetric method

Potassium iodate (KIO3) was used as the standard substance. The

working solution concentration was found according to Eq. (8):

Int Graph 3. Determination of O2 . C =

KIO3III

experimental data on the extent of this effect are rare. In the litera-

m × × × m

× m × P

1000 1000

ture more sources of iodine-related errors have been described [25], KIO s KIO I transf KIO II transf KIO

3 3 3 3 (8)

such as hydrolysis of iodine by formation of oxyacid anions, which M × m × m × m

KIO3 KIO3 I KIO3 II KIO3 III

are not capable of oxidizing thiosulphate at the pH of the titration

−1

and iodine adsorption on glass surfaces. All these effectively lead where KIO3 III [mol kg ] is the concentration of the KIO3 working

to the loss of the iodine. At the same time under strongly acidic solution, KIO3 s [g] is the mass of the solid KIO3, KIO3 [–] is the

−1

conditions additional iodine may form via light-induced oxidation purity (mass fraction) of KIO3, KIO3 [mg mol ] is molar mass of

m m

of iodide by air oxygen [21,26]: KIO3, KIO3 I [g], KIO3 II [g] and KIO3 III [g] are the masses of the

prepared solutions, respectively, m [g] and m

− + KIO3 I transf KIO3 II transf

4I + 4H + O2 → 2I2 + 2H2O (7)

[g] are the masses of the transferred solutions for diluting the pre-

vious solution.

This process leads to the increase of iodine concentration. All

Concentration of the Na2S2O3 titrant was found by titrating

these factors can have inﬂuence both during titration of the sample

iodine liberated from the KIO3 standard substance in acidic solution

and during titrant standardization. There are also other inﬂuencing

of KI. The titrant concentration was found according to Eq. (9).

factors: pH, temperature and intensity of light in the laboratory.

In our experiments these factors were found to have negligible KIO

C = × C × 3 × Fm Na2S2O3 6 KIO3 m KIO

inﬂuence. Na2S2O3 KIO3 3

× n

In our procedure in the case of titration of the sample it is pos- 2

× F I2 vol t

m × Fm − (9)

sible to minimize the volatilization by adding about 80–90% of Na2S2O3 KIO3 KIO3 endp m

Na2S2O3 KIO3

the expected titrant consumption into the titration vessel before

−1

transferring the iodine-containing sample solution to the titration C m

where Na2S2O3 is the titrant concentration [mol kg ], KIO3 [g]

vessel (so-called “pre-titration”). This way the main part of the m

is the mass of the KIO3 solution taken for titration, Na2S2O3 KIO3

iodine reacts immediately, signiﬁcantly minimizing volatilization. [g] is the mass of the Na2S2O3 titrant used for titrating the iodine

At the same time, evaporation of iodine occurs during transfer of the liberated from KIO3, nI2 vol t [mmol] evaporated iodine from the

iodine solution formed from the sample into the titration vessel and solution during the titration for determination of titrant concen- m

KIO

this has to be taken into account also. The pre-titration approach tration. Value of m 3 is calculated by Eq. (10) and it is the

Na2S2O3 KIO3

is not possible in the case of determination of the titrant concen-

average (from seven parallel determinations) ratio of the masses of

tration because there it is necessary to stir the solution containing

KIO3 and Na2S2O3 solutions, used in the analysis.

iodate, iodide and sulphuric acid properly before starting the titra-

m /m

tion. If this is not done then thiosulphate can react directly with m i KIO3 Na2S2O3 KIO3 m KIO3 = (10)

Na S O KIO

iodate, not with iodine and the reaction loses its stoichiometry. For 2 2 3 3 7

both titrations the volatilization has been taken into account by

Such approach is needed (differently from volumetry), because

introducing two corrections, nI2 vol s and nI2 vol t, for titration of

it is impossible to take exactly the same mass of KIO3 for titration

the sample and standardizing of the titrant, respectively. KIO

in all parallel titrations. The uncertainty of m 3 takes into

Na2S2O3 KIO3

For evaluating the effect of iodine volatilization on titrant stan-

account only the repeatability of titration. In order to account for

dardization four parallel measurements of a solution of 5 mL with

−1 the remaining uncertainty sources three factors F are introduced.

iodine concentration of 1.9 ␮mol g were made by keeping them

Fm Fm

KIO [–] and Na S O KIO [–] are factors taking into account

for different times, 1, 5 an 10 min while stirring at 800 rpm (PTFE 3 2 2 3 3

the uncertainties of weighing of these solutions. m endp [–]

stirrer bar: length 21 mm, diameter 6 mm). The results were plot- KIO3

ted as iodine loss (in ␮mol) against time (see Graph 6 in ESM) and is the factor taking into account the uncertainty of determining

the estimates for the loss of iodine in 1 min were found as the the titration end-point. These factors have unity values and their

−1

␮

slopes of the four graphs: 0.051, 0.040, 0.048, 0.035 mol min . uncertainties correspond to the respective relative uncertainty con- m

−1 KIO

␮ tributions to m 3 . The average iodine loss is thus 0.043 mol min with standard Na S O KIO

−1 2 2 3 3

␮

deviation of 0.007 mol min . The titration time during standard- The DO concentration in the sample was found according to Eq.

ization ranges from 30 s to 60 s. The average time of 45 s was used (11):

as the estimate of titration time.

For evaluating the effect of iodine volatilization on titration of 1 m

Na S O s

C = × M × × C × 2 2 3 × Fm

O2 s O2 Na2S2O3 ms s

the sample, we have done experiments on two different days, 7 4

replicates on both days. Every experiment consisted in titration of

× n

2 p

ca 10 mL of iodine solution (prepared from KIO3) with concentra- × F I2 vol s

m × Fm + + IntO − CFO × (11) −

␮ 1 Na2S2O3 s s end p m 2 2 p

tion of 0.5 mol g (the concentration of iodine is in processed s n

26 I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31

−3

C The drift of the balance was found to be proportional to the where O2 s [mg dm ] is the DO mass concentration in the sam-

−3

ple, [kg dm ] is the density of water saturated with air (see the mass and was quantiﬁed as u(drift) = 0.000064%; calibration of

Na S O s

2 2 3 the balance, u(calibration) = 0.000042%. The experimental details

ESM for details), ms is the average (from seven parallel

determinations) ratio of the masses of Na2S2O3 and sample solu- of estimating these uncertainty contributions are given in the ESM.

tions, used in the analysis and is deﬁned analogously to Eq. (10). Two additional uncertainty sources related to weighing were

As was explained in the beginning of this section, the uncertainty taken into account: possible partial evaporation of water from the

Na S O s

2 2 3 KIO solution (u = 0.002 g) and the “warm hand” effect when weigh-

of ms takes into account only the repeatability of titra- 3

tion, nI2 vol s [mmol] is the estimated amount evaporated iodine ing the titrant syringe after titration (u = 0.00046 g). The latter leads

from the solution during the solution transfer from sample bottle to lower mass of the syringe because it has been warmed by hand

to titration vessel and during the titration for determination of sam- during titration and this causes ascending air ﬂow in the balance

ple concentration, ms is the average mass of the sample. In order compartment.

to account for the remaining uncertainty sources three factors F The uncertainty of water density is sufﬁciently low to be negli-

are introduced. Fm [–] and Fm [–] are factors taking into gible for our purposes.

Na2S2O3 s

account the uncertainties of weighing of these solutions weigh-

3.3. Uncertainty of purity of standard titrimetric substance KIO

ing. Fm endp [–] is the factor taking into account the uncertainty of 3

determining the titration end-point. These factors have unity values

The highest purity KIO standard substance available was used.

and uncertainties corresponding to the relative uncertainties of the 3

−

1 We consider its declared purity as too optimistic and use the fol-

Int

effects they account for. O2 [mg kg ] is the correction taking into

lowing purity estimate: 100.0% ± 0.1%. The true content of KIO in

account the contamination of the sample by the parasitic oxygen 3

the substance was assumed to be rectangularly distributed in the

introduced through the junction between the stopper and the ﬂask

−

1 range of 99.9–100.1%, leading to the standard uncertainty of purity

neck. O2 [mg kg ] is the correction accounting for the parasitic

0.058%. KIO is known for its negligible hygroscopicity [26]. We

oxygen introduced with reagent solutions. Both these effects lead 3

◦

additionally tested this by drying the substance at 110 C for 4 h. It

to apparent increase of DO concentration in the sample (therefore

was not possible to detect a mass decrease.

the negative signs of the corrections). O2 is normalized to the sea-

level pressure by multiplying it with the ratio of pressures p [Pa]

3.4. Uncertainty of determination of the equivalence point

and pn [Pa], which are air pressures in the measurement location

at the time of the measuring and the normal sea-level pressure,

respectively. The random effects on the titration equivalence point are taken

into account by the uncertainties of the factors, as explained

in Sections 2.4 and 3.2. The uncertainty contribution of the possi-

3. Measurement uncertainty

ble systematic effects was estimated as ± half of the drop of titrant

(assuming rectangular distribution), whereby the drop mass is esti-

3.1. General notes

mated as 0.0105 g of titrant. This leads to standard uncertainty

estimate of 0.0029 g, which is a conservative estimate, because it is

Uncertainty estimation has been carried out according to the

possible (and was used in the experiments) to dispense the titrant in

ISO GUM modelling approach [27] using the Kragten spreadsheet

amounts approximately equal to a tenth of a drop. The magnitude of

method [28]. The measurand is concentration of DO in the water

this uncertainty estimate covers the human factor (deviation from

−3

sample (CO s) expressed in mg dm . The measurement model is

2 the point where the operator considers that the equivalence has

presented in Eqs. (8)–(11). All uncertainties of molar masses are

been reached), the possible uncertainty of the background current

estimated as it has been done in Ref. [32]. In all cases where uncer-

as well as the possible uncertainty of the reading of the amperomet-

tainty estimates are obtained as ±X without additional information

ric device used for equivalence point determination. In calculations

on the probability distribution we assume rectangular distribution

this uncertainty is divided by the respective titrant mass and is

(the safest assumption) and convert such uncertainty estimates to

assigned as standard uncertainty to the respective F factors corre-

the respective standard uncertainties by dividing with square root

sponding to the equivalence point uncertainty (see ESM for more

of three [27].

details).

3.2. Uncertainty of weighing 3.5. Uncertainty of the iodine volatilization

Weighing was done on a Precisa XR205SM-DR balance. The Determination of the effect of iodine volatilization has been

balance has two measurement ranges: low: 0–92 g and high: explained in Section 2.3.7. Based on the different ways of carrying

92–205 g with 4 and 5 decimal places, respectively. So, some out the experiments for determination of the titrant concentra-

of the components of weighing uncertainties have two differ- tion and titration of the sample two different approaches of taking

ent values – for higher and for lower range. Which one is used iodine volatilization into account were used.

depends on the mass of the object together with tare. The uncer- In the case of determination of titrant concentration where

tainty components of weighing are: repeatability, rounding of pre-titration is not possible the volatilized iodine is accounted

the digital reading, drift of the balance and calibration of the as nI2 vol t and it has two uncertainty components: repeatability

balance. The repeatability uncertainty components for the two (expressed as experimental standard deviation) of the iodine lost

ranges were determined as u(repeatability low) = 0.000043 g and from the solution determined from three parallel measurements

u(repeatability high) = 0.000057 g. These estimates are used for u(repI2 vol t) = 0.0000074 mmol and possible variability of the dura-

weighing of KIO3 and its solutions. The repeatability of weigh- tion of the ﬁrst part of titration, estimated as 15 s. The ﬁrst part of

ing during titration is accounted for by the factors based titration is the one where the iodine concentration in the solution

on the actual parallel titrations data as detailed in Section 2.4. is still high and according to our experience it lasts until the current

␮

Rounding of the digital reading is taken into account in the con- between the electrodes becomes around 3 A. nI2 vol t corresponds

ventional way, as half of the last digit of the reading assuming to the amount of escaped iodine in 1 min, so in ﬁfteen seconds this

rectangular distribution leading to standard uncertainty estimates amount is four times smaller. Assuming rectangular distribution

u(rounding low) = 0.0000029 g and u(rounding high) = 0.000029 g. u(time) = 0.0000047 mmol.

I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31 27

Fig. 1. Uncertainty budget of the gravimetric Winkler method on 30.01.12.

In the case of sample titration pre-titration is possible, which (Ser No. G37300007, manufactured by Vaisala Oyj, Finland, cal-

strongly reduces the extent of iodine volatilization. Nevertheless, ibrated by manufacturer 19.09.11) with standard uncertainty of

even under these conditions iodine evaporation is non-negligible calibration u(pcal) = 3.5 Pa. Including additionally the contributions

and in order to achieve the lowest possible uncertainty this iodine from reading instability (u = 1.5 Pa) and possible drift (u = 3.5 Pa)

volatilization has to be taken into account. The estimated loss leads to a combined standard uncertainty estimate of pressure

of iodine is taken into account by the correction nI2 vol s. This uc(pcal) = 5.2 Pa.

correction was estimated using iodine solutions prepared from

KIO3 and KI with accurately known iodine concentrations (resem-

3.8. Validation

bling that in routine samples). These solutions were handled and

titrated exactly the same way as routine samples. The value of

Validation of the method includes a number of tests: determina-

␮ ␮

nI2 vol s = 0.0116 mol (with standard uncertainty 0.0014 mol)

tion of parasitic oxygen from different sources, iodine volatilization

was found from the difference of the prepared and found amounts

in two different cases, weighing tests and in addition the test

of iodine. The experimental data are given in the ESM.

for trueness. For evaluation of trueness water saturated with air

(below termed as saturation conditions) under carefully controlled

3.6. Uncertainty of the correction for oxygen introduced from the

conditions (air source, temperature, air pressure, air humidity)

reagents

was created in a double-bath thermostat. Freshly dispensed MilliQ

◦

water was saturated with air at 5–30 C using the procedure

Determination of the correction CFO has been explained in Sec-

2 described in the ESM. Every trueness test consisted of taking seven

tion 2.3.5. Although the mean value of CFO is used as correction the

2 samples, measuring their DO concentration with our method and

standard deviation of the single results (not the mean) is used as its

comparing the obtained average DO concentration with the refer-

uncertainty estimate, because this uncertainty takes into account

ence DO values evaluated according to the standard ISO 5814 [12]

the variability of CFO and is not averaged during the measurements

2 by an empirical formula originally published by Benson and Krause

in any way.

[13]. The uncertainties of the reference values were calculated as

detailed in the ESM. The agreement was quantiﬁed using the En

3.7. Uncertainty of the pressure number approach [29].

The repeatability of the method obtained as the pooled stan-

The corrections O2 depend on atmospheric pressure. Atmo- dard deviation [30] from 15 sets of seven parallel measurement

spheric pressure was measured by digital barometer PTB330 results (made on 14 different days during six months) was found

28 I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31 (%) C ◦ 0.026 0.29% 0.063 0.013 0.2 14.10.11 20 9.180 9.167 transf

II 3

KIO

m 3 2 4 5 3 9 4 3 4 4 4 6 4 3

◦ 0.001 0.028 0.31% 0.063 0.0 9.189 9.190 (%) 28.10.11 20 − 3 transf

KIO

I C

KIO

C m 9 8 9 9 8 7 9 7 8 9 6 5 ◦ 0.034 0.27% 0.063 0.019 0.3 10 11

11.11.11 5 12.968 12.949 (%) 3

KIO

10 Components P 16 14 19 17 16 16 14 12 17 14 15 18 12

◦ effect.

0.031 0.28% 0.062 0.022 0.3 (%) 14.11.11 10 11.241 11.218 3 out

KIO 30 C 29 25 34 32 27 34 26 22 25 27 33 22 18

conditions.

salting

(%) C

◦ s the

3 0.026 0.29% 0.061 0.013 0.2 30.12.11 20 8.876 8.863 O 2 S 2 Na s

m m

account experimental

5 2 8 2 4 3 2 5 6 1 8 3 3

C 11 ◦

0.001 0.029 0.29% 0.061 0.0 9.941 9.942 into

2.01.12 15 − (%) 3 O different

2 endp

S taking

2 3

Na C KIO C

◦

under

m ) of F 1 1 2 2 1 1 1 2 1 1 2 2 2

0.025 0.31% 0.062 0.012 0.2 3.01.12 25 8.176 8.164 3 −

function

dm (%)

C vol

◦

I2 (in

0.024 0.34% 0.061 0.011 0.2 5.01.12 30 7.286 7.276 n Components 19 16 29 32 17 18 16 24 19 22 32 28 22 additional

an [12]

(%)

Ref. O

samples.

using

C 2 ◦

Na 0.028 0.28% 0.062 0.000 0.0 from

C 45 74 69 57 48 41 62 53 51 75 57 44 10.052 10.052 16.01.12 15 ESM.

due

different

the (%)

of s and

obtained

vol C

◦

I2 n 2 1 2 2 2 3 2 2 2 1 2 3 Ref) given 0.028 0.31% 0.062 0.000 0.0 23.01.12 20 8.999 8.999

titration O is

C ( conditions of

(%)

endp

case

C s values ◦

m 0.004 0.1 0.025 0.30% 0.065 8.538 8.542 the days.

5 3 4 6 7 7 5 5 6 3 5 8 F 30.01.12 25 − − in

contributions

uncertainty) experimental

(%)

s reference

different

method 1 1 1 1 1 1 1 1 1 1 1 1 F

the overall

13 C

◦ 0.017 0.2 0.035 0.28% 0.062 different

20.02.12 5 12.680 12.698 − − uncertainty on

(%)

the

to with

3 the Winkler

KIO

due C from of 3

◦ O 2 (% 3 S .

conditions KIO

b Na

larger m value.

M, m

[31]

comparison

2 3 9 3 5 2 8 5 1

21 12 gravimetric in

0.023 0.38% 0.100 0.025 0.2 6.172 6.197 Ref. to

Calculation

15.03.12 KCl

− − . (%) the

2 GW) saturation 2.4 O

of reference 2

contributions from

C C 3 3 4 4 3 3 4 2 3 5 Int ( ◦

the

estimated under 25

values Section (%)

sources . and

M, 2

out in

b c method

[29] 30 2723 16 419 26 22228 528 324 2 24 415 424 1 16 34 6 1 2 5 55 2 62 22 2 Uncertainty CF

using

value 0.01

level.

Ref. 0.012 0.1 0.028 0.100 8.298 8.310 2

carried 15.03.12

deﬁned − − = measured

k uncertainty 2 Winkler

]

3 are =

the − were

reference calculated

)

2 main is dm

O deﬁned

the C

( the as of

0.026 0.028 0.034 0.031 0.026 0.029 0.025 0.024 0.028 0.028 0.025 0.035 U [mg

between uncertainty value of

quantities gravimetric

) 0.34%

conditions KCl a b

a rel score the

KCl 0.028

input measurements E GW) GW Ref) of

2 2 2

1 2 KCl 0.023

C C C C C C C C C C O O O

GW Ref ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ e C C C C C 2 2 d The The Expanded Reference Uncertainty Difference The ( ( ( ◦ ◦ M

O O n c a a e 20 Date C Conditions 20 5 10 20 15 25 30 15 20 25 5 0.01 1 U C E Saturation U U b b d Table Table Results Contributions

I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31 29

−3

as 0.009 mg dm (0.105% relative). It is important to note that in The next most important contribution is the uncertainty due to

no case were any of the parallel measurement results rejected. the oxygen introduced with the solutions of the Winkler reagents

u CF

(MnSO4 solution and alkaline KI solution) ( O2 ) during titration

of the sample. Due to its large effect this uncertainty also has been

4. Results

u CF

reduced by the use of a correction, so that ( O2 ) in fact stands for

the uncertainty of the correction.

4.1. Validation of the method by comparison with independent

Iodine volatilization effect has been minimized in the case of

reference values

titration of the sample by the so-called “pre-titration” but it is

still corrected (uncertainty of this correction is u(nI2 vol s)). The

The method was validated by measuring DO concentration

resulting uncertainty contribution is similar to the one obtained

in water saturated with air. The average results of 7 parallel

for determination of Na2S2O3 with correction.

measurements (as detailed in Section 2) in comparison with the

The repeatability of titration of the sample solution expressed

reference values from Ref. [12] are presented in Table 1. Na S O s

2 2 3

by ms is also an important uncertainty source, but its con-

As it is seen from Table 1, the agreement between two meth-

tribution differs greatly between samples, being dependent on the

−3

ods in the concentration range from 7 to 13 mg dm (temperature

◦ repeatability of the results of a particular sample. This effect is

range 30–5 C) is very good: the absolute values of En numbers [29]

further strengthened by the non-rejection of any parallel titration

are below 1 in all cases. Because the uncertainties of the reference data.

values in this case are higher than the uncertainties estimated by

The remaining inﬂuential uncertainty sources are due to end-

us for our method, we cannot use comparison with the reference

point determination (Fm s endp) and oxygen diffusing into the

values for conﬁrming the uncertainties of our values. However, this

sample solution where oxygen has been converted to Mn(OH)3

comparison is usable for ﬁnding problems with our results: if the En

through the junction between the ﬂask neck and the stopper. The

values were larger than 1 then this would indicate underestimated

overall contribution of uncertainty sources related to mass mea-

uncertainty of our values.

surement is between 8% and 15% as opposed to the more than 50%

found in the case of our earlier syringe-based volumetric method

[32].

4.2. Measurement uncertainty

In order to reduce the uncertainty of the method the most

important uncertainty component that has to be reduced is the

Comprehensive uncertainty evaluation was made by taking into

uncertainty of the correction for DO content in the reagents (CF ).

account the contributions of 22 individual uncertainty components O2

However, its reduction is not easy. Our attempts to deoxygenize

having at least a measurable effect. Detailed uncertainty calcula-

the reagents did not lead to a robust method. In our opinion the

tions as well as the full uncertainty budget are available in the

only viable way to reduce this uncertainty (and also some others)

ESM. Depending on the exact measurement conditions the com-

is to transfer the method (either wholly or in part – adding the

bined standard uncertainty of the method (at saturation conditions)

−

3 reagents until the generation of iodine) into an inert-gas glovebox.

varies in the range of 0.012–0.018 mg dm corresponding to the

−

3 This, however, would make the method very much more complex

k = 2 expanded uncertainty in the range of 0.023–0.035 mg dm

and clumsy to operate and would make it unusable by many routine

(0.27–0.38%, relative), see Table 1.

analytical laboratories because of the lack of the equipment.

Fig. 1 shows a sample cause and effect diagram with contribu-

tions of the uncertainty sources. The number of effective degrees

5.2. Comparison with the uncertainties of other Winkler methods

of freedom as estimated using the Welch–Satterthwaite approach

published in the literature

[27] ranges from 50 to 75 depending on the measurement condi-

tions. The k = 2 coverage factor thus corresponds to roughly 95%

There are only few publications where the uncertainties of the

conﬁdence level.

Winkler method are presented and analyzed [32,33]. The relia-

This low uncertainty is achieved mostly by using weighing

bility of the results is mostly discussed in terms of repeatability

instead of volumetry, amperometric end-point determination and

and agreement with other methods’ data. Table 3 summarizes the

using the purest reagents available. In this work also iodine

available literature data.

volatilization and the effect of any kind of incoming oxygen is esti-

The last column of the table indicates the meaning of the accu-

mated and accounted for.

racy estimate. There is a large variety of the ways how accuracy

was estimated.

5. Discussion

From the point of view of practical usage of the methods the

most useful accuracy characteristic is the measurement uncer-

5.1. Main uncertainty sources

tainty taking into account all important effects – both random and

systematic – that inﬂuence the measurement results. A number

Table 2 reveals that 41–75% of uncertainty originates from the

of authors characterize their data by repeatability [27] estimates,

concentration determination of the Na S O solution.

2 2 3 which by deﬁnition do not take into account any systematic effects

This uncertainty in turn is mostly caused by the purity of KIO

3 and may give a false impression of high accuracy. Such estimates

(which is the biggest compound by the concentration of the stan-

(presented in italics in Table 3) cannot be compared with measure-

dard substance KIO solution), repeatability of titration of the

3 ment uncertainties and we leave them out of consideration.

standard iodine solutions prepared from KIO and uncertainty

3 As it is seen from Tables 1 and 3 the gravimetric Winkler method

due to partial volatilization of iodine from that solution. Iodine

described in the present work has the lowest uncertainty.

volatilization is under our conditions the most important effect

causing the uncertainty of the Na S O solution concentration. Fur-

2 2 3 5.3. Comparison of the gravimetric Winkler method with

thermore, iodine volatilization has most probably an effect on the

saturation method for calibration of DO sensors m

KIO

repeatability of titration (the m 3 value). Because of these

Na2S2O3 KIO3

effects a correction nI2 vol t has been introduced and the uncer- Today calibration of electrochemical and optical sensors is gen-

tainty contribution u(nI2 vol t) is in fact the standard uncertainty of erally done by using the saturation method. The reference values of

the correction. DO saturation concentrations are usually found using the equation

30 I. Helm et al. / Analytica Chimica Acta 741 (2012) 21–31

Table 3

Accuracy information of DO from different sources. Accuracies estimated as repeatabilities are given in italic.

Reference Accuracy estimate Remarks, the meaning of the accuracy estimate −3

(mg dm )

Carritt and 0.07 The precision or repeatability that can be achieved by a

Carpenter [21] good analyst during the replication of certain

standardization procedures

Standard ISO 5813 0.03–0.05 Repeatability, 4 separate laboratories, batch standard

[15] deviation

Standard methods 0.02 Repeatability in distilled water. In wastewater the

−3

for wastewater repeatability is around 0.06 mg dm

[34]

Labasque et al. [35] 0.068 Within-lab reproducibility over ten consecutive days

Krogh [36] 0.27 Uncertainty (k = 2), re-estimated by Jalukse et al. [33]

Fox and Wingﬁeld 0.03–0.23 Uncertainty (k = 2), re-estimated by Jalukse et al. [33]

[37]

Whitney [38] 0.22 Uncertainty (k = 2), re-estimated by Jalukse et al. [33]

Helm et al. [32] 0.08–0.14 Uncertainty (k = 2), well documented uncertainty

estimation information

−1

Langdon [6] 0.005 0.15 ␮mol kg , stated as precision. Calculations with data

presented in the article gave average relative repeatability

−3

0.35% that corresponds on DO concentration of 9 mg dm

−3

to 0.03 mg dm

−1

Horstkotte et al. 0.02–0.15 Repeatabilities at 1.3–7.0 mg L dissolved O2 levels,

[39] in-line monitoring

−1

Sahoo et al. [40] 0.00014–0.11 The repeatability in measurement at mg L levels is

−1 −1

0.11 mg L with RSD 1.9% and at 10 ␮g L level is

␮ −1

0.14 g L , RSD 1.4%

Carpenter [24] 0.004 Repeatability recalculated to the saturated DO

◦

concentration at 20 C

All repeatability and reproducibility estimates are given as the respective standard deviations.

by Benson and Krause [12–14], which takes into account water (4) amperometric determination of the titration equivalence point.

temperature, air pressure and air humidity. For obtaining accu- To the best of our knowledge the presented method is the most

rate results an accurate barometer, an accurate thermometer and accurate published Winkler method available.

a very stable thermostat are needed. Even with good equipment

the saturation method is tricky to use and prone to errors. One 7. Electronic supplementary material

of the main issues is the super- or under-saturation. The smaller

are the bubbles used for saturation the faster the saturation con- Additional details of experiments and uncertainty evaluation

ditions are achieved. At the same time small bubbles may lead to (ﬁle ESM GW.pdf), sample calculation worksheet of the result and

supersaturation [41]. Use of the larger bubbles avoids supersatura- measurement uncertainty of DO concentration determined with

tion, but makes the time necessary for saturation long. The result is the gravimetric Winkler procedure (ﬁle U GW 300112 25C.xls) and

that if the operator is not patient enough the solution is undersatu- sample calculation worksheet of the reference DO concentration

rated. Furthermore, it is not documented in refs [12–14] what was value and its uncertainty (ﬁle U ref 300112 25C.xls) are available

the geometry of the nozzle and the bubble size. If uncertainty due as Electronic supplementary material.

to the possible super- or under-saturation is carefully taken into

account then the resulting uncertainty is by 2–3 times higher than Acknowledgments

the uncertainty of our method.

When measuring DO concentration with optical or ampero- This work was supported by the ETF grant no. 7449 and by the

metric sensors in water with high salinity, e.g. seawater, then European Metrology Research Programme (EMRP), project ENV05

calibration should be carried out in water with similar salinity. This Metrology for ocean salinity and acidity. The EMRP is jointly funded

is very difﬁcult to do rigorously with the saturation method because by the EMRP participating countries within EURAMET and the Euro-

the available saturation values of DO concentration in seawater are pean Union. We thank Dr. Michal Máriássy from the Slovak Institute

signiﬁcantly less accurate than the respective values in pure water. of Metrology for helpful comments on the manuscript.

An alternative approach is to calibrate in water and apply a slainity

correction, but this again introduces a substantial uncertainty from

Appendix A. Supplementary data

the correction. At the same time, the dissolved salts do not hinder

usage of the Winkler method.

Supplementary data associated with this article can be found, in

the online version, at http://dx.doi.org/10.1016/j.aca.2012.06.049.

6. Conclusions

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CURRICULUM VITAE

Irja Helm

Born: 17th of August 1984., Võru county, Estonia Citizenship: Estonian Address: Institute of Chemistry University of Tartu Ravila 14A, Tartu 50411, Estonia Phone: +372 53476517 E-mail: [email protected]

Education 2008 – University of Tartu, PhD student, doctoral advisors Dr. Lauri Jalukse and Prof. Ivo Leito 2006–2008 University of Tartu, M. Sc. (Analytical and Physical Chemistry), 2008 2003–2006 University of Tartu, B. Sc. (Chemistry), 2006

Professional employement 2011– University of Tartu, Faculty of Science and Technology, Institute of Chemistry, Chair of Analytical Chemistry, chemist (0.5)

Main scientific publications 1. Jalukse, L.; Helm, I.; Saks, O.; Leito, I.. On the accuracy of micro Winkler titration procedures: a case study. Accreditation and Quality Assurance, 2008, 13 (10), 575–579. 2. Helm, I; Jalukse, L; Vilbaste, M.; Leito, I. Micro-Winkler titration method for dissolved oxygen concentration measurement. Analytica Chimica Acta. 2009, 648 (2), 167–173. 3. Helm I., Jalukse L., Leito I. Measurement Uncertainty Estimation in Amperometric Sensors: A Tutorial Review. Sensors. 2010, 10 (5), 4430– 4455. 4. I. Helm, L. Jalukse, I. Leito, A new primary method for determination of dissolved oxygen: gravimetric Winkler method. Analytica Chimica Acta, 2012, 741, 21–31.

131 CURRICULUM VITAE

Irja Helm Sünniaeg ja koht: 17. august 1984 a., Võrumaa, Eesti Kodakondsus: eesti Aadress: Keemia instituut Tartu Ülikool Ravila 14A, Tartu 50411, Eesti Telefon: +372 53476517 E-mail: [email protected]

Haridus 2008 – Tartu Ülikool, Keemia instituudi doktoriõppe üliõpilane, juhendajad Dr. Lauri Jalukse ja Prof. Ivo Leito 2006–2008 Tartu Ülikool, Keemia instituut, M. Sc. (analüütiline ja füüsikaline keemia) 2003–2006 Tartu Ülikool, Füüsika-Keemiateaduskond, B. Sc. (keemia)

Erialane töökogemus Tartu Ülikool, Keemia Instituut, analüütilise ja füüsikalise keemia doktorant, keemik (0,5)

Tähtsamad teaduspublikatsioonid 1. Jalukse, L.; Helm, I.; Saks, O.; Leito, I.. On the accuracy of micro Winkler titration procedures: a case study. Accreditation and Quality Assurance, 2008, 13 (10), 575–579. 2. Helm, I; Jalukse, L; Vilbaste, M.; Leito, I. Micro-Winkler titration method for dissolved oxygen concentration measurement. Analytica Chimica Acta. 2009, 648 (2), 167–173. 3. Helm I., Jalukse L., Leito I. Measurement Uncertainty Estimation in Amperometric Sensors: A Tutorial Review. Sensors. 2010, 10 (5), 4430– 4455. 4. I. Helm, L. Jalukse, I. Leito, A new primary method for determination of dissolved oxygen: gravimetric Winkler method. Analytica Chimica Acta, 2012, 741, 21–31.

132 DISSERTATIONES CHIMICAE UNIVERSITATIS TARTUENSIS

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138 117. Vladislav Ivaništšev. Double layer structure and adsorption kinetics of ions at metal electrodes in room temperature ionic liquids. Tartu, 2012, 128 p.