Titration Handbook THEORY and PRACTICE of TITRATION Dr

Home , Cerimetry, Thermometric Titration, Titration

Titration Handbook THEORY AND PRACTICE OF TITRATION Dr. Robert Reining Managing Director

Welcome to Xylem Analytics Germany!

Xylem Analytics Germany distributes a large number of high- quality analyzers and sensors through its numerous well-known brands. Our Mainz brand SI Analytics has emerged from the history of SCHOTT® AG and now has more than 80 years of experience in glass technology and the development of analyzers and sensors. Our products are manufactured with high standards of innovation and quality in Mainz, Germany. The electrodes, titrators and capillary viscometers will continue to be at home wherever precision and quality in analytical measurement technology is required.

Since 2011, SI Analytics has been part of the publicly traded company Xylem Inc., headquartered in Rye Brook, N.Y., USA. Xylem is a world leader in solving water related problems. In 2016, the German companies were finally merged to Xylem Analytics Germany and continue to represent the established brands at the known locations. We herewith present to you our Titration handbook.

The focus has been consciously put on linking application information with our lab findings and making this accessible to you in a practical format.

If you have any questions about the very large field of titration, we look forward to helping you with words and deeds.

We at Xylem Analytics Germany in Mainz would be happy to keep on working successfully together with you in the future.

Xylem Analytics Germany

Sincerely, Robert Reining CONTENTS

Introduction and definition

SECTION 1 Basics 1.1 Definitions and foundations ...... 13 1.2 Titration reactions...... 15 Acid-base titration...... 15 Precipitation titration, complexometric titration...... 16 Redox titration, charge transfer titration, chemical, visual...... 17 Potentiometric...... 18 Biamperometric...... 20 Photometric, conductometric, thermometric...... 22 1.3 Titration types...... 23 Direct titration, back titration...... 23 Indirect titration, substitution titration, phase transfer titration...... 24 1.4 Overview of the used methods...... 24

SECTION 2 Volume measurement devices, manual and automatic titration 2.1 Volume measurement devices and standards...... 28 2.2 Volume measurement devices in the laboratory...... 30 Pipettes and graduated pipettes...... 30 Piston-stroke pipettes...... 33 Volumetric flasks, measuring cylinders, burettes...... 34 Piston burettes...... 36 2.3 Verification of the correct volume...... 38 2.4 Cleaning and care...... 40 2.5 Manual titration...... 43 2.6 Comparison of manual and automatic titration...... 47 SECTION 3 Sample handling Basics...... 50 Direct volume...... 52 Direct weighed sample ...... 53 Aliquoting...... 53 Weigh out small solid quantities...... 54

SECTION 4 Sensors and reagents 4.1 Overview of the sensors...... 56 4.2 Electrolyte solutions...... 61 4.3 Calibration of electrodes...... 61 4.4 Reagents...... 64 Sodium hydroxide, hydrochloric acid...... 64

Na2EDTA , AgNO3, Na2S2O3,, Ce(SO4)2, (NH4)2Fe2(SO4)2,

KOH in ethanol or isopropyl, HClO4 in glacial acetic acid...... 65 4.5 Titer determination...... 66 Titer determination of bases...... 68 Titer determination of acids...... 70 Titer determination of silver nitrate...... 72 Titer determination of perchloric acid...... 74 Titer determination of thiosulphate...... 76 Titer determination of iodine...... 78 SECTION 5 Titration parameters and calculations 5.1 Overview...... 81 5.2 Control of the dosage...... 82 Linear titration...... 82 Dynamic titration...... 86 5.3 Response behavior of the electrode and speed...... 90 5.4 Definition of the titration end...... 94 Titration interruption at maximum volume...... 95 Titration interruption at a certain measured value...... 95 Titration interruption when recognizing an EQ...... 95 5.5 Evaluation of the titration...... 97

SECTION 6 Applications 6.1 Acid-base titrations...... 102 Titration of citric acid in drinks...... 102 Titration of a strong acid...... 104 Titration of phosphoric acid...... 106

Titration of Alk. 8.2 and Alk.4.3...... 108 Titration of sodium carbonate...... 110 Determination of pharmaceutical bases as hydrochlorides with NaOH...... 112 Determination of pharmaceutical bases with perchloric acid in glacial acetic acid...... 114 Determination of the free fatty acids in vegetable oils (FFA)...... 116 Determination of acids in oil (TAN, ASTM 664)...... 118 Determination of bases in oil (TBN, ISO 3771)...... 121 6.2 Argentometric titrations...... 123 Titration of salt in butter...... 124 Titration of chloride in drinking water...... 125 6.3 Potentiometric redox titrations...... 127 Iodine number for characterizing fats and oils...... 127 Determination of the vitamin C content with DCPIP...... 130 6.4 Dead Stop titrations...... 133 Direct iodometric determination of vitamin C...... 134

Determination of the SO2 content in wine...... 135 6.5 Complexometric titrations...... 137 Calcium and magnesium in drinking water...... 138 Total hardness in drinking water...... 140 6.6 Determination of molecular weights by titration...... 142

6.7 Determination of pKs values...... 143 6.8 pH-Stat titrations...... 146 6.9 Gran titrations...... 148

SECTION 7 Photometric titrations 7.1 The OptiLine 6...... 153 7.2 Measurement principle...... 154 7.3 Error sources...... 155 Air bubbles...... 155 Ambient light...... 155 7.4 Applicators...... 155

Determination of the alkalinity Alk. 4.3...... 155 Photometric determination of acids in oils (TAN)...... 158 Determination of carboxyl end groups in PET...... 162 SECTION 8 Karl Fischer titration 8.1 The Karl Fischer reaction and reagents...... 165 8.2 The detection of the KF titration and titration curves...... 169 8.3 Sample handling...... 170 8.4 Coulometry...... 172

SECTION 9 Verification of the titration 9.1 Overview...... 175 9.2 Qualifications...... 176 9.3 Validation...... 178 9.4 Verification and correctness of the titration...... 179 9.5. Measurement uncertainty...... 184

Bibliography

Authors

Dr.-Ing. Jens Hillerich

Dr. rer. nat. Jürgen Peters Titration guide

INTRODUCTION AND DEFINITION

Titration is one of the oldest Titration finds broad use in methods for content determina- chemical analysis. On the one tion in chemistry. hand, a titration can be performed very easily and quickly, In contrast to gravimetry, no on the other hand, the titration sparingly soluble compounds provides a very accurate mea- are dried and weighed, but a surement result after only a reagent of known concentration few minutes - under optimal is added to the dissolved sample conditions. A relative standard until the chemical conversion is deviation of below one percent complete. For the definition of is normal. It is not without reason titration, there are a number of that numerous standards require formulations that have changed titration as a method. over time. The IUPC (Compen- dium of chemical Technology) Even with a very common and defines titration as: proven method of analysis, there is a need for support. This guide Quantitative analysis method in builds on the basic principles which a sample of known com- of titration and addresses the position but unknown content user of potentiometric titration. is converted with a reagent of Therefore, the basics of poten- known concentration (also called tiometry is discussed with the standard solution) in a chemical Nernst equation. The "manual reaction of known stoichiometry. titration" is almost completely left out. A general overview of From the very precisely added titration can be found in the volume of the reagent, the classic standard work of titration, unknown content in the sample the Jander / Jahr [1]. can be calculated on the basis of the calculation factors.

11 Titration guide This guide requires chemical Furthermore, application areas knowledge, e.g. the reading of are mentioned and various titra- reaction equations, knowledge tion methods are presented. The of important technical terms, individual calculations always basic knowledge of working in give rise to questions and are the chemical laboratory, as well therefore explained and sum- as the handling of devices such marized with the most important as scales, burettes, pipettes, formulas. Typical titrations with electrodes and the safety regula- their titration curves and calculations in the laboratory. tions are presented by means of examples. Titration is also called volumetry. Even when working with a pH Evaluation and quality are more electrode, the measurement and more in the foreground. unit of the titration remains the Therefore, the final chapter is volume and not the pH value. devoted to the qualification of The correctness of the volume is the devices, verification and thus essential for every titration. validation of results, as well as Coulometry is an exception, measurement uncertainty. which is a titration method, but which is not performed volumetrically.

In the first step, this guide deals with the volume and its correctness. Thereafter, the focus is on the sample and its handling. Subsequently, the used reagents, electrodes and the titration parameters are dealt with in detail.

12 13 Titration guide SECTION 1 BASICS

1.1 Definitions and foundations The definition of titration is valid This definition has to be extend- unchanged in its core: We need ed or limited nowadays: there a stoichiometric reaction, a pre- are many reactions that do not cisely dosable, stable reagent take place stoichiometrically. In and a detection of the end of the the Karl Fischer reaction, this has reaction end or a curve showing been discussed controversially the course of the reaction. for decades (1: 1 or 2: 1). With some reactions it is completely The standard work for Volumetric unclear how they actually take Analysis [1] also falls back on place. It is only certain that they these characteristics and defines: run equally under the same conditions (e.g., the determi-  The chemical reaction on which nation of chondroitin sulphate). the titration is based must proceed Validations are then performed rapidly, quantitatively and unam- by means of linearity tests with biguously in the manner indicated standards, which enable a quan- by the reaction equation. tification of the sample. There  It must be possible to prepare are also numerous applications a reagent solution of defined con- that go beyond simple content centration or to determine the determination. These include concentration of the solution in a stability studies, long-term ex- suitable way. tractions and monitoring of crystallizations (sometimes over  The endpoint of the titration must months), determination of pK be clearly recognizable. It should s values, pKb values and still fur- coincide with the equivalence point ther methods with very specific at which the reagent amount equiv- statements. alent to the substance amount of the searched substance was added or at least come very close to it. 12 13 Titration guide When validating a titration meth- The detection can be carried out od, the following aspects must by colour indicators or by means be observed: of electrochemical methods, which are be dealt with here in  chemical reaction essence.  accurately adjusted reagent  the sensor for detection. The predominant method is The chemical reaction must be potentiometry using e.g. pH fast, clear and quantitative. An and redox sensors with indicator indication of whether a reaction and reference electrodes, which is suitable for the titration is can detect potentials according given by the law of mass action: to the electrochemical series.

aA +bB ↔ cC + dD The Nernst equation is the basis of potentiometry. It describes with the equilibrium constant K this electrochemical potential at

c d a b an electrode as a function of the K = [C] ∗[D] / [A] ∗[B] activity of the ions in the solution. For the titrations, the reaction RT a equilibrium should be on the Ε = Ε° + ln ox right side of the reaction equa- zeF aRed tion, thus K >> 1. E Electrode potential After the reaction has been E° Standard electrode potential determined, particular attention R Universal or molar gas constant, R = 8.31447 J mol−1 K−1 must be paid in the laboratory T absolute temperature in Kelvin to the exact dosage of the set ze Number of electrons transferred reagent and the selection of a (also equivalence number) suitable sensor. The core function F Faraday constant, −1 of a modern titrator is the exact F = 96485.34 C mol a Activity of the respective redox dosage of the titrant. The stan- partner dard ISO 8655 [2] describes the requirements and check of the exact dosing.

14 15 Titration guide A pH electrode is used in most 1.2 Titration reactions cases. In order to establish a comparability with previous Acid-base titration results obtained manually by In acid-base or neutralization colour indicators, it is possible titration, acids are titrated with a to titrate to a fixed pH value, base (or vice versa). The detec- which corresponds to a colour tion of the equivalence point can change. For such an endpoint take place by colour indicators titration (EP = endpoint) to a or potentiometrically with a glass fixed pH value, a calibration of electrode. The reaction is the the electrode is required. same for all acid/base titrations, water results from a proton and a Other titrations are carried out hydroxide ion + − to an equivalence point (EQ = H + OH ↔ H2O Equivalence Point). Here, it If several acids with different pK depends only on the change of s values are contained in a solution, the potential or the pH value. they show several equivalence The calibration of a pH electrode points in a potentiometric ti- serves only for quality monitor- tration and can be determined ing in this case. next to each other if the alkalinity values are distinguished by at The measured value of the least 2 - 3 powers of ten. titration is the volume. The correctness of the volume must be + ↔ + + − verifiable for each consumption. HX H2O H3O X Consumption at the EQ, EP or with colour change thus indicates the equivalence of sample sub- c(H O+)∗c(X−) K = 3 stance and added reagent. s c(HX)

14 15 Titration guide Precipitation titration Complexometric titration The precipitation titration is In the complexometric titration, based on the formation of hardly metal ions are titrated with a soluble salts of sample and re- strong complexing agent. The agent. The solubility of salts can equivalence point is detected by be described by the solubility a colour indicator (also a com- product K.L For the dissociation plexing agent) or by ion-sensitive of a salt MmXx in saturated solu- electrodes. For the formation tion, the following applies: of the complex from a divalent metal ion and probably the x+ m− most commonly used 6-tooth Mm Xx ↔ mM + xX complexing agent ethylene with diamine tetra acetic acid (EDTA)

m x the following applies: x+ m− K L = c(M ) ∗ c(x ) M2+ +EDTA4− ↔ [MEDTA]2− If several ions are contained in with a solution, which form products c([MEDTA)2−) = which are hardly soluble with dif- K 2+ 4− c(M ) + c(EDTA ) ferent solubility product with the reagent, they show several equivalence points in a potentiometric Divalent metal ions are deter- titration and can be determined mined often during complexometric titration. The stability of next to each other if the KL values differ by at least 2 - 3 powers of these complexes depends on the ten. pH value (a buffer must therefore be added to the sample if neces- A classic application of the pre- sary). An important application cipitation titration is the deter- for complexometric titration is mination of the halogenides e.g. the determination of water - - - hardness in drinking water. (Cl , Br und I ) by means of AgNO3 solution or the determination of the silver content with a NaCl solution.

16 17 Titration guide Redox titration Charge transfer titration In a redox titration, oxidizing In charge transfer titration, components are titrated with a negative charges are titrated reducing agent, or vice versa. with positive charges (or vice The oxidation states of the versa) to a charge transfer neutral reactants and thus the redox point. An important application potential of the sample change. for this is the characterization of The detection of the EQ can be pulp suspensions by polyelectro- carried out by colour change lyte titration in paper manufac- (of colour indicators or the sam- ture. ple solution), potentiometrically with a redox electrode (usually a Chemical / visual Pt electrode) or biamperomet- A classification of the titrations is rically with a double platinum also often carried out according electrode. to the type of detection of the titration end. The oldest type + − M+X ↔ M + X of equivalence point determi- An important application for nation is the chemical/ visual redox titration is e.g. the deter- type. Hereby, the detection of mination of vitamin C in fruit the end or equivalence point is juices or the Karl Fischer titra- takes place by a colour change tion. of the sample solution (or of the precipitate with precipitation titrations). This usually requires the addition of a colour indicator, but there are also reactions where the sample or titrant changes colour at the EQ. This type of EQ determination is mostly used in manual titrations.

16 17 Titration guide Potentiometric With the potentiometric titration, The dependence of this voltage the determination of the end or on the concentrations c1 and c2 equivalence point takes place by or the ion activities a1 and a2 in the chemical potential that is es- the individual half-cells can be tablished at a suitable electrode. formulated according to the Nernst equation: This potential depends on the concentration of ions to which a =fc ∗c the electrode responds. If the electrode is "inert", that is, not a = activity fc = activity coefficient sensitive to ions contained in the (dependent on concentration) solution, the redox potential of c = concentration the solution can be determined. The electrode potentials follow By measuring the electrode the Nernst eqution: potential, it is therefore not possible to determine a concen- U = UN∗lg a 1/ a2 tration directly with the Nernst equation, but only the ion activity. The potential which adjusts At very high dilution, the activity itself at an individual electrode coefficient is about 1 and there- cannot be measured directly. fore the activity is approximately All that can be measured is equal to the concentration. Fig. 2 a voltage U as the difference shows the course of a typical between two electrode poten- titration curve. tials in a closed circuit. In the example (Fig. 1), two electrodes made of the same metal are immersed in solutions of one of their salts.

18 19 Titration guide

Conductor 1st order U

a 1 < a 2

Conductor 2nd order

a 1 a 2

Diaphragm Fig. 1 Circuit in an electrochemical measurement cell [5]

200.0

14.34 ml 150.0 144.8 mV

100.0

50.0

0.0 ml

-50.0 0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 mV/ml dmV/dml y-axis measurement signal mV value

x-axis Titration volume in ml reagent addition

Fig. 2 mV titration curve of a chloride titration

18 19 Titration guide Biamperometric Biamperometric or Dead Stop Fig. 3 shows a typical titration titrations can be carried out if curve of an iodometric Dead reversible redox systems are Stop titrations: formed or consumed in the course of the reaction. In this As long as reducing agents are type of detection, a double plat- still present in the sample, added inum electrode is used which is iodine is consumed immediately, polarized at a low voltage. If a in solution there is only iodide, reversible redox couple is pres- no current flows. When all the ent, a current flows between the reducing components have electrodes. As long as is no re- been consumed, iodine and versible redox couple is present, iodide are present next to each no current flows between the other as a reversible redox pair, two electrodes. a current flows between the electrodes. Important examples for this are the Karl Fischer titration and In contrast to iodometry, the iodometric titrations. The revers- current is not plotted versus ible redox system, which is used the titration volume with the to detect the endpoint, is hereby: Karl Fischer titration, but the titration volume versus time. − − l2 + 2e ↔ 2l More information about the course of the reaction, as e.g. Iodide is oxidized to iodine at the secondary reactions, can be anode, while iodine is simultane- obtained (see Fig. 4). ously reduced to iodide at the cathode.

20 21 Titration guide

µA

2.5

2.0 µA 1.449 ml 2.0

1.5

1.0

0.5

0.0 ml

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 µA/ml y-axis measurement signal μA value

x-axis titration volume in ml reagent addition

Fig. 3 Dead Stop titration curve

ml 3.375

3.0

2.625

2.25

1.875

1.5

1.125

0.75

0.375

y-axis with KF reagent addition 0.0 s 0 12.5 25.0 37.5 50.0 62.5 75.0 87.5 100.0 112.5 ml/s

x-axis titration duration

Fig. 4 Karl Fischer titration curve 20 21 Titration guide Photometric Conductometric In a photometric titration, the In the conductometric titration, colour change of an indicator is the determination of the EQ detected with an optical sensor takes place via changing the (e.g., OptiLine 6). The basis for conductivity of the sample this is Lambert Beer's law, which solution during the titration. describes the relationship The conductivity Κ of a sample between concentration, sample solution depends on the ion properties and absorption: mobility ui, the concentration ci

and the ion charge zi: l lg 0 = ε∗c ∗l l l κ = ∗ Const ∑ uiz ic i

I0: Intensity of the incident light beam

Il: Intensity of the transmitted light beam Thermometric ε: molar extinction coefficient All voluntarily running chemical (dependent on wavelength) c: Concentration reactions release energy that l: Path of the light beam through the leads to a temperature increase. sample This temperature of the reaction solution is exploited in At the EQ, the colour indicator the thermometric titration for reacts with the titrant; the colour the determination of the EQ. and thus also the extinction It is determined with a sensitive coefficient of the titrated solution temperature sensor. Typically, change. The intensity of the light the temperature increases up to arriving at the sensor changes. the EQ, in order to fall thereafter by addition of further (colder) titrant solution.

22 23 Titration guide 1.3 Titration types Titrations can be carried out in different manners [1].

Direct titration Back titration The best known is the direct In the back titration, the sample titration, in which the sample is is mixed with a defined amount titrated directly with a suitable of reagent A. Reagent A must be standard solution. The amount present in excess. After a reaction of reagent consumed to the time, the excess is titrated with equivalence point (or endpoint) another reagent solution B. The is the amount of substance to difference between the added be determined. reagent solution A and reagent A still present after the reaction Direct titrations also include the corresponds to the amount of inverse titration, in which the the substance to be determined. reagent solution is presented Both reagent A and reagent B and titrated with the sample. must be dosed exactly. Back Reasons for inverse titration may titrations are e.g. used when be e.g. a better recognizability the reaction speed between of the equivalence point, the sample and reagent A is low, no stability of the reactants, or a suitable sensor is available, or the greater reaction speed. equivalence point can only be determined with difficulty.

22 23 Titration guide Indirect titration 11.4 Overview of the In the indirect titration, the sub- used methods stance to be determined, which The past 200 years offered suffi- is contained in the sample in a cient time for the development non-titratable form, is converted of new titration methods. Several into a titratable compound by thousand methods or modifica- a chemical reaction. A known tions exist nowadays. Areas, in example of an indirect titration which titrations are carried out is the determination of nitrogen are: according to Kjeldahl; non- titratable nitrogen compounds  Water and environmental are converted to readily titratable analysis ammonium borate.  Food industry  Chemical industry Substitution titration  Pharmaceutical industry In a substitution titration, a good  Coating and metal processing, titratable component is released electroplating from the substance to be deter-  Oil industry mined by addition of suitable substances in excess, which can In food analytics, a number be titrated directly. of products or contents are quantified in these products by Phase transfer titration means of titration according to § 64 LFGB (food requirement In phase transfer titration, the de- objects and feed code). The tection of the EQ takes place in a methods include the determi- different phase than the reaction. nation of acids in drinks and An application for this is e.g. the other foods, the determination surfactant titration according to of the salt content, content of Epton. proteins and nitrogen functions, bases, oxidation components or oxidation protection and much more.

24 25 Titration guide An important area is the deter- Pharmacy uses strictly regulated, mination of humidity or water consistent methods that are de- content in food. The Karl Fischer fined in pharmacopoeias. These titration is the method of choice are often content determinations here, as it is also comparatively of the pharmaceutically active selective in addition to a high substances. The humidity content accuracy. The water content in- is also determined by Karl Fischer fluences numerous properties, titration. such as durability, processabili- ty, taste and much more. The samples in electroplating are very challenging. They often In the environmental field, water contain high concentrations of analysis is of particular impor- strong acids and various metals. tance. Titrations for waste water, Titration is the most important surface water and seawater method here and is often used are added to the methods of directly in the production area. drinking water analysis [1], [10]. Oil can also be titrated. This works In the chemical industry, various in suitable solvents. Often, acids methods are used, which mainly are determined in the oil to give serve to determine key Figures a measure of the aging of the oil for production raw materials or by oxidation and realization with finished products. Wastewater air. Base numbers and water con- must also be examined. Numer- tent are also typically titrated. ous methods are recorded in standards. The ISO standards Some of the most important and also the ASTM regulations methods are presented in the are used worldwide. following.

24 25 Titration guide

Acid-base titrations are used The accurate CO2 content is widely. These are endpoint determined by means of Gran titrations to a fixed pH value. The titration, a method that can be endpoints are therefore often easily automated with a sample pH 7.0, pH 8.1 or pH 8.2. This changer. depends on the type of acids and the comparative values de- With the frequent determination termined in the past with colour of chloride or "salt", a calibration indicators. A glass electrode is of the electrode is not necessary. used for the pH measurement, The titrant is silver nitrate and a which must be calibrated. For silver or silver chloride electrode this, the buffers 4.01 pH and 6.87 is used. However, the potentials pH are recommended. Due to may vary depending on the state possible problems with alkaline of the electrode, concentration buffers (CO2 absorption, low and sample matrix. This is why durability), a correct two-point titration is performed here until calibration without alkaline an EQ is detected. It does not buffers is often more accurate depend on the potential itself than the more elaborate three- then, but on the potentialchange. point calibration. Another common titration type Further information on calibrat- is iodometry. Here, a sample is ing the pH electrodes can be usually mixed with an excess of found in our pH guide. iodine. The iodine oxidizes a part of a sample. The iodine which A special method is the determi- is not converted is then titrated nation of alkalinity in seawater. with thiosulphate. This is a back

A multiple of the CO2 of the titration, as both the reagent atmosphere is dissolved in iodine (or a mixture of iodate seawater. The pH value of the sea with iodide) must be precisely drops, the temperature rises and dosed or weighed, as well as the thus less CO2 can be dissolved back titration must be done with in the seawater. a well-defined concentration.

26 27 Titration guide For drinking and mineral water, with perchloric acid in glacial water hardness is an important acetic acid, in which the nitrogen parameter. Calcium und magne- functions are determined. sium are relevant with respect to As many bases are present health and are titrated with EDTA as hydrochloride, an indirect (Ethylene-Diamine-Tetra-Acetic- determination is also possible. acid). For the detection, either a Free hydrochloric acid is added calcium ion-sensitive electrode and the free HCl is first titrated (ISE) is used for the determi- with sodium hydroxide solution, nation of both parameters or a then the HCl bound to the copper electrode for the deter- nitrogen. Two equivalence mination of the total hardness. points result whose difference Instead of the usual combination corresponds to the number of electrodes, separate measuring amine groups. chains (ISE indicator electrode with separate reference elec- With a glass electrode, acid-base trode) are often used, which are titration is possible even in black somewhat more robust. The oil. The most important titration calcium electrode can directly parameters in oils are, apart detect the signal of Ca and Mg, from the Karl Fischer titration for while the copper electrode is water determination, the TAN required for the indication of (Total Acid Number) and TBN copper EDTA to detect the total (Total Base Number) determi- hardness. nations. The TAN is titrated in toluene/isopropanol with KOH In electroplating, many metals in in isopropanol. A glass electrode the sample are also determined and a reference electrode with complexometrically. One often ground-joint diaphragm, often as titrates with EDTA as titrant and a combination electrode is used the Cu-ISE as electrode. The as the electrode. detection takes place as complex displacement reaction by the The examples should briefly show addition of Cu-EDTA. the range of the extent to which titration methods are used for In pharmacy, many complex quantification. A number of com- bases are titrated. The most pleted application specifications important method is the titration can be found on our website. 26 27 Titration guide SECTION 2 VOLUME MEASUREMENT DEVICES, MANUAL AND AUTOMATIC TITRATION 2.1 Volume measurement devices and standards The volume has a special As a rule, volume vessels are importance in titration. It is the checked with water. The water measured value of the titration amount corresponding to the and most samples are measured volume is weighed and divided volumetrically with pipettes. by the density. (Motor piston) burettes are tested according The analysis scale continues to ISO 8655 part 6 (Gravimetric to be the basic instrument. test with water) [2] . A factor Z is The volume is attributed to the used hereby, the reciprocal of weight. All volume measurement the density, corrected by the devices have their nominal following factors: volume at 20°C (attention: the electrochemistry relates to 25°C).  Temperature At other temperatures correc-  Buoyancy corrections (scales tions of the volume must be weights, weighed sample) applied. It should be noted,  Correction of the cubic expan- however, that the density for sion coefficient of the glass different solutions with different  Air humidity temperatures does not always behave identically. The correct volume is then the weight weight of the water multiplied by Volume = density the factor Z (Fig.5). [g] with the units [ml] = [g] [ml]

28 29 Titration guide

Air pressure in kPA (Z values in ml/g) Temperature in °C 80.0 85.3 90.7 96.0 101.3 106.7

15.0 1.0018 1.0018 1.0019 1.0019 1.0020 1.0020 15.5 1.0018 1.0018 1.0019 1.0020 1.0020 1.0021 16.0 1.0019 1.0020 1.0020 1.0021 1.0021 1.0022 16.5 1.0020 1.0020 1.0021 1.0022 1.0022 1.0023 17.0 1.0021 1.0021 1.0022 1.0022 1.0023 1.0023 17.5 1.0022 1.0022 1.0023 1.0023 1.0024 1.0024 18.0 1.0022 1.0023 1.0024 1.0024 1.0025 1.0025 18.5 1.0023 1.0024 1.0025 1.0025 1.0026 1.0026 19.0 1.0024 1.0025 1.0025 1.0026 1.0027 1.0027 19.5 1.0025 1.0026 1.0026 1.0027 1.0028 1.0028 20.0 1.0026 1.0027 1.0027 1.0028 1.0029 1.0029 20.5 1.0027 1.0028 1.0028 1.0029 1.0030 1.0030 21.0 1.0028 1.0029 1.0030 1.0030 1.0031 1.0031 21.5 1.0030 1.0030 1.0031 1.0031 1.0032 1.0032 22.0 1.0031 1.0031 1.0032 1.0032 1.0033 1.0033 22.5 1.0032 1.0032 1.0033 1.0033 1.0034 1.0035 23.0 1.0033 1.0033 1.0034 1.0035 1.0035 1.0036 23.5 1.0034 1.0035 1.0035 1.0036 1.0036 1.0037 24.0 1.0035 1.0036 1.0036 1.0037 1.0038 1.0038 24.5 1.0037 1.0037 1.0038 1.0038 1.0039 1.0039 25.0 1.0038 1.0038 1.0039 1.0039 1.0040 1.0041 25.5 1.0039 1.0040 1.0040 1.0041 1.0041 1.0042 26.0 1.0040 1.0041 1.0042 1.0042 1.0043 1.0043 26.5 1.0042 1.0042 1.0043 1.0043 1.0044 1.0045 27.0 1.0043 1.0044 1.0044 1.0045 1.0045 1.0046 27.5 1.0046 1.0046 1.0047 1.0048 1.0048 1.0049 28.0 1.0046 1.0046 1.0047 1.0048 1.0048 1.0049 28.5 1.0047 1.0048 1.0048 1.0049 1.0050 1.0050 29.0 1.0049 1.0049 1.0050 1.0050 1.0051 1.0052 29.5 1.0050 1.0051 1.0051 1.0052 1.0052 1.0053 30.0 1.0052 1.0052 1.0053 1.0053 1.0054 1.0055

Fig. 5 Factor Z in dependence on temperature and air pressure

28 29 Titration guide In the “Guideline for the volume 2.2 Volume measurement determination in reference devices in the laboratory measurement procedures in medical reference laboratories” Pipettes and graduated of the DAkkS (German accred- pipettes itation body), the standards of Pipettes serve for measuring the individual volume measure- samples. One distinguishes ment vessels are listed [3]: between graduated pipettes and volumetric pipettes (Fig. 6).  Volumetric flasks Preferably, volumetric pipettes (DIN EN ISO 1042, DIN 12664-1, with a volume greater than 5 ml DIN 12664-2) are used due to the higher  Volumetric pipettes accuracy and easier handling. (DIN 12687, DIN 12688, DIN 12691, For smaller volumes, piston- DIN 12690) stroke pipettes are preferably used. The size of the opening  Graduated pipettes and the discharge time are (DIN 12689, DIN 12695, DIN 12696, optimized on water with its DIN 12 697, DIN 12 699) surface tension. If an organic solvent is used, this usually  Piston-stroke pipettes has a lower surface tension. (DIN EN ISO 8655-2, DIN EN ISO However, this also effects a 8655-6) faster discharge in addition to smaller drops. If one drop is  Piston burettes smaller than the opening and (DIN EN ISO 8655-3, DIN EN ISO 8655-6) the surface tension is small, the solution will easily run out of  Diluters the pipette without opening the (DIN EN ISO 8655-4, DIN EN ISO Peleus ball. 8655-6) Pipettes are filled up to the mark  Dispensers (using a pipetting aid such as (DIN EN ISO 8655-5, DIN EN ISO the Peleus ball) and are read off 8655-6) at the lower meniscus (Fig. 7).

30 31 Titration guide

ISO 835 10 ml

DIN

2 10 ml

6 Partial line Meniscus 7

A B

Fig. 6 Volumetric (A) and graduated Fig. 7 Meniscus pipette (B) 30 31 Titration guide All pipettes must always be Accordingly, graduated pipettes held vertically. The liquid is are used to measure liquids discharged on an obliquely that are used as auxiliary held beaker on the side wall. reagents and that often require The follow-up time must be different volumes. For accurate observed. Fig. 8 gives an over- volumetric measurements, that view of the accuracy of the directly enter into a calculation, measurement and volumetric only volumetric pipettes are pipettes. suitable.

Graduated pipette Content Error limit Division Color coding Elapsed time ml ± ml ml DIN 12 621 s 1 0.006 0.01 yellow 2-8 2 0.01 0.02 black 2-8 5 0.03 0.05 red 5-11 10 0.05 0.1 orange 5-11 25 0.1 0.1 white 9-15

Content Error limit Color coding Elapsed time ml ± ml DIN 12 621 s 1 0.007 blue 7-11 2 0.01 orange 7-11 5 0.015 white 9-13 10 0.02 red 11-15 20 0.03 yellow 12-16 25 0.03 blue 15-20 50 0.05 red 20-25 100 0.08 yellow 25-30

Fig. 8 Accuracy of a volumetric and of a graduated pipette

32 33 Titration guide Piston-stroke pipettes Piston-stroke pipettes up to 10 ml sample volume, preferably from 1 to 5 ml, are particularly safe and easy in its handling.

Piston-stroke pipettes (Fig. 9) can be equipped with a fixed or variable volume. Handling is usually easier than with volumetric pipettes. The pipettes must be checked regularly according to ISO 8655 part 6 (such as also the motor piston burettes).

Fig. 9 Piston-stroke pipette

32 33 Titration guide Volumetric flasks Measurement cylinders Volumetric flasks are used to pre- Measuring cylinders are used pare solutions. A certain amount to be able to add a defined is weighed and transferred amount of reagent quickly and quantitatively into the volumetric accurately. They are not suitable flask. In the titration, the follow- for measuring a sample. In water ing work steps are often carried analysis, 100 ml sample volumes out with a volumetric flask: are often used. But also for this, the volumetric pipette and not  Preparation of comparison the measuring cylinder is recom- solutions and reagent addi- mended. As with the pipettes, tions. A defined amount of a the fill level is reached when the substance is weighed into a meniscus rests on the ring mark. weighing boat and transferred quantitatively (e.g. with distilled Burettes water) to the volumetric flask by Manual burettes (Fig.10) are means of a funnel or rinsed. still used for manual titration. In contrast to motor piston  Many solid samples are and bottle-top burettes, they dissolved and transferred into have no digitaldisplay. Read- the volumetric flask via a funnel. ing errors can easily lead The unit of such samples is then to false results (Fig.11). The weight/volume, e.g. mg/l or g/l. reagents must be protected more against disturbing influ- It is filled up to the ring mark. ences, as e.g. CO2, which can As with the pipettes, the fill level falsify the content of alkaline is reached when the meniscus titrants. Some titrations, such rests on the ring mark. as the Karl Fischer titration are virtually impossible with glass burettes.

34 35 Titration guide

1 0

2 2

3 3 4

5 4

5 7

6 9

Fig. 10 Glass burette and pellet burette

Glass burette AS Content Error limit Division Elapsed time ml ± ml ml s 10 0.02 0.02 35-45 25 0.03 0.05 35-45 50 0.05 0.1 35-45

Fig. 11 Accuracy of a glass burette AS 34 35 Titration guide Piston burettes Piston burettes offer the most Criteria for the selection of a accurate way to dose volumes motor piston burette could be from 1 to 100 ml. This can be the following: done by means of a bottle-top burette (with or without motor)  Accuracy or as a motor piston burette. The  Automatic filling accuracy depends on the cylinder  Automation volume, the length to diameter  Interfaces ratio, the motor and the transmis-  Exchangeable units sion. Thus, accuracy specifica-  Handling tions going beyond the specifications of the ISO 8655 also exist (Fig. 12). The motor piston burette TITRONIC® 500 (Fig.13) exceeds for example the required standard values.

Table 1 - Maximum permissible errors for motor-driven piston burettes

Nominal volume Maximum permissible systematic error Maximum permissible random error

ml ± % ± μla ± %b μlc ≤ 1 0.6 6.0 0.1 1.0 2 0.5 10 0.1 2.0 5 0.3 15 0.1 5.0 10 0.2 20 0.07 7.0 20 0.2 40 0.07 14 25 0.2 50 0.07 17.5 50 0.2 100 0.05 25 100 0.2 200 0.03 30

a Expressed as the deviation of the mean of a tenfold measurement from the nominal volume or from the selected volume, (see ISO 8655-6:202, 8.4).

b Expressed as the coefficient of variation of a measurement (see ISO 8655-6:202, 8.5).

c Expressed as the repeatability standard deviation of a tenfold measurement (see ISO 8655-6:202, 8.5).

Fig. 12 Accuracy of motor piston burettes ISO 8655 part 3 [2] 36 37 Titration guide

Fig. 13 Motor piston burette TITRONIC® 500 with exchangable unit 36 37 Titration guide 2.3 Verification of the correct volume The verification of the volume The calculation formulas are: correctness usually takes place according to ISO 8655 part 6 and V = m ⋅ Ζ is documented in a check table i i 1 n (Fig. 14). = V ∗∑Vi 10 i=1 10 doses each are carried out es = 100(V − Vs ) / V0 on an analytical balance at 10%, n 50% and 100% of the cylinder 2 V − V volume with water (with defined ∑( i ) s = i=1 purity). For these 30 dosages, r n −1 the weighing results are multi- s V cv = 1 0 0 r ∗ s plied by a numerical factor Z (see V V Fig. 5). 0

The difference of the average Vi Dosed individual volume value is compared to the mi Weight in [g] of this individual vol- displayed volume. The system- ume atic error is calculated from the V̅ Average value of the same 10 volumes difference. The "fluctuations" are es Relative systematic error of the calculated as the relative individual measurement standard deviation and represent sr Random error as the standard devi- the random error. ation cv Relative, random error

Vs Target volume

V0 Nominal volume cylinder

38 39 Titration guide

5 ] 0 % [ . 0 0 Variation coefficient

6 ] 3 % [ . 0 0 deviation Systematic measurement

1 0 1 1 1 1 1 0 0 0

1 6 8 1 4 8 5 3 2 1 ] l 1 0 0 1 1 0 1 0 0 0 m . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 [ 0 0 0 0 0 0 0 0 0 0

- -

Difference (target vol.- actual volume)

9 0 9 0 9 9 9 9 0 0

] 8 4 1 2 8 5 1 4 1 7 l 8 9 9 0 8 8 9 8 0 9 m [ . 9 . 9 . 9 . 0 . 9 . 9 . 9 . 9 . 0 . 9 1 1 1 2 1 1 1 1 2 1 volume Calculated

0 0 0 0 0 0 0 0 0 0

2 7 5 5 2 9 5 8 4 0 ] 8 8 8 9 8 7 8 7 9 9 g [ . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 Weight 1 1 1 1 1 1 1 1 1 1

] 0 l 0 m [ . 0 2 volume Displayed

)

x 0 % E 1 ( Cylinder

0 1 2 3 4 5 6 7 8 9

1 No.

Fig. 14 Test according to ISO 8655 Teil 6: here, the first 10 dosages of a 20 ml unit are given

38 39 Titration guide 2.4 Cleaning and care All piston burettes require a small but careful care effort. This shall be shown in detail using the example of motor piston burettes (Fig. 15). The care naturally also depends on the type and frequency of its use (Fig. 16).

An important element is the seal between the piston and the glass wall of the cylinder. If the sealing lips are leaking, the piston and/or the cylinder must be replaced.

At the latest when the space between the two lower sealing lips (Fig. 17) is filled with liquid, a replacement is absolutely necessary. If the dosing system is not used for more than two weeks, we recommend that the dosing attachment be emptied and cleaned. This applies in particular to the operating conditions cited under "High demand". Failure to do so may cause the piston or valve to leak and the titrator is damaged.

40 41 Titration guide

We recommend the following test and maintenance work High demand Normal demand

Simple cleaning: Always during use, Always during use, • External wiping of chemical splashes when necessary when necessary Visual check: • Check for untightness in the area

of the dosing system? Monthly, and when Weekly, and when • Is the piston tight? restarting restarting • Is the valve tight? • Titrating tip free? Basic cleaning of the dosing system: • Clean all parts of the dosing system Every three months When necessary individually. Technical check:

• Check for air bubbles in the dosing system. Half-yearly, and when Half-yearly, and when

• Visual check restarting restarting

• Check electrical connections Check of the volume according to ISO 8655: • Carry out basic cleaning Half-yearly Yearly • Check according to ISO 8655 part 6 or part 7

Fig. 15 Maintenance and check plant at piston burettes

High demand: Use of concentrated dissolutions, reagents and chemicals (> 0.5 mol/l); chemicals which attack glass such as fluorides, phosphates, alkaline solutions, solutions which tend to crystallize; FE(III) chloride solutions; oxidizing and corroding solutions such as iodine, potassium permanganate; Cerium(IV), Karl Fischer titrants, HCl; solutions with a viscosity > 5 mm2/s; use often, daily. Normal demand: Use of for example solutions which do not attack glass, do not crystallize or do not corrode, reagents and chemicals (< 0.5 mol/l).

Fig. 16 Usage of burettes

40 41 Titration guide

Sealing lips

Fig. 17 There may not be any liquid between the sealing lips

42 43 Titration guide 2.5 Manual titration 0 The manual titration can be

carried out with simple glass 1 burettes or with piston burettes.

It still has its legitimacy when it 2 comes to carrying out very few individual content determina- 3 tions with minimal effort. 4 Manual titration (Fig.18) is still in- 5 cluded in many older standards Standard solution

as prescribed methods. How- 6 ever, the automated methods

have prevailed today. They can 7 be implemented analogously to the "old" methods, optimize and 8 accelerate the processes. 9 In manual titration, an indicator is usually used that changes its colour at the EQ.

Sample solution

Fig. 18 Manual titration with the sample solution in an Erlenmeyer flask and the reagent in a glass burette 42 43 Titration guide Indicators exist for nearly all Colour indicators have some titrations. Acid-base, redox and considerable disadvantages: metal indicators are the most common (Fig. 19, general over-  They are not suitable for view in [16]). In the acid titration heavily coloured samples with sodium hydroxide, phenolphthalein is often used, which  The colour changes are turns from colourless to pink at perceived subjectively the endpoint (Fig. 20). In some titrations, the colour also chang-  The colour changes are often es by the titrant itself, so that no only temporary or sluggish indicator has to be added, e.g. with potassium permanganate.  The indicators change colour in a larger transition area and participate in the reaction.

Indicator Indicator range Colour changeover Manufacture Bromophenol blue 3.0 – 4.6 yellow-violet 0.1 g, ethanol (20%) Kongo red 3.0 – 5.2 blue-red 0.1 g, water Bromocresol green 3.1 – 4.4 red-yellow orange 0.04 g, water Bromocresol green 3.8 – 5.4 yellow-blue 0.1 g, ethanol (20%) 2.5 dinitrophenol 4.0 – 5.8 colorless yellow 0.05 – 1 g, ethanol (20%) Alizarin S 4.3 – 6.3 yellow-violet 0.1 g, water Methyl red 4.4 – 6.2 red-yellow 0.1 g, ethanol Litmus 5.0 – 8.0 red-blue 0.2 g, ethanol Bromocresol purple 5.2 – 6.8 yellow-purple 0.1 g, ethanol (20%) Bromophenol red 5.2 – 6.8 yellow-purple 0.1 g, ethanol (20%) Bromothymol blue 6.0 – 7.6 yellow-blue 0.1 g, ethanol (20%) Phenol red 6.4 – 8.2 yellow-red 0.1 g, ethanol (20%) Neutral red 6.8 – 8.0 red-yellow 0.1 g, ethanol (70%) Phenolphthalein 8.2 – 9.8 colorless-red 0.1 g, ethanol Thymolphthalein 9.3 – 10.5 colorless-blue 0.04 – 0.1 g, ethanol (50%)

Fig. 19 Some examples of acid base indicators with pH indicator ranges, colour changeover and manufacture [16] 44 45 Titration guide

A B Fig. 20 Acid titration with sodium hydroxide, with phenolphthalein as indicator; close before the EQ (A), at the EQ (B) 44 45 Titration guide

Fig 21 Modern titrator TitroLine® with sample changer in use

46 47 Titration guide 2.6 Comparison of manual and automatic titration Even if manual titrations are With manual titration, the sensor still carried out today, the many and thus its influence on the advantages speak in favor of total titration time are elimi- using an automatic titrator nated. In slow reactions, too (Fig. 21). fast manual titration can lead to over- or under- findings. Thus, In Fig. 22, the two application some redox reactions are so forms are compared. Manual slow that they run at higher titration is often faster. The dura- temperatures or that catalysts tion of the titration consists of the must be added. There is a risk reaction duration and the setting here that the titration in manual of the sensor potential. determination is too fast and the chemical conversion cannot follow.

Manual titration Automatic titration

 very fast  fast  exact  very exact  simple  simple after implementation  versatile  versatile  very many standards and regulations  very many standards and regulations  reproducibility  reproducibility, documentation  comparability  correctness and comparability  automation capacity  automation capacity

Fig. 22 Comparison of manual and automatic titration

46 47 Titration guide The automatic potentiometric With the endpoint titration, one titration works in a drift-controlled also titrates to one point. The manner, that is, the progress of direct potentiometric implemen- the reaction can be monitored tation of a manual titration is thus by means of a sensor. With an endpoint titration to the point manual titration with indicator, where the indicator changes one titrates until the colour colour. In contrast to manual titra- changes. With the content tion, a complete titration curve is calculation, exactly one point of also available here for evaluation. the entire titration is thus used for the evaluation. There thus does In Fig. 23, the equivalence point not exist any possibility to get is at pH 7.42. The colour change information about: starts at pH 6.80, an endpoint titration would be ended at pH  Reaction process 7.00. However, as the titration  Signal/noise ratio curve is very steep, differences  Behavior directly before and in consumption, which is in effect after the endpoint the measurement unit of the  Characteristics for an uncer- titration, are very low. For flat tainty consideration titration curves, in contrast,  Are there several endpoints? significant differences can occur. The three different detections With the potentiometric titration, (optical manual, EP titration and the entire titration curve is avail- EQ titration) must therefore be able and thus also evaluation regarded as (slightly) different criteria for the above points. In methods. addition, several measurement points in the region of the equivalence point are used for an equivalence point calculation.

48 49 Titration guide

pH 11.0

10.0

9.0 8.0 10.77 ml Changeover area neutral red 7.418 pH 7.0

6.0

5.0

4.0

3.0

2.0

1.0 ml 0 1.25 2.5 3.75 5.0 6.25 7.5 8.75 10.0 11.25 pH/ml dpH/dml

Fig. 23 Changeover area and equivalence point with a suitable indicator

48 49 Titration guide SECTION 3 SAMPLE HANDLING 3.1 Basics Sampling and homogenization In any case, a sample must first are important prerequisites for be brought into a homoge- achieving a "correct" result. neous, dissolved form in order to be titrated. This happens When transporting a sample, according to the scheme in it cannot always be ensured Fig. 24. For this, it is import- that it will remain unchanged ant to remove enough sample upon arrival. An example are from the material, as it is not samples that can absorb or always ensured that the content release humidity. There are of a sample is homogeneously only a few packagings that are distributed in a material. The really absolutely impermeable following points should be to water vapor. Many plastic observed: bottles are permeable to water vapor to a small extent.  Is there a sediment for liquid Temperature fluctuations and samples? other influences of the transport should also be considered. For  Is there a difference in concen- this reason, care must already tration due to a temperature be taken when sampling to difference in the vessel? see how it can be transported without changing.  Is it natural samples, which e.g. have a shell and an inner part?

 Do the samples have a coating?

 Does the surface absorb humidity?

50 51 Titration guide Another issue is the release of A homogenizer can be used the parameter to be determined. profitably in the sample prepa- For example, the chloride con- ration of many samples. It can tent in cheese is an important shred many food samples faster indicator of shelf life and taste. and ensure a fine distribution. If there is not enough chloride The analysis components to be in the cheese, it spoils. If there determined are released from is too much salt in the cheese, the samples of water or solvent it does not taste good. For the and are well distributed at the determination of the chloride same time. content, a piece of cheese (about 0.5 to 1 g) may well be placed in a beaker and filled with water. But almost nothing happens. The cheese floats in the water and the salt stays in the cheese. Only with increased temperature and a homogenizer, the largely complete release of the salt succeeds.

Solid sample • • •

Liquid sample • •

Gaseous sample •

Fig. 24 Processing of samples

50 51 Titration guide With special titrations, a strategy 3.2 Direct volume must be developed in advance In most cases of general titration, to ensure that the quantity to be a specific volume of the sample determined is also obtained in is pipetted directly into the titra- a quantitative manner. Fig. 25 tion vessel. For volumes up to illustrates the procedure. In the 5 ml, the piston-stroke pipette case of water determination, has proven itself. For volumes e.g. according to Karl Fischer, above 5 ml to 100 ml, the volu- an attempt is made to dissolve metric pipette is the instrument the sample completely. If this of choice. Usually, 50 to 150 ml is not possible, the water of the beakers are used as the titration sample must be evaporated in vessel. The samples are then an oven or only the adhering filled with solvent, usually water is determined. An attempt water, until the titration tip and is made to change the duration the electrode are immersed in of the dissolution process and the solution. At the electrode, the polarity of the solvent, or the diaphragm must be covered to increase the temperature. In with solvent. order to change the polarity, one works with different solvents or mixtures.

Polarity

Duration Methanol and formamide

Dissolving trials Polarity of the solvent Methanol

Temperature Methanol + chloroform

Fig. 25 Sample preparation for KF titration

52 53 Titration guide 3.3 Direct weighed sample Soluble samples are weighed in a volumetric flask to a certain directly into the titration vessel. volume in order to use a specific The direct weighed sample aliquot for the titration. should be over 100 mg. Other- wise, the method as described Example: in section 3.4 is recommended. 5 ml of a highly concentrated The solid samples are also filled sample are filled up to 100 ml in with solvent as described with a volumetric flask. Of these, 20 the solutions. ml are taken with a volumetric pipette for the determination. 3.4 Aliquoting The calculation formula for a It is not always possible to use result in [mol/l] without dilution a sample as a solid or liquid step is: sample directly for a titration. Thus, a high content in a sample Result [mol/l] = consumption may require titration with a high [ml] x concentration of the titrant concentration of titrant or [mol/l] / sample volume [ml] effect high consumption. This can lead to high costs (e.g. with As the 5 ml sample is diluted to silver nitrate), to long titration 100 ml, each ml of this dilution times or to unfavorable handling contains 0.05 ml of original sam- (e.g. due to large volumes). The ple, thus 1.00 ml original sample

size of the sample vessels are for 20 ml dilution: Polarity often predetermined by the degree of automation and thus also Duration Methanol and formamide Result [mol/l] = consumption the sample amounts are limited. [ml] x concentration of the titrant In addition, the high accuracy Dissolving trials Polarity of the solvent Methanol [mol/l] / (volume aliquot [ml] x of the motor piston burettes no 5/100) longer requires high consump- Temperature Methanol + chloroform tion in order to obtain a safe result. Samples with a high content are therefore often filled

52 53 Titration guide 3.5 Weigh out small solid amounts Solid samples are often weighed With many solid samples, the directly into a beaker, dissolved accuracy can be increased by or homogenized and titrated. one order of magnitude when The 4-digit analytical balance operating with the procedure is the right instrument for this. shown in (Fig. 26). Nevertheless, handling weighed samples less than 100 mg is dif- A larger amount of the sample ficult and often involves large er- (e.g., 5.8443 g NaCl) is weighed rors. This may be due to the scale in, plus water in a larger amount or the handling of the sample, (e.g. 95.000 g). A portion of this but also to the installation condi- solution is removed and weighed tions of the balance in its place. again (e.g. 1.0000 g). The NaCl part can be calculated according to the following formula:

Τ∗Ε sample part [ g] = Ε + W

Example sodium chloride (salt)

Symb. Description Example values Unit

sample part = 0.057953 Fig. 26 Calculation of a partial amount (PA) with gravimetric manufacture of the solution 54 55 Titration guide

In practice, the following procedure has been proven to be successful:

The solution is drawn into a syringe, placed on an analytical balance and is tared (Fig.27). An arbitrary partial amount is added to the titration vessel from the syringe and the syringe is weighed back.

The direct weighed sample of NaCl with 0.0580 g would already have an uncertainty of +/- 0.0002 g through the balance. Handling errors and other influences are not yet included.

Fig. 27 Syringe with sample on analytical balance 54 55 Titration guide SECTION 4 SENSORS AND REAGENTS 4.1 Overview of the sensors The following electrodes are part of the standard equipment of a titration laboratory:

 pH combination electrode with platinum diaphragm (for all aqueous acid-base titrations)

 Silver combination electrode (for the determination of e.g. chloride…)

 Platinum combination electrode (for all redox reactions)

56 57 Titration guide

 Platinum double electrode (for reversible redox reactions with dead stop detection)

 pH combination electrode with ground-joint diaphragm (with organic electrolyte solutions for titration in organic solutions)

 Ion-sensitive electrodes (ISE), such as Ca electrode, Cu electrode, fluoride electrode as combination electrode or with a separate reference electrode (depending on the task and type of the samples)

56 57 Titration guide Individual electrode potentials cannot be measured directly, but only the difference between two electrode potentials. Therefore, a combination of indicator and reference electrode must always be used. The potential of the reference electrode must not change during the titration. Either a combined measuring chain or separate indicator and reference electrodes can be used (see Fig. 28).

Details regarding the measuring chains are represented in detail in our pH guide [5].

Combination electrodes, i.e. combined electrodes containing the indicator and reference electrodes, are usually used nowadays. In special cases, an indicator electrode is used together with a separate reference electrode. Separate measuring chains are often used with ISE electrodes, as their durability - depending on the application - of indicator and reference electrodes is different.

58 59 Titration guide

KCI refill opening KCI refill opening Shielding

KCl solution KCl solution

Inner buffer Reference element

Discharge line

Inner buffer Reference element Silamid®

Discharge line Diaphragm Diaphragm

Discharge element

Membrane Membrane

A B C

Fig. 28 pH indicator electrode (A) reference electrode (B) and combined measuring chain (C) [5]

58 59 Titration guide The conductive connection When using a glass electrode of the reference electrode is as a reference electrode, it must made via the diaphragm. In the be noted that the glass elec- case of electrodes with liquid trode must be connected to electrolyte, a small amount of the high-impedance measuring the reference electrolyte must input due to its high resistance, always flow out here. The used and not to the measuring diaphragms are shown in Fig. 29. input for the reference electrode. The titration curves change their For titrations, electrodes with direction. platinum diaphragms are mainly used. For applications in organic solvents, electrodes with a ground-joint diaphragm are recommended, as they are less prone to clogging due to the higher discharge.

Type Resistance Discharge Application / Properties + general application. robust, - juniversally, short response time, constant Ceramic 1 kΩ 0,2 ml/d insensible against dirt and chemical reactions, tend to pollution/blockage

+ universal, fast setting, constant contamination-resistant, clean Platinum 0,5 kΩ 1 ml/d deﬁned discharge channels, less diﬀusion tension - only clean chemically, not mechanically

+ Emulsion, pastes, purest water, easy cleaning, Ground - discharge deviations due to different placement 0,2 kΩ 3 ml/d joint of the ground joint; loosening of the ground joint difficult with internal overpressure, filigree + Annular gap symmetrical, easy handling, resistant Annular solid to contamination 0,1 kΩ gap electrolyte - sample can reach the reference system, cleaning of the reference system not possible

+ fast setting, easy handling, solid Fibre 1 kΩ - sample can reach the reference system, cleaning electrolyte of the reference system not possible

Fig. 29 Diaphragm types [5] 60 61 Titration guide 4.2 Electrolyte solutions 4.3 Calibration of The reference electrodes can electrodes provide their ions in different Only pH electrodes in aqueous ways: solutions are calibrated. Accord- ing to DIN 19268, the buffers  Solid electrolyte contribute the highest uncertain-  Thickened liquid electrolyte ty factor to the calibration. The  Liquid electrolyte with different most stable buffers are e.g. the concentration buffers 4.00 pH, 4.01 pH, 6.87 pH, 7.00 pH. Alkaline buffers KCl 3 mol/l is often used as can absorb CO2, have a greater electrolyte. KNO3 2 mol/l with temperature dependence and, KCl 0.001 mol/l is inserted into depending on the composition, silver combination electrodes, are more affected by fungal since as little chloride as pos- growth and bacterial attack. sible should escape. In some As the electrodes behave in a surfactant titrations sodium very linear manner, there is no chloride is recommended, in need to calibrate with more organic solvents LiCl in ethanol than 2 buffers, even if measured or glacial acetic acid is used outside the range of pH 4 to 7. depending on the solvent. Calibration is only mandatory if an endpoint titration is carried out to a fixed pH. In a titration with EQ evaluation, it only depends on the change in the measured value, and not on the value itself. The maximum of the first derivation is consulted for the EQ calculation. The calibration values are however a quality criterion for the electrode.

60 61 Titration guide The slope and the zero point All other electrodes are checked are calculated. Their limits by the titration of a standard and depend on their own requi- evaluation of the titration curve. rements of the measurement uncertainty. The following limits The criteria are: are widely used, within which an electrode is still considered to be (1) Is the content found again? trustworthy: (2) Is the EQ in the expected potential range (Fig. 30 )?  Slope > 95 % to 102 % (3) Does the titration take longer  Zero point pH 6.5 to pH 7.2 than normal? (4) Are the start and stop poten- The slope of the electrode and tials in the expected range the response time are often (Fig. 30 and)? linked. A slow electrode also (5) Does the first derivation has a low slope. The response have the usual height or the behavior is important for the usual value at the maximum? titration. We recommend an (6) Is the titration free from exchange with a slope below noise? 95%. Too slow electrodes can lead to errors: If the titration is If one or even more of the criteria carried out with an electrode is not met, the electrode should which is too slow, a value that be exchanged after a thorough is too high is often found. error analysis.

62 63 Titration guide

mV 300.0  250.0

6.77 ml 200.0  196.3 mV

150.0

100.0

50.0 

0.0 ml 0 0.875 1.75 2.625 3.5 4.375 5.25 6.125 7.0 7.875 mV/ml dmV/dml Fig. 30 Criteria for evaluating the electrode quality

62 63 Titration guide 4.4 Reagents Sodium hydroxide The most commonly used Sodium hydroxide is used in reagents are (sorted by the a concentration of 0.01 mol/l frequency of their applications): to 1 mol/l. The highly diluted

solutions can absorb CO2 from  NaOH, sodium hydroxide (for the atmosphere and thus alter the determination of acids in their content. They are used for aqueous systems) very accurate titrations under inert gas. The reagent bottles  HCl, hydrochloric acid (for the with alkaline reagents are closed determination of bases, carbon- with CO2 absorption tubes. ates and bicarbonates in aque- These contain soda lime, a mix- ous systems) ture of solid NaOH and Ca(OH)2. This must be exchanged regularly. An indicator in soda lime  Na2EDTA (for complexometric determinations) indicates the exchange too late. Higher concentrations than 0.1 mol/l can attack the glass  HClO4, perchloric acid in glacial acetic acid (determination of the cylinder. Therefore, the of bases in organic solvents) tightness of the pistons must be specially observed. When using the reagents, in addition to the safety regulations, Hydrochloric acid some matters must be observed: Hydrochloric acid in concentrations up to 0.1 mol/l is easy to handle. It is corrosive in higher concentration and can cause damages in the titrator. It is recommended to remove the unit from the titrator when not in use.

64 65 Titration guide

Na2EDTA (NH4)2Fe2(SO4)2

Na2EDTA contains some NaOH. Ammonium iron (II) sulphate is a The same aspects apply as with reducing agent. It is often stabi- sodium hydroxide Concentra- lized with sulfuric acid and there- tions of 0.01 mol/l to 0.1 mol/l fore has a corrosive effect. are common. KOH in Ethanol or isopropanol AgNO 3 Potassium hydroxide in alcohol Silver nitrate can be used over a is a very strong base. The same wide concentration range and is aspects apply here as with also very stable. Due to the high sodium hydroxide. molecular weight and the easy

solubility, a silver nitrate standard HClO4 in glacial acetic acid solution can be produced very Perchloric acid in glacial acetic accurately. Silver nitrate is sensi- acid is a very strong acid. tive to light and must be stored Perchloric acid is usually used in dark bottles. with 0.1 mol/l. Solutions which are more diluted lead to flatter Na S O 2 2 3 titration curves. Sodium thiosulphate is a reducing agent and is stabilized with commercially available titrants. If you make it yourself, the titer is only stable after some time.

Ce(SO4)2 Cerium sulphate is a strong oxidizer and must correspondingly be handled with care. It is corrosive.

64 65 Titration guide 4.5 Titer determination The titration is an absolute The real concentration of the method which is directly attrib- titrant is often calculated during utable to the chemical conver- the titer determination: sion. The measured value is the volume of titrant that is convert- W real concentration T = ed during the reaction. This as- EQ∗M sumes that the concentration of the titrant is actually correct. It In the software of the titration is therefore always the first step devices from SI Analytics®, of an application to determine the term “Titer“ describes the its concentration accurately. If real concentration and not the this is carried out with a certi- dimensionless factor. We also fied standard, the concentration use this term in the examples can be traced back to a nation- of titration applications in this al standard (original titer sub- guide. stance) and its concentration can be determined accurately W ∗ F2 at the same time. The certified T[mol /l] = (EQ −B) ∗M ∗F1 standards must be treated carefully. They should be kept dry at 15 - 25 °C in their original T: Real concentration of the titrant W: Weighed sample standard / sealed packaging. If necessary sample in [g] they must be dried before use EQ: Consumption titrant (Fig. 31). M: molar mass of the standard B: Blank value of the solvent The titer is a dimensionless num- F1, F2: variable factors e.g. for the conversion of units, stoichiometry ber for correcting the indicated c: Target concentration of the concentration. The titer is about titrant 1.0.

W Titer = EQ∗ c∗M

66 67 Titration guide

Standard titer Molar mass Application Formula Drying substance [g/mol]

Acidimetry sodium carbonate Na2CO3 105.99 180 °C free of water C4H11N03 121.14 105 °C Tris(hydroxyl-methyl- aminomethan (TRIS)

Alkalimetry Benzoic acid C7H602 122.12 -

Potassium hydrogen phthalate C8H5K04 204.23 105 °C /3h

Argentometry Sodium chloride NaCl 58.443 110 °C

Karl Fischer Di-sodium tartrate C4H4Na2O6*2H20 230.08 - titration Di-hydrate

Complexometry Calcium carbonate CaCO3 100.09 105 °C

Zinc Zn 65.37 -

Oxidimetry di-arsenic trioxide As2O3 197.84 105 °C /3h Cerimetry di-sodium oxalate C2Na2O4 133.999 105 °C

Iron(II) ethylene (CH2NH3)2 S04 * 382.15 - diammonium sulfate FeSO4*4H20

potassium dichromate K2Cr2O7 294.19 105°C

potassium iodate KI03 214.00 150 °C / 180 °C

Fig. 31 Standard titer substances and reference materials for the titration

66 67 Titration guide Titer determination of bases Alkalis can be adjusted with Instruction for the titer determi- acids. Suitable acids are nation of a 0.1 mol/l NaOH potassium hydrogen phthalate, Approximately 200 mg of benzoic acid, oxalic acid dihy- potassium hydrogen phthal- drate or amidosulfonic acid. ate are weighed into a 150 ml In water or acetic acid as solvent, beaker with an analytical potassium hydrogen phthalate is balance to four digits after the recommended, in organic solu- decimal point and are filled up tions, e.g. in the pharmaceutical with deionized carbonate-free sector, benzoic acid is usually water to approx. 100 ml. used. After complete dissolution, the titration is started to a pH 11 or The reaction equation for the up to an equivalence point. The titer determination with potassi- equivalence point is evaluated. um hydrogen phthalate is: The consumption is approximately 10 ml. 2- + PhtKH + NaOH → Pht + H2O + Na + K+ Handling of the standard Potassium hydrogen phthalate  Drying: (Fig. 32) is only weakly dissociated two hours at 120 °C in aqueous solution. The titration  Storage: curve therefore increases initially, Tightly closed in the original similar to acetic acid, to show packaging, protect from light a steep jump after a plateau. and humidity, at room temperature (+15 - 25 ° C) The pKs2 value is 5.41.  Observe the minimum usability

68 69 Titration guide

The following must be Calculation of the titer observed: W ∗ F2 T[mol /l] =  The slope of the pH (EQ −B) ∗M ∗F1 electrode is > 95 % for the aqueous titration T: real concentration of the  The NaOH solution in the titrant storage bottle must be W: Weighed sample standard / sample in [g] protected against CO2 influence with soda lime EQ: Consumption titrant in [ml] B: Blank value of the solvent in [ml]  All crystals of the standard M: 204,22 g/mol (molar mass of must be completely dissolved potassium hydrogen phthalate) at the start of the titration F1: 1 F2: 1000 (conversion ml - L) The following titration parameters are recommended:  Dynamic titration  Normal (average) titration speed  Dynamics: steep  No damping  End criterion 1 EQ with slope value 700 mV/ml and pH 11

pH 10.5

9.625 10.13 ml 8.568 pH 8.75

7.875

7.0

6.125

5.25

4.375

3.5 ml 0 1.25 2.5 3.75 5.0 6.25 7.5 8.75 10.0 pH/ml dpH/dml

Fig. 32 Titer determination of an 0.1 mol/l NaOH with potassium hydrogen phthalate 68 69

Titration guide Titer determination of acids Acids can be adjusted with Instruction for the titer determi- bases. As a base, e.g. sodium nation of a 0.1 mol/l HCl carbonate and TRIS (tris(hy- Approx. 120 mg TRIS are droxymethyl)-aminomethane, weighed into a 150 ml or according to IUPAC 2-amino- beaker with an analytical 2-hydroxymethyl-propane-1.3- balance to four digits after the diol) are suitable. TRIS is recom- decimal point, and filled with mended, as the handling is deionized, carbonate-free water simpler and more secure. to approx. 100 ml. After complete dissolution, the titration is The reaction equation for titer started to a pH 2.5 or up to an determination with TRIS is: equivalence point. The equivalence point is evaluated. The + C(CH2OH)3NH2 + H3O → consumption is approximately + 10 ml. C(CH2OH)3NH3 + H2O

A falling titration curve (Fig. 33) Handling of the standard results, which can be interrupted  Drying: at the EQ or which can be 24 hours via desiccant in the counted back after overtitration desiccator of the EQ. The latter method is  Storage: recommended if carbonates are Tightly closed in the original expected. packaging, protect from light and humidity, at room temperature (+15 - 25 ° C)  Observe the minimum usability

70 71 Titration guide

The following must be Calculation of the titer observed: W ∗ F2 T[mol /l] =  The slope of the pH (EQ −B) ∗M ∗F1 electrode is > 95 % for the aqueous titration T: Real concentration of the titrant  The added solvent must W: Weighed sample standard / sample in [g] be free from CO2  All crystals of the standard EQ: Consumption titrant in [ml] must be completely dissolved B: Blank value of the solvent in [ml] M: 121.14 g/mol (molar mass of TRIS) at the start of the titration F1: 1 F2: 1000 (conversion ml - l) The following titration parameters are recommended:  Dynamic titration  Normal (average) titration speed  Dynamics: steep  No damping  End criterion 1 EQ with slope value 700 mV/ml and pH 2.5

pH 9.625

8.75

7.875

7.0

6.125

5.25

8.76 ml 4.375 4.857 pH

3.5

2.625 ml 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 pH/ml dpH/dml

Fig. 33 Titer determination of an 0.1 mol/l HCl with TRIS 70 71

Titration guide Titer determination of silver nitrate Silver nitrate is often adjusted Instruction for the titer determi- with NaCl. This is available as nation of a 0.1 mol/L AgNO3 a secondary NIST standard. Approx. 58 mg of NaCl are Although KCl would have a accurately weighed into a higher molecular weight, it is 150 ml beaker to four digits often not available in the neces- after the decimal point using sary purity. an analytical balance, filled with deionized water up to The reaction equation for the ti- approx. 100 ml, and 2 ml of semi- ter determination with NaCl is: concentrated HNO3 or H2SO4 are added. The equivalence Na+ + Cl- + Ag++ NO - 3 → point is evaluated. The Na+ + NO - + AgCl 3 ↓ consumption is approximately 10 ml. A white precipitation An increasing titration curve forms during titration. (Fig. 34) results, which can be interrupted at the EQ or which Handling of the standard can be counted back after overtitration of the EQ. When a glass  Drying: at 110 °C 3 hours electrode is used as a reference,  Storage: Tightly closed in a falling titration curve results. the original packaging, protect from light and humidity, at room temperature (+15 - 25 ° C).  Observe the minimum usability

The following must be observed:  The titration shall last between three and five minutes.

72 73 Titration guide

The following titration Calculation of the titer parameters are recommended: W ∗ F2 T[mol /l] =  Dynamic titration (EQ −B) ∗M ∗F1  Measuring speed: Measurement time 3 s T: Real concentration of the Drift 10 mV/min titrant Min time 3 s W: Weighed sample standard / Max time 15 s sample in [g]  Dynamics: steep EQ: Consumption titrant in [ml]  No damping B: Blank value of the solvent in [ml] M: 58.433 g/mol (molar mass of  End criterion 1 EQ with NaCl) slope value 400 mV/ml F1: 1 F2: 1000 (conversion ml - l)

mV 300.0

250.0

10.02 ml 201.7 mV 200.0

150.0

100.0

50.0

0.0 ml 0 1.25 2.5 3.75 5.0 6.25 7.5 8.75 10.0 mV/ml dmV/dml

Fig. 34 Titer determination of a silver nitrate solution with sodium chloride

72 73 Titration guide Titer determination of perchloric acid Perchloric acid is a very strong Handling of the standard acid that can be used to titrate  Drying: potassium hydrogen phthalate two hours at 120 °C as the base in acetic acid.  Storage: Tightly closed in the original The reaction equation for the packaging, protect from light titer determination with potassi- and humidity, at room tem- um hydrogen phthalate is: perature (+15 - 25 ° C).  Observe the minimum PhtKH + HClO4 → usability + - PhtH2 + K + ClO4 The following must be The titration is performed as mV observed: titration. It therefore increases  and does not fall, as would be All crystals of the standard the case with a titration with acid must be completely dissolved in the pH range. at the start of the titration!  LiCl in ethanol or in glacial Instruction for the titer determi- acetic acid should be used as electrolyte. nation of a 0.1 mol/l HClO4 Approximately 200 mg of potassium hydrogen phthalate (Fig. 35) are weighed into a 150 ml beaker with an analytical balance to four digits after the decimal point and are filled up with glacial acetic acid to approx. 80 - 100 ml. After complete dissolution, the titration is started up to an equivalence point. The equivalence point is evaluated. The consumption is approximately 10 ml.

74 75 Titration guide

The following titration Calculation of the titer parameters are recommended: W ∗ F2 T[mol /l] =  Dynamic titration (EQ −B) ∗M ∗F1  Measuring speed: Measurement time 2 s T: Real concentration of the Drift 10 mV/min titrant Min time 3 s W: Weighed sample standard / Max time 15 s sample in [g]  Dynamics: average EQ: Consumption titrant in [ml]  average damping B: Blank value of the solvent in [ml] M: 20422 g/mol (molar mass of  End criterion 1 EQ with potassium hydrogen phthalate) slope value 300 mV/ml F1: 1 F2: 1000 (conversion ml - l)

mV 575.0

9.94 ml 550.0 540.2 mV

525.0

500.0

475.0

450.0

425.0

400.0

375.0

350.0 ml 0 1.25 2.5 3.75 5.0 6.25 7.5 8.75 10.0 mV/ml dmV/dml

Fig. 35 Titer determination of a perchloric acid with potassium hydrogen phthalate 74 75

Titration guide Titer determination of thiosulphate Thiosulphate is usually adjust- Handling of the standard: ed with potassium iodate. This  Drying: is available as a secondary NIST at 150 °C 3 hours standard.  Storage: Tightly closed in the original The reaction equation for the packaging, protect from light titer determination with KIO is: 3 and humidity, at room temperature (+15 - 25 ° C) 5 I- + IO - + 6 S O 2- + 6 H+ 3 2 3 →  Observe the minimum 3 S O 2- + 3 H O + 6 I- 4 6 2 usability

A falling titration curve results The following must be (Fig.36), which can be interrupt- observed: ed at the EQ or which can be counted back after overtitration  A platinum combination elec- of the EQ. trode is used as electrode  Potassium iodate and potassi- Instruction of a 0.1 mol/l um iodide react iodine in acid, thiosulphate solution with their oxidizing properties  Sufficient acid must be present Approx. 50 mg KIO are weighed 3 in the solution into a 150 ml beaker with an ana-  The iodide must be present lytical balance to four digits after in a very high excess the decimal point; approx. 1 g potassium iodide is added and filled with deionized water to approx. 100 ml. 5 ml of approx. 5% HCl is added. The equivalence point is evaluated. The consumption is approximately 14 ml.

76 77 Titration guide

The following titration Calculation of the titer parameters are recommended: W ∗ F2 T[mol /l] =  Dynamic titration (EQ −B) ∗M ∗F1  Measuring speed: Measurement time 2 s T: Real concentration of the titrant Drift 10 mV/min W: Weighed sample standard / Min time 3 s sample in [g] Max time 15 s EQ: Consumption titrant in [ml]  Dynamics: average B: Blank value of the solvent in [ml]  No damping M: 214.00 g/mol (molar mass of potassium iodate)  End criterion 1 EQ with F1: 1 / 6 as stoichiometric factor from slope value 300 mV/ml the reaction equation F2: 1000 (conversion ml - l)

mV 450.0

375.0

300.0 4.67 ml 312.3 mV

225.0

150.0 ml 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 mV/ml dmV/dml

Fig. 36 Titer determination of a Na2S2O3 solution

76 77 Titration guide Titer determination of iodine The titer of an iodine solution Instruction for the titer deter- can be set directly with arsenic mination: a 0.05 mol/l iodine (III) oxide. However, this is not solution recommended due to the tox- 5 ml of a 0.1 mol/l sodium thio- icity of arsenic. Nowadays it is sulphate solution is pipetted best to use an adjusted sodium into a 150 ml beaker, filled with thiosulphate solution, which is deionized water to approx. titrated with the iodine solution. 100 ml and 5 ml of approx. 5% HCl is added.The titration The reaction equation for the can be carried out both as a titer determination is: potentiometric titration with a redox electrode and as a Dead I + 2 S O 2- S O 2- + 2 I- 2 2 3 → 4 6 Stop titration. The consumption is at approx. 5 ml (Fig. 37).

78 79 Titration guide

The following titration Calculation of the titer parameters are recommended: V ∗F2 T[mol /l] =  Dead Stop titration (EP−B) ∗M∗F1  linear steps: 0.02 ml  Pre-titration: none T: Real concentration of the  Dosing speed 20 % titrant -  Titration direction: V: Volume of the Na2S2O3 increasing solution [ml]  Measuring speed: EP: Consumption titrant in [ml] B: Blank value of the solvent in [ml]  fixed waiting time 1s M: 1  Polarization voltage: 100 mV F1: 2 as stoichiometric factor from  Delta endpoint: 1.0 µA the reaction equation F2: Concentration of the Na S O -  Titration end: 2.0 µA 2 2 3 solution [mol/L]  Endpoint delay: 5 s

µA 7.875 7.0 6.125 5.25 4.375 3.5 2.625 2.0 µA 5.191 ml 1.75 0.875 0.0 ml

0 0.625 1.25 1.875 2.5 3.125 3.75 4.375 5.0 µA/ml

Fig. 37 Titer determination of an iodine solution (Dead Stop)

78 79 Titration guide

80 81 Titration guide SECTION 5 TITRATION PARAMETERS AND CALCULATIONS 5.1 Overview Titration methods have to be The titration takes place in many adapted to the type of appli- individual steps. It is true that cation and partly to the type of part of the titration volume can samples. be added in one step or continuously. However, the part of the This adjustment requires the titration curve that is used for selection of the measured vari- the calculation is created in de- able (and the associated sensor), fined steps as a list of data with the appropriate titrator or attach- consumption, measured value, ment with the associated reagent time and possibly additional and the correct parameters in the information. From these data, the titration device or the software. endpoint or equivalence point The selection of the measurand is calculated with appropriate and the reagent can be found functions. in the application description. The settings in the methods An important requirement is that and the theory behind them the measured values are also shall be briefly described here. reliable. This is achieved by A titration is parameterized by monitoring the measured values five elements: and only taking them into a titration curve when they are stable.  Control of the dosage From the calculated equivalence  Response behavior of the or endpoint, the result can then electrode and speed be calculated taking into account  Definition of the titration end the weighed sample, titer and  Calculation(s) blank value in the correct unit.  Documentation of the result.

80 81 Titration guide 5.2 Control of the dosage Linear Titration Reagent addition can be done in In linear titration, the reagent is titrators in three different ways: added in equal steps. Usually, it is waited after each step until the  Continuous addition potential has adjusted or it can  Equidistant steps be assumed after a fixed waiting (Linear titration) time that the potential is stable.  Step size dependent on the A titration curve should not have gradient of the titration curve too many but also not too few (dynamic titration) measuring points. Too few measurement points lead to a less These can also be used in a com- accurate calculation, but also too bined manner. For example, it is many. This is due to the small possible to add continuously in potential change with small steps, order to then continue to titrate resulting in less stable measured in a linear or dynamic manner. values and less accurate dosages. In addition, it is not always en- The continuous addition has the sured that small volumes actually advantage of a fast addition. arrive at the titration tip. As a rule Even if measurements can be of thumb, a linear titration should generated during the addition, have 20 to 50 measured values this does not mean that the re- and only exceed 100 measured action speed is set correctly or values in special cases. that the adjustment behavior of the sensor is taken into account. In Fig. 38 a/b, the influence of the In practice, for most titrations, too smaller number of titration steps much would clearly be found in is shown. this manner with fast continuous addition, but too little with a kinetically inhibited reaction.

82 83 Titration guide

60 500 Ca with EDTA linear 0.1 ml steps 40 450

20 400

0 350 0 2 4 6 8 10 12 14 -20 300 dmV mV -40 dmL 250 -60 A 200 -80 150 -100

100 -120

-140 50

-160 0 ml EDTA

60 500 Ca with EDTA 0.2 ml steps 40 450

20 400

0 0 2 4 6 8 10 12 14 350 -20 300 dmV mV -40 dmL 250 -60 200 -80 B 150 -100

100 -120

-140 50

-160 0 ml EDTA

Fig. 38 a Ca determination with EDTA linear with 126 (A) and 64 (B) measured values 82 83 Titration guide

60 50 Ca with EDTA 0.5 ml steps 40 45

20 40

0 0 2 4 6 8 10 12 14 35 -20 30 dmV mV -40 dmL 25 C -60 20 -80 15 -100

10 -120

-140 5

-160 0 ml EDTA

60 35 Ca with EDTA 1.0 ml steps 40 30 20

0 25 0 2 4 6 8 10 12 14 -20

20 dmV mV -40 dmL

-60 D 15 -80

-100 10

-120 5 -140

-160 0 ml EDTA

Fig. 38 b Ca determination with EDTA linear with 26 (C) and 13 (D) measured values

84 85 Titration guide A titration curve with 126 titration Application areas of linear titra- steps is clearly overloaded, 64 tion are e.g.: measuring points result in a per- fect titration curve (with many  titrations in organic measuring points in the low ml solvents, range). At 26 measuring points,  titration of very small small changes of the distribut- contents, ed first derivation can already  conductivity titrations, be observed. At 13 measuring  photometric titrations points, it may no longer be possi-  µA titrations ble to carry out a correct evaluation, as measuring points may be It has important advantages: missing for the EQ calculation. With such a titration curve, it is  more stable potentials result, recommended to select smaller as usually sufficient reagent titration steps in order to obtain is converted in order to a larger number of measuring achieve a significant potential points and a titration curve that change, can be evaluated in a better  disturbances of potentials only manner. have a small influence on the titration curve.

The disadvantages can be seen clearly:

 too many measurement points in areas where little happens.  only a few measurement points in the EQ area.

84 85 Titration guide Dynamic Titration This means that in the flat part of Dynamic titration is the preferred the curve large volume steps are form of reagent addition. It is dosed and in the steep part small used in most titrations according steps. to the Nernst equation, for example: Fig. 39 clearly shows what matters: The titration shall be carried  Acid-base titrations in aque- out quickly, but also very accu- ous and alcoholic solutions rately with high resolution. Due  Chloride determinations to the high resolution, e.g. errors  Redox titrations can be found in the titrant: The KOH in Fig. 40 is contaminated It has many advantages: with carbonate. This is often not detected in a titration. For this,  High accuracy the titration in the steep part,  Fast titration but also only there, must be  Only the number of data points titrated with a particularly high which is really necessary resolution, so that both EQs are recognizable. It is not used when: Fig. 39 shows the individual  A connection according to the addition steps with dynamic Nernst equation does not exist titration. In the beginning, it is  Stable potentials do not exist carefully started with small steps  With very small contents so that it is not over-titrated.  Organic solvents are used Then a few large volume steps follow until just before the EQs. With dynamic titration, the step The EQ area is then titrated with is calculated as a function of the small steps. Even if the distance slope of the titration curve. of the steps in the jump area appears to be different, on the x-axis with the ml values, the volume steps are all equal to the smallest set step.

86 87 Titration guide

KOH with HCl dynamic 12.00

10.00

8.00 pH

6.00

4.00

2.00 0 2 4 6 8 10 12 14 16 ml HCl

Fig. 39 Representation of the measure values on the titration curve

14.00 2500 14.00 2500 KOH with HCl dynamic 12.00 12.00 2000 2000 10.00 10.00

1500 8.00 dmV 1500 8.00 pH dmL dmV 6.00 pH 1000 dmL 6.00 1000 4.00

500 4.00 2.00

500

0.00 0 2.00 0 2 4 6 8 10 12 14 16 ml HCl

0.00 0 9 9.5 10 10.5 11 ml HCl

Fig. 40 Titration curve of a carbonate-containing KOH dynamically titrated with HCl

86 87 Titration guide The calculation of the step takes This hyperbolic function is de- place on the basis of a hyper- rived from the Nernst equation, bolic function: which represents an "In" function. a The derivation of the ln(x)- Step size [ml] = + c Gradientb function is 1/x, which is behind this formula. with "a", "b" and "c" as calculation factors, which are automatically Fig. 41 shows that large steps are determined from the titration titrated with a small slope value curve. and small steps with a large slope.

Fig. 41 Function for calculating the step of the titration curve

88 89 Titration guide

2500

12.00

2000

10.00

1500

8.00 dmV pH dmL

1000 6.00 ml Gradient ml per step 2.300 3 1.000 3.300 4 1.000 4.300 5 1.000 500 5.300 6 1.000 4.00 6.300 8 1.000 7.300 11 1.000 8.240 17 0.940 8.796 28 0.556 2.00 0 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 9.548 149 0.044 mL 9.580 179 0.032 9.610 206 0.030 9.632 244 0.022 9.652 310 0.020 Fig. 42 Regulation area of the dynamics 9.672 413 0.020

Fig. 42 shows the regulation  Largest step in [ml] areas of the titration. Within the  Smallest step in [ml] blue area, the step is reduced  Gradient, until which the larg- or increased again, in the orange est step shall be dosed area, the smallest step is dosed [dmV/dml] with a defined accuracy. The  Gradient, from which the following entries are required smallest step shall be dosed for the parameterization: [dmV/dml] In the above example these are:  1.000 ml  0.020 ml  15 mV/ml  250 mV/ml 88 89 Titration guide In order to obtain meaningful 5.3 Response behavior of results, the settings "steep, the electrode and speed average or weak jump" are usually sufficient. Steps that The adjustment of the step are too large steps can lead to alone is not sufficient to control over-titration, too small lead to a titration curve. It must also be potential differences and thus ensured that the "correct" stable to strong noise of the curve. measuring signal is applied to This reduces the accuracy of the the electrode. In certain circum- titration. As a rule of thumb, stances measuring signal needs approx. 5-10 % of the total titra- some time until stable values are tion volume are suitable as the adjusted. This time depends on largest step, 2 % for the smallest various factors, such as type, age step. Certain requirements for and condition of the electrode extra accuracy or speed may and the concentration of the require different settings. material to be measured. In practice, therefore, the setting behavior of the electrode is observed and evaluated the course of the measured value per unit time. The change in the measured value per time is called drift (Fig. 43). The measurement unit is [mV/min].

Fig. 44 clearly shows that most of the titration time is used for accurate drift control in the area of the equivalence points. The graph shows a linear titration with the same step size, in order to avoid effects due to several small volume additions instead of one large addition.

90 91 Titration guide

Drift as measured value per time 280

260

240

220

200

180 Measured value [mV] 160

140

120

100 0 0.5 1 1.5 2 2.5 Time [s] Fig. 43 Measured value change per time

H3PO4 Titration curve and time behavior 12 300

10 250

8 200 ] H

p 6 150 pH curve time curve Titration duration [ s

4 100

2 50

0 0 0 2 4 6 8 10 12 NaOH [ml]

Fig. 44 Titration curve (blue) and titration duration (green) 90 91 Titration guide As parameters, It is recommended to select the minimum time not too short, as  the minimum waiting time, an alternating system can build  the maximum waiting time, up. The current value is accepted  the window for the testing very quickly, but causes the next time, value to take longer to adjust.  the drift value, can be set (Fig. 45). In some cases, it may be sensible to work with fixed waiting times The minimum waiting time must instead of a drift-controlled be waited for in any case, even waiting time; especially for if the drift within the testing time applications that provide only is already monitored during this a few stable measured values, time. low potential changes, or do not provide mV or pH values A minimum waiting time of 10 according to the Nernst equation seconds is waited for in Fig. 46. (e.g. μA values, mS values, or Within the last five seconds temperatures). Fixed waiting (testing time), however, the times are usually set in the range drift is already determined and of 5 - 30 seconds. compared with the target value (Fig. 47). The window for the testing time will continue to move until the maximum drift time or drift value is reached. The value represents the gradient of the drift curve.

Titration Minimum waiting time Maximum drift time Measurement time Drift value

duration t_min [s] t_max [s] t_p [s] [mV/min] Fast 1 5 1 50 Average 2 15 2 20 Exact 5 20 2 10

Fig. 45 Setting parameters for the drift (practical values) 92 93 Titration guide

Time = x[n]

280

260

240

220

200

180

Measured value [mV] 160

140

120

100 0 5 10 Time [s] 15 20 25

t_p t_min t_max

Fig. 46 Setting the drift and the necessary parameters (description of the parameters, see Fig. 45)

Time = x[n]

280

260

240

220

200

180

Measured value [mV] 160

140

120

100 0 5 10 15 20 25 Time [s]

t_p t_min t_max

Fig. 47 Setting the drift with control time window (labeling see Fig. 45, parameter “Exact”) 92 93 Titration guide 5.4 Definition of the Titration up to: titration end  a maximum volume of the titrant With a manual titration, the  a certain endpoint (pH or mV, titrator stops as soon as the also µA or µS are possible) "manual button" is released.  a certain duration What if the user cannot be (pH Stat, KF titration) present for the entire time? This  one or several EQs is often the case during titration.  a calculated result  a manual interruption In order to terminate an automatic titration, several criteria The essential criteria for stopping exist: a titration are listed in Fig. 48.

Measured Titration curve and derivation Lidocaine HCl value 12 2500

11 EQ end 10 2000

8 1500 pH 7

6 Value derivation 1000 Titration duration [s]

4 500

2 0 0 1 2 3 4 5 6 7 8 9 NaOH 0.1 mol/l ml] ml end pH value Derivation

Fig. 48 Criteria for ending the titration

94 95 Titration guide Titration interruption at Titration interruption when maximum volume recognizing an EQ This criterion should always be For titrations in which a clearly there, as beakers are limited in recognizable EQ is calculated, their volume. Usually 20 to 50 ml this is also the most sensible end are used as an additional criterion. criterion. An EQ is calculated as For some titrations with very small the maximum of the first and the changes in potential (e.g. TAN) zero point of the second it can also be the only criterion. derivation. It is therefore associated with the value of the first Titration interruption at derivation. The first derivation a certain measured value must reach a certain (adjustable) value in order for the EQ to be If it is not known how many accepted as such. equivalence points can be calculated, this criterion will be used. E.g. a maximum pH value is defined at which the titration stops. Then it can be decided in the calculation whether one or more EQs should be calculated. For EP titrations to a defined endpoint, the interruption criterion is the desired endpoint. This endpoint must be exceeded for a defined time (endpoint delay) or by a certain value.

94 95 Titration guide For some applications, other With the Karl Fischer titration, criteria exist for terminating the one titrates to one endpoint. titration. During the pH Stat A voltage is applied to the indi- titration (the pH value is kept cator double platinum electrode. constant for a while), the duration A current flows if a reversible of the titration is used as a crite- redox couple is present in the rion (Fig. 49). The total volume solution (iodine and iodide). The should always be a criterion, as titration is stopped if this reaches the titration cell can also over- the set end value. flow.

pH-Stat 10 8

9 7

8 6 7

5 6

ml NaOH 5 4 pH

4 3

3 2 2

1 1

0 0 0 50 100 150 200 250 Duration [s] Consumption [ml] pH value

Fig. 49 pH stat titration with stat phase of 180 s

96 97 Titration guide 5.5 Evaluation of the titration During the titration, endpoints In practice, the EQs are almost (EP) or equivalence points (EQs) always used to calculate the are evaluated. result. In order to calculate an EQ, it is over-titrated by a few ti- In a titration to an endpoint (EP), tration points and interpolated the titration is typically interrupt- from the titration points around ed at the point that would cor- the EQ. The result is the more respond to the colour change accurate the smaller the titration of an indicator. EP titrations are steps. If measuring points are thus conventional methods that missing after the EQ, it may be are primarily intended to provide possible that a calculation is not good comparability. EPs are thus possible. It is therefore import- also the last point of a titration ant to ensure that there are still or partial titration. Titrations with enough measuring points for a several partial titrations with up calculation after an EQ (see Fig. to three endpoints exist. 50). The calculated pH or mV value of the EQ is of minor impor- An equivalence point (EQ) is tance for very steep curves. The determined based on a turning slope of the titration curves can point of the titration curve. The be very high, so that the changes maximum of the first derivation of the pH value in the volume and the zero point of the sec- often have practically no effect. ond derivation are calculated for The volume is however used for this. Typically, the turning point the evaluation and calculation of corresponds to the equivalent the result. conversion of the reagent with the sample. With several turning points, however, it may happen that the actual equivalence point has not yet been reached when the curve "bends" for another EQ. In some cases corrections to the EQ are advantageous. Their complex calculation shall not be 96 discussed here. 97 Titration guide If the correct EP or EQ is deter- Formula for the titer mined, the desired result can be W ∗F2 calculated from this. Titer = EQ ∗C ∗M∗F1 Basically, only 2 types of formulas Titer: Dimensionless number, for example 1.0 are used hereby: on the one hand, W: Weighed sample standard / the calculation of the titer or the sample [g] concentration of the titrant, and EQ: Consumption titrant [ml] on the other hand the calculation C: specified concentration of the titrant [mol/l] of the concentration of a sample. M: molar mass of the standard [g/mol] F1: 1 F2: 1000 (conversion ml - l)

10 1400

1200 9

1000 8

10 1400 800

7 pH 9.5 dpH/dml 1200 600

6 9 1000 400

8.5 5 800 200 8 pH dpH/dml 600 4 0 0 2 4 6 8 10 12 7.5

400 7

200 6.5

6 0 9.5 9.6 9.7 9.8 9.9 10 10.1

Fig. 50 Interpolation of an EQ

98 99 Titration guide Sometimes a blank value has to Formula for the content in % as be included in the calculation of back titration the result. Some solvents have (B−EQ) ∗T ∗M ∗F1 Content [%]= a (small) self-consumption of W ∗F2 titrant. This self-consumption is deducted from the EQ or EP, so B: Consumption during titration of the added reagent without that only the consumption of sample [ml] the sample contributes to the EQ: Consumption titrant [ml] result in the calculation. Another T: Exact concentration of the titrant type of blank value can be found [mol/l] M: molar mass of the substance to in the back titration: The blank be determined [g/mol] value is the consumption of the W: Weighed sample standard/ used reagent without sample. sample [g] Here the consumption of EP or F1: 100 conversion in % EQ is deducted from the blank F2: 1000 (conversion ml - l) value. The titration often has an "accuracy" of four significant digits Formula for the content in % in total (regardless of whether with blank value in the solvent before or after the decimal (EQ− B)∗ T∗M∗F1 separator). However, all the Content [%]= W∗F2 individual components in the formula must also be defined EQ: Consumption titrant [ml] B: Blank value of the solvent [ml] with this number of digits, T: Exact concentration of the starting with the weighed titrant [mol/l] sample through the molar M: molar mass of the substance to weights to the consumption. be determined [g/mol] To achieve higher accuracy, all W: Weighed sample standard / sample [g] numbers in the formula must F1: 100 conversion in % always be defined with a higher F2: 1000 (conversion ml - l) number of digits.

98 99 Titration guide Examples: Titer of silver nitrate with NaCl NaCl content in % The titer of a 0.1 mol/l silver The NaCl content of a sample nitrate solution shall be deter- shall be determined with the mined with NaCl: above-mentioned standard solution:  the molar mass of NaCl is 58.44 g/mol,  the exact concentration is  the weighed sample W was 00994 mol/l 0.584 g,  the molar mass of NaCl is  the consumption EQ was at 58.44 g/mol 10.05 ml,  the weighed sample W was  with F1 = 1 and 1.12 g F2 = 1000 (conversion ml - l),  the consumption EQ was at the following results: 10.05 ml, ∗  with F1 = 1 and Titer = o  g  F2 = 1000 (conversion ml - l),   ∗   ∗   o the following results:

= Content [%] = or the exact concentration used mol  g  10.05[ml]∗0.0994   ∗58.44   ∗100% for most calculations T:  l  mol 1.12[g]∗1000 mol mol T   = Titer ∗0.1   l   l  =5.21% 0.0584 ∗1000 In the example, the sample =  g  would have a sodium chloride 10.05[ml]∗58.44   content of 5.21%. mol mol = 0.0994    l 

The 0.1 mol/l AgNO3 solution thus has a concentration of 0.0994 mol/l.

100 101 Titration guide SECTION 6 APPLICATIONS Examples from the application database For many applications, application documents can be down- loaded from our homepage. Some applications shall be listed here as examples.

100 101 Titration guide 6.1 Acid-base titrations Titration of citric acid in drinks Almost all drinks contain acids The following must be that are usually already contained observed: in the raw fruit materials. They  A titer determination takes improve the taste and the place with potassium hydro- durability. Acids are still added gen phthalate. to some soft drinks. Citric acid (Fig. 51) is a tribasic acid, whose  The sodium hydroxide must pKs values are very close be protected with a CO2 together and therefore difficult absorption means. to titrate individually. As drinks Soda lime is recommended. often also contain other acids, an endpoint titration to a pH of  The electrode must be calibrat- 8.2 (in some cases also 8.1, 8.3 ed. The buffers pH 4.01 and pH or 8.5) is carried out in practice 6.87 are recommended. (Fig. 52).This corresponds to the change of phenolphthalein.

The manual titration with colour indicator is often difficult to carry out in contrast to the potentiometric titration due to the inherent colour of the drinks. The calculation is also carried out for other acids with the molecular weight of citric acid (192.13 g/mol). One usually titrates with a NaOH 0.1 mol/l.

Fig. 51 Structural formula citric acid

102 103 Titration guide

The following titration Formula for the acid value in g/l: parameters are recommended: EP∗ T ∗M∗F1 acidity [g /l] =  Endpoint titration to pH 8.2 V ∗F2  Dosing speed 40 %  Linear step: 0.04 ml normal EP: Consumption titrant [ml] to pH (average) titration speed 8.2  Delta value for the linear T: Excact concentration of the titrant end part: 1.2 M: Molar mass of citric acid  192.13 g/mol Endpoint delay 5 s V: Volume sample [ml]  No damping F1: 1 F2: 3 (stoichiometric factor, 3-basic acid)

pH 8.75 12.12 ml pH 8.200 8.125

7.5

6.875

6.25

5.625

5.0

4.375

3.75

3.125 ml 0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 pH/ml

Abb. 52 Titration curve orange juice

102 103 Titration guide Titration of a strong acid Many applications contain The calculation is different, strong, completely dissociat- depending on the type of ed acids such as HCl, H2SO4 application (Fig. 54) and the or HNO3. These behave the sample weight (volume vs. same for the acid-base titration. mass). The result can be cal- Sulfuric acid e.g. behaves in culated as acid concentration aqueous solutions as a dibasic mol/l, acid content g/kg, mg/g strong acid and it is thus or g/l or mg/ml. For some difficult to distinguish it from applications it is sensible to "two" monobasic strong acids. indicate the acid content as base Different organic acids as e.g. consumption/g sample, thus mg salicylic acid (Fig. 53), whose (NaOH)/g or mg (KOH)/g. One pKs value is approximately in usually titrates with a NaOH 0.1 the area of the 1st protons mol/l. of phosphoric acid, behave like a strong acid during titra- The following must be tion. The titration usually takes observed: place in a dynamic manner up  A titer determination takes to an EQ. With an endpoint place with potassium hydro- titration, the indicator would gen phthalate. depend on the type of acid.  The sodium hydroxide must

be protected with a CO2 absorption means. Soda lime is recommended.  The electrode can be calibrated. Buffers pH 4.01 and pH 6.87 are recommended. The calibration parameters serve as proof of the state of the pH electrode. The slope Fig. 53 Structural formula salicylic should be > 95 %. acid with proton of the carboxyl group 104 105 Titration guide

The following titration Formula for the acid value in g/l: parameters are recommended:  Dynamic titration (EQ−B) ∗T ∗M∗F1 Content [%]=  Normal (average) titration W∗F2 speed  Dynamics: steep EQ: Consumption titrant at the  No damping equivalence point  End criterion 1 EQ with slope B: Blank value of the solvent value 700 mV/ml and pH 12 T: Exact concentration of the titrant  M: Molar mass of salicylic acid Dosing speed 100 % 138.12 g/mol W: Weighed sample [g] F1: 100 (conversion %) F2: 1000 conversion ml - l)

pH 10.5

9.625

8.75

11.20 ml 7.875 7.464 pH 7.0

6.125

5.25

4.375

3.5

2.625

1.75 ml 0 1.25 2.5 3.75 5.0 6.25 7.5 8.75 10.0 11.25 pH/ml dpH/dml

Fig. 54 Titration curve salicylic acid

104 105 Titration guide Titration of phosphoric acid The phosphoric acid is a tribasic The following must be acid, of which only the first two observed: protons can be titrated in aque-  A titer determination takes ous solutions. The third proton place with potassium hydro- has such a high pK value that S gen phthalate. the aqueous sodium hydroxide solution is not basic enough.  The sodium hydroxide must Some methods are based on be protected with a CO2 the fact that phosphates form absorption means. compounds with heavy metal Soda lime is recommended. ions, in which the protons are then released in an equivalent  The electrode can be calibrat- amount. The direct titration ed. Buffers pH 4.01 and pH with sodium hydroxide and the 6.87 are recommended. calculation of the content is The calibration parameters described here as difference serve as proof of the state of of the two EQs (Fig. 55). Strong the pH electrode. The slope acids do not interfere, but weak should be > 95 %. or multibasic ones such as e.g. citric acid. The following titration parameters are recommended: One usually titrates with a NaOH 0.1 mol/l.  Dynamic titration  Normal (average) titration speed  Dynamics: steep or average  No damping  End criterion 2 EQ with slope value > 200 mV/ml  Dosing speed 65 %

106 107 Titration guide

Formula for the phosphoric acid in %: (EQ2−EQ1) ∗T ∗M∗F1 Content [%]= W∗F2 EQ1, EQ2: Consumption of titrant at the respective equivalence point T: Exact concentration of the titrant M: Molar mass of phosphoric acid 98.00 g/mol F1: 100 (conversion %) H Po with NaOH 0.1 mol/l W: Weighed sample [g] 3 4 F2: 1000 (conversion ml - l) 10 600

9 500

400 7

pH 6 300 dpH/dml

5 200

100 3

2 0 0 2 4 6 8 10 NaOH [ml] mV dmV/dml Fig. 55 Titration curve phosphorous acid with two EQs 106 107 Titration guide

Titration of Alk. 8.2 and Alk.S 4.3 The titration of the alkalinity The following must be (Alk.) is carried out with HCl observed: and determines which pro-  A titer determination takes portions of carbonate and place with TRIS bicarbonate are contained in  The electrode must be cali- the water (Fig. 56). The alkalinity brated. Buffers pH 4.01 and values are a measure of the 6.87 are recommended temporary hardness of the water, which can be removed The following titration by boiling. Scale = lime precip- parameters are recommended: itates during boiling, the CO2 is boiled away. So that the results of manual titration can  Titration to two endpoints pH be compared with an indicator 8.2 and pH 4.3 (phenolphthalein and methyl  Normal (average) titration orange, often referred to as the Speed p and m value), one titrates to  No damping endpoints (pH 8.2 and pH 4.3)  Dosing speed 15 % [6]. The electrode must thus be  Delta value for the linear end calibrated. part: 1.0  Endpoint delay 10 s The basis is the carbonate/hydro-  Linear steps 0.02 ml gen carbonate system in water:

+ - H2CO3 + H2O ↔ H3O + HCO3 - + 2- HCO3 + H2O ↔ H3O + CO3

CO2 + H2O ↔ H2CO3

The endpoint at pH 8.2 corresponds approximately to the carbonate content, the consumption between pH 8.2 and pH 4.3 to the hydrogen carbonate content. One usually titrates with a HCl 0.1 mol/l. 108 109 Titration guide

Formula for the Alk.8.2: Formula for the Alk.4.3:

EP1∗T ∗ M∗ F1 EP1∗T ∗ M∗ F1 Alk. [ mmol /l] = Alk. [ mmol /l] = 8.2 V ∗ F2 4.3 V ∗ F2 EP1: Consumption titrant [ml] EP2: Consumption titrant [ml] to pH 8.2 to pH 4.3 T: Exact concentration of the titrant T: Exact concentration of the titrant M: 1 M: 1 V: Volume sample [ml] F1: 1000 (conversion mol - mmol) F1: 1000 (conversion mol - mmol) V: Volume sample [ml] F2: 1 F2: 1

pH 11.375

10.5

9.625

8.75

7.875 1.92 ml pH 8.200 7.0

6.125

5.25

4.375 6.05 ml 3.5 pH 4.300 ml 0 0.75 1.5 2.25 3.0 3.75 4.5 5.25 6.0 pH/ml

Fig. 56 Titration curve carbonate system with HCl on 2 EPs

108 109 Titration guide Titration of sodium carbonate Sodium carbonate is the sodium The following titration salt of carbon acid. It is titrated parameters are recommended: with hydrochloric acid. Sodium bicarbonate is formed in the  Dynamic titration to two EQs first step, which is converted to  Dynamics: flat carbonic acid in the second step  Dosing speed 100% (Fig. 57).  Normal (average) titration speed +  No damping Na2CO3 + H3O ↔ H O + Na++NaHCO 2 3 With pure sodium carbonate it would be sufficient to calculate NaHCO + H O+ ↔ 3 3 only one EQ. However, if free H O + Na++H CO 2 2 3 alkali is still present or more hydrogen carbonate through One usually titrates with a HCl 0.1 CO intake, the difference of the mol/l. 2 two EQs is often evaluated. The following must be observed:  A titer determination takes place with potassium hydrogen phthalate.

 The electrode can be calibrated. Buffers pH 4.01 and pH 6.87 are recommended. The calibration parameters serve as proof of the state of the pH electrode. The slope should be > 95%.

110 111 Titration guide

Formula for the carbonate in g/l Formula for the hydrogen carbonate in g/l EQ1∗T ∗ M∗ F1 CO 2−[g /l] = 3 V ∗ F2 (EQ2− EQ1)∗ T ∗ M∗ F1 HCO −[g /l] = 3 V ∗ F2 EQ1: Consumption titrant [ml] until the first equivalence point T: Exact concentration of the titrant EQ1: Consumption titrant [ml] until the 2- M: Molar weight of CO3 first equivalence point (60.01 g/mol) EQ2: Consumption titrant [ml] until the V: Volume sample [ml] second equivalence point F1: 1 T: Exact concentration of the titrant - F2: 1 M: Molar weight of HCO3 (61.017 g/mol) V: Volume sample [ml] F1: 1 F2: 1

pH 12.0

11.0

10.0 3.75 ml 9.0 8.346 pH

8.0

7.0

6.0

5.0

4.0 7.46 ml 4.481 pH 3.0

2.0 ml 0 0.875 1.75 2.625 3.5 4.375 5.25 6.125 7.0 7.875 pH/ml dpH/dml

Fig. 57 Titration curve sodium carbonate with two EQs

110 111 Titration guide Determination of pharmaceutical bases as hydrochlorides with NaOH Pharmaceutical bases are usually The following titration titrated in acetic acid with per- parameters are recommended: chloric acid.  Dynamic titration to two equivalence points Another method is the determi-  Normal (average) nation of the hydrochloride of titration speed the base. For this, the sample is  weak damping mixed with an excess of HCl and  Dynamics: steep titrated with NaOH. As the  Titration end: 2 EQs, pKa values of free HCl and the slope value flat hydrochloride differ significantly, one obtains two EQs whose Formula for Lidocaine in % difference corresponds to the hydrochloride of the base. (EQ2 −EQ1) ∗T ∗M ∗F1 Lidocaine [%]= W ∗F2 One example is the determination of lidocaine as hydrochlo- EQ1: Consumption titrant [ml] until the ride. The titration is carried out first equivalence point in ethanol with aqueous NaOH EQ2: Consumption titrant [ml] until the (Fig. 58). The first jump corre- second equivalence point sponds to the excess amount T: Exact concentration of the titrant M: Molar weight of lidocaine (234.34 of HCl (2 ml 0.1 mol/l). The g/mol) difference between the two W: Weighed sample [g] EQs corresponds to the hydro- F1: 0.1 (conversion l – ml and %) chloride of the nitrogen base. F2: 1 PharmEur describes the method with the addition of 5 ml of 0.01 molar HCl (or in an even lower concentration).

112 113 Titration guide

300.0 0.44 ml 244.2 mV

225.0

150.0

75.0

0.0 ml

-75.0

-150.0 8.16 ml -151.5 mV -225.0 0 0.875 1.75 2.625 3.5 4.375 5.25 6.125 7.0 7.875 mV/ml dmV/dml

Fig. 58 Titration curve lidocaine hydrochloride

112 113 Titration guide Determination of pharmaceutical bases with perchloric acid in glacial acetic acid The most common method for The following must be the determination of pharma- observed: ceutical bases is the direct  Determination of a blank titration with perchloric acid in value of the glacial acetic acid glacial acetic acid.  Consideration of the humidity A titer determination of per- of the molecule chloric acid is carried out with potassium hydrogen phthalate.  Humidity in glacial acetic acid A blank value of the glacial or at the sample flattens the acetic acid should be deter- curve mined, even if the PharmEur does not require this. A pH As the jump is very clear, a dy- electrode with a ground-joint namic titration can be performed diaphragm and a filling of LiCl up to an equivalence point. in glacial acetic acid or ethanol A ml end criterion ensures that is used as electrode. In our an overflow of the titration vessel example, the titration of is impossible. diclofenac sodium is shown. Approx. 0.250 g dichlophenac The following titration sodium are dissolved in approx. parameters are recommended: 30 ml glacial acetic acid (Fig. 59 and Fig. 60).  Dynamic titration, mV  Dynamics: average  Normal measurement speed  average damping  Titration end:1 EQ, slope value 300 mV/ml

Fig. 59 Diclofenac sodium

114 115 Titration guide

Formula for diclofenac sodium in %

(EQ1−B)∗ T ∗M∗F1 Lidocaine [%]= W ∗F2

EQ1: Consumption titrant [ml] until the equivalence point B: Blank value of the solvent T: Exact concentration of the titrant M: Molar weight of dichlorfenac sodium (318.1 g/mol) W: Weighed sample [g] F1: 0.1 (conversion l – ml and %) F2: 1

675.0 7.59 ml 641.6 mV

600.0

525.0

450.0

375.0 ml 0 0.875 1.75 2.625 3.5 4.375 5.25 6.125 7.0 7.875 mV/ml dmV/dml

Fig. 60 Titration curve dichlorfenac sodium

114 115 Titration guide Determination of the free fatty acids in vegetable oils (FFA) The determination of free fatty A fixed waiting period of 15 s is acids in unsaturated oils and fats suitable for the blank value. A pH is a measure of their freshness. electrode with a ground-joint The lower the content, the diaphragm and a filling of LiCl in fresher the oils. ethanol is used as electrode.

The titration is carried out with The following titration KOH in isopropanol or ethanol. parameters are recommended: Ethanol/diethyl ether 1:1 is used  Linear titration, mV as the solvent. The blank value  Step size 0.05 ml of the solvent mixture must be  Measuring speed: determined (Fig. 61). Both the Measurement time 4 s titration of the blank value and Drift 10 mV/min of the sample are carried out in a Min time 7 s linear manner. The titration of the Max time 20 s blank value takes place with an  strong damping end consumption of 0.3 ml and  Titration end: 1 EQ, slope an step size of 0.01 ml or 0.02 ml. value flat

0.0 ml

-22.5

-45.0

-67.5 0.05 ml -61.7 mV -90.0

-112.5

-135.0

-157.5

-180.0

-202.5 0 0.05 0.1 0.15 0.2 0.25 0.3 mV/ml dmV/dml

Fig. 61 Blank value solvent mixtures FFA 116 117 Titration guide Formula for FFA in mg KOH / g Formula for FFA in % acid (EQ1−B)∗ T ∗M∗F1 (EQ1−B)∗ T ∗M∗F1 FFA [mg KOH/g] = FFA [%] = W ∗F2 W ∗F2 EQ1: Consumption titrant [ml] until the EQ1: Consumption titrant [ml] until the equivalence point equivalence point B: Blank value of the solvent B: Blank value of the solvent T: Exact concentration of the titrant T: Exact concentration of the titrant M: Molar weight oleic acid M: Molar weight KOH (56.1 g/mol) (282.46 g/mol) W: Weighed sample [g] W: Weighed sample [g] F1: 1 F1: 0.1 (conversion l – ml and %) F2: 1 F2: 1 The adaptation of the amplifier The sample for FFA should be to the titration in organic media is in the range of 0.2 - 1 mg KOH/g important. The adaptation of the at 10 - 20 g and in the range of damping has been proven to be 1 - 10 mg KOH/g at 1 - 3 g. efficient, which can be adjusted in the method parameters. The In the example, the FFA is given strongest damping is adjusted as mg KOH/g. In other cases, here (Fig. 62). however, the reference magnitude is not the amount of KOH, but the molecular weight of the titrated oil, usually the oleic acid (molar weight 282 g/mol) is assumed: mV

50.0

0.0

-50.0

-100.0 1.81 ml -92.9 mV

-150.0

-200.0

0 0.375 0.75 1.125 1.5 1.875 2.25 mV/ml dmV/dml Fig. 62 Titration curves FFA in rapeseed oil 116 117 Titration guide Determination of acids in oil (TAN, ASTM 664) The titration of acids in oils is one A titer determination is carried of the most difficult applications. out with potassium hydrogen A mixture of toluene (50%), phthalate and the blank value of isopropanol (49.5%) and water the solvent is determined. The (0.5%) is often used as solvent. blank value is performed as an Titrant is KOH in isopropanol. EQ titration. The challenge for the pH electrode is the titration in a medium The titration of the blank value that contains hardly any protons is carried out as a linear titration or ions at all. In addition, the glass with steps size of 0.01 ml up to membrane is occupied by the oil, an EQ or a consumption of about which additionally complicates 0.3 ml. One preferably titrates an exchange [5]. with a fixed waiting time of 10 to 20 s. At a higher consumption, A pH electrode with ground-joint the solvent mixture should be diaphragm is used, with LiCl exchanged. in ethanol as electrolyte. The electrode must be cleaned, In some cases it is so small that conditioned and be re-adapted no EQ can be detected. Then, to the solvent after each titration. one titrates with very small steps, For this, the electrode is rinsed e.g. 0.004 ml to the potential at successively in different solvents: which the EQ of the sample is found.  1 minute in toluene or toluene/ isopropanol  1 minute in water  1 minute in clean toluene/ isopropanol / water.

118 119 Titration guide

Fig. 63 shows a typical titration Fig. 64 shows the titration curve curve for the blank value of the of a used transformer oil. The EQ solvent mixture. Here the BW is can be evaluated very well here. high enough to detect an EQ. For different oils, the titration curve may be too shallow or too The TAN titration is carried out restless to detect an EQ. In this in a linear manner. The titration case, one has to titrate to an end end is set to 4 to 6 ml or until an potential. The potential which EQ is detected. The drift is often adjusts at the electrode in an parameterized with a fixed aqueous buffer of pH 11 is used waiting time of 15 s. This as the end potential. waiting time is adapted to the sample until a titration curve results, which enables a clear evaluation of the EQ.

mV 80.0

60.0

40.0

20.0

0.07 ml 13.0 mV 0.0 ml

-20.0

0 0.0125 0.025 0.0375 0.05 0.0625 0.075 0.0875 0.1 0.1125 mV/ml dmV/dml

Fig. 63 Blank value titration TAN

118 119 Titration guide The following titration Formula for TAN in mg KOH / g parameters are recommended: (EQ1− B)∗ T∗M∗F1 TAN [mg KOH/ g]=  Linear titration, mV W ∗F2  Step size 0.05 ml EQ1: Consumption titrant [ml] until the  Measuring speed: equivalence point fixed waiting time 15 s or B: Blank value of the solvent measurement time 4 s T: Exact concentration of the titrant Drift 10 mVmin M: Molar weight KOH (56.1 g/mol) Min time 7 s W: Weighed sample [g] Max time 20 s F1: 1 F2: 1  strong damping  Titration end: 1 EQ, slope value flat

150.0

100.0

50.0

0.0 ml

2.94 ml -50.0 -34.2 mV 0 0.375 0.75 1.125 1.5 1.875 2.25 2.625 3.0 mV/ml dmV/dml

Fig. 64 Titration curve TAN of an oil sample

120 121 Titration guide Determination of bases in oil (TBN, ISO 3771) The base number in oils, like A rule of thumb for the sample TAN, is a sum parameter and amount is: g sample = 28 / ex- is determined according to pected TBN. The TBN titration is ASTM 2896 / ISO 3771. carried out as a linear titration. The titration end is set to 4 to A pH electrode with a ground- 6 ml or until an EQ is detected joint diaphragm and LiCl in (Fig. 65). The step size should not glacial acetic acid is used as the be too small, e.g. 0.1 ml. electrolyte. If the base number of the sample is not too low, The titration is carried out as a it is also possible to work with mV titration either drift-controlled LiCl/ethanol. Many electrode or with a fixed waiting time of adhesives are not resistant to 15 - 20 s. acetic acid. The electrolyte LiCl in glacial acetic acid should therefore only be filled into electrodes that are intended for this purpose.

The solvent for the titration is acetic acid/chlorobenzene, the titrant is perchloric acid in glacial acetic acid. Potassium hydrogen phthalate is used for the titer determination. The blank value of the solvent must be determined. The result is calculated as mg KOH needed to neutralize 1 g of sample. The consumption should not exceed 4-6 ml, the sample amount must be adjusted accordingly.

120 121 Titration guide The following titration Formula for TBN in mg KOH / g parameters are recommended: (EQ1− B)∗ T∗M∗F1 TBN [mg KOH/ g] =  Linear titration, mV W ∗F2  Step size 0.1 ml  Measuring speed: EQ1: Consumption titrant [ml] until the Measurement time 4s equivalence point Drift 10mV/min B: Blank value of the solvent Min time 7s T: Exact concentration of the titrant Max time 20s M: Molar weight KOH (56.1 g/mol) or fixed waiting time 15-20 s W: Weighed sample [g]  strong damping F1: 1 F2: 1  Titration end: 1 EQ,  Slope value flat

mV 750.0

700.0 3.25 ml 668.2 mV

650.0

600.0

550.0

500.0

450.0 ml 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 mV/ml dmV/dml

Fig. 65 Titration curve TBN

122 123 Titration guide 6.2 Argentometric titrations

Argentometric titrations are AgNO3 is used as titration solu- carried out with silver nitrate trion. The concentration can be as titrant and silver electrodes. 0.001 to 0.1 mol/l. The potential A combination electrode with jump is more pronounced, the silver indicator electrode and higher the concentration (Nernst Ag/AgCl reference electrode law). As it is a precipitation is usually used. The reference titration, the formed precipitate electrolyte should contain as few can contaminate the electrode

chloride ions as possible: KNO3 and disrupt the titration. This can 2 mol/l with little KCl (0.001 mol/l) be prevented by the addition of is recommended. polyvinyl alcohol (1 ml of a 0.5% PVA solution). Such an addition The reaction equation is as fol- is not necessary with very low lows: contents. The titration must take place in an acid environment AgNO3+NaCl → + - so that no silver hydroxide is Na + NO3 +AgCl↓ formed. Diluted HNO3 is suitable for acidification. For samples in which the pH is constant or also in organic The titration can be carried solvents, a silver electrode can out with samples with chloride be used which has a glass elec- contents of a few ppm - 100%. trode as the reference electrode. Depending on the chloride Due to its resistance, the glass content, the amount of sample electrode is connected to the should be adjusted: indicator measuring input and the silver indicator electrode to Chloride content [%] weighed the reference measuring input. sample [g] < 0.1 > 10 0.1 – 1 1 – 10 1 – 10 0.1 – 2 10 - 50 0.05 - 0.1 50 – 100 0.05

122 123 Titration guide Titration of salt in butter For food, sample preparation The following titration is important to capture all the parameters are recommended: chloride. Often the sample is  Dynamic titration to an crushed (also automatically with equivalence point a homogenizer) or stirred in hot  Dynamics: steep water.  Measuring speed: Measurement time 3 s Approximately 2-3 g of butter Drift 10 mV/min are weighed in, 100 ml of boil- Min time 3 s Max time 15 s ing water is added, 1 ml of HNO3 1 mol/l is added, the electrode  no damping  and the titration tip are dipped Titration end: 1 EQ, Slope value 400 into the solution and the titration is started. The titration is carried Formula for sodium chloride out up to an EQ (Fig. 66). It can be in % seen from the increasing titration (EQ1−B) ∗T ∗M∗F1 curve that an Ag indicator NaCl [%]= electrode and an Ag/AgCl refer- W ∗F2 ence electrode were used here. The result is calculated as % NaCl. EQ1: Consumption titrant [ml] until the equivalence point B: Blank value of the solvent T: Exact concentration of the titrant M: Molar weight NaCl (58.443 g/mol) W: Weighed sample [g] F1: 0.1 (conversion l – ml and %) F2: 1

124 125 Titration guide

mV 200.0 175.0 7.25 ml 150.0 141.8 mV 125.0 100.0 75.0 50.0 25.0 0.0 ml -25.0 0 0.875 1.75 2.625 3.5 4.375 5.25 6.125 7.0 mV/ml dmV/dml

Fig. 66 Titration curve chloride in butter

Titration of chloride in drinking water Up to 250 mg/l of chloride may The following titration be contained in drinking water, parameters are recommended: thus significantly less than e.g. in  Dynamic titration to an butter. The titration is analogous equivalence point to the titration of salt in butter,  Dynamics: steep only the slope of the EQ has to  Measuring speed: be adjusted due to the flatter Measurement time 3 s jump. Drift 10 mV/min Min time 3 s 100 ml water is mixed with 1 ml Max time 15 s

HNO3 1 mol/l and the titration  no damping is started. The curve in Fig. 67  Titration end: 1 EQ, gradient shows a falling titration, typical value 150 mV/ml for a silver electrode with a glass reference electrode. The calculation takes place as mg Cl/l.

124 125 Titration guide Formula for chloride in mg/l

− (EQ1− B)∗ T∗M∗F1 Cl [ mg /l] = V∗ F2

EQ1: Consumption titrant [ml] until the equivalence point B: Blank value of the solvent T: Exact concentration of the titrant M: Molar weight Cl- (35,45 g/mol) V: Volume sample [ml] F1: 1000 (conversion g – mg) F2: 1

120.0

100.0

80.0

60.0

40.0

20.0

0.71 ml 0.0 13.6 mV ml

-20.0

-40.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 mV/ml dmV/dml

Fig. 67 Titration curve chloride in drinking water

126 127 Titration guide 6.3 Potentiometric redox Iodine number for character- titrations izing fats and oils In redox titrations, oxidizable or In the determination of the reducible samples are titrated iodine number of an oil or fat, with oxidizing or reducing the oxidizable components and agents. double bonds are determined. The more double bonds an oil Titrations with oxidizing agents contains, the higher the iodine generally show increasing titra- number. The iodine number is tion curves falling with reducing defined as the amount of iodine agents. A titer determination of that can be added to 100 grams the titrant is recommended. of fat or oil. The detection is performed with a combined platinum indicator One form of the determination electrode with an Ag/AgCl refer- takes place according to ence electrode. DIN 53241-1:1995-05 with Wijs reagent (organic solvent, acetic The titrations can be carried acid, iodine, iodine trichloride). out as direct titration or as back In an upstream reaction, the titration. iodine trichloride and iodine react to iodine monochloride. In the back titration, e.g. an The reaction mixture must excess of oxidant is added and be anhydrous, otherwise the the reagent which is not convert- formed iodine monochloride will decompose to HCl, I and ed is back titrated with a reduc- 2 ing agent. Even if back titration HI. ICl + I 3ICl shows the errors of back and 3 2 → forth titration, benefits such as faster response and better detec- However, iodine monochloride tion are clearly in the foreground. in pure form is also available, so that one can also use a solution of iodine monochloride in glacial acetic acid (16.2 g / l).

126 127 Titration guide The iodine monochloride reacts The sample is weighed into a in an electrophilic addition to the 200 ml Erlenmeyer flask, 20 ml double bond of the oil: of glacial acetic acid, 25 ml of iodine monochloride solution R1CH = CH - R2 + ICl → and 20 ml of magnesium acetate

R1CHI - CHCl - R2 solution are added. The flask is closed, shaken, allowed to stand The excess iodine monochloride in the dark for 5 minutes and ti- is converted with KI to I : 2 trated after addition of 15 ml of

ICl + Kl → I2 + KCl KI solution and 50 ml of distilled water (Fig. 68). The resulting I2 is then titrated with sodium thiosulphate in a 1:1 reaction: A blank value titration is carried out under the same conditions. I + 2 NA S O 2 2 2 3 → As it is a back titration, the

2 NaI + Na2S4O6 consumption of the sample is subtracted from the blank value The iodine monochloride is (Fig. 69). dissolved in glacial acetic acid (16.2 g/l), the KI solution is aqueous (25 g/250 ml), magnesium acetate (45 g/l glacial acetic acid) is used as catalyst.

350.0

300.0

250.0 45.89 ml 250.2 mV

200.0

150.0 ml 0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 mV/ml dmV/dml

Fig. 68 Titration curve blank value iodine number 128 129 Titration guide The following titration para- Formula for iodine number in

meters are recommended for g(iodine/100g(sample) the titration and blank value determination: (B−EQ1) ∗T ∗M∗F1  Dynamic titration to an IZ = W ∗F2 equivalence point  Dynamics: average  Measuring speed: B: Consumption without sample Measurement time 3 s EQ1: Consumption titrant [ml] until the Drift 10 mV/min equivalence point T: Exact concentration of the titrant Min time 3 s M: Molar weight I (126.9 g/mol) Max time 15 s W: Weighed sample [g]  no damping F1: 0.1 (conversion l – ml and  Titration end: reference to 100 g) 1 EQ, slope value 350 F2: 1

350.0

300.0

250.0 28.79 ml 247.6 mV

200.0

150.0 ml 0 5.0 10.0 15.0 20.0 25.0 mV/ml dmV/dml

Fig. 69 Titration curve iodine number of olive oil 128 129 Titration guide Determination of the vitamin C content with DCPIP Vitamin C is added to many As the DCPIP is not very stable, drinks as an antioxidant and also the titer is determined with specified with its content. Lots of freshly dissolved ascorbic acid natural vitamin C contain citrus in a first titration. Fig. 71 and 72 fruits and their juices. show the titration curve with calculations for the titer determi- The titration of ascorbic acid = nation and sample titration. vitamin C is possible as a redox titration with DCPIP (di-chloro- For the preparation of the DCPIP phenol-indo-phenol) (Fig. 70). solution, 163.1 mg of DCPIP is The ascorbic acid reduces the added to 250 ml water and stirred disodium DCPIP (Tillmann's at 50° C for 20 minutes. The solu- reagent), a 1:1 reaction. As the tion is then filtered, transferred to redox potential drops during a 500 ml volumetric flask, 50 mg

the titration and then increas- KHCO3 (for stabilization) added es again, a large step is initially and filled up to 500 ml. For the dosed before the titration is titer determination, freshly pre- continued in a linear manner. pared ascorbic acid solution is The blue DCPIP is decolourized used: 50 mg of ascorbic acid is during the titration. dissolved in water in a 100 ml volumetric flask, 10-20 ml of oxalic acid solution (100 g/l) is added and filled up to 100 ml.

Fig. 70 Redox reaction DCPIP

130 131 Titration guide

For the titer determination, 10 ml The following titration of oxalic acid solution (100 g/l), parameters are recommended: 15 ml of distilled water and 1 ml  Linear titration to an of sodium acetate solution equivalence point (100 g/l) are placed in a beaker,  Step size: 0.05 ml 1 ml of the ascorbic acid solution  Measuring speed: is added and is titrated with the Measurement time 2 s DCPIP solution. Drift 40 mV/min Min time 5 s Max time 10 s  Pre-titration 1.2 ml, 10s waiting time  no damping  Titration end: 1 EQ, slope value 80

320.0

300.0 2.97ml 294.7mV

280.0

260.0 ml 0 0.375 0.75 1.125 1.5 1.875 2.25 2.625 3.0 mV/ml dmV/dml

Fig. 71 Titer determination of DCPIP with ascorbic acid 130 131 Titration guide For the titration of a juice Formula for ascorbic acid sample, 0.5 - 5 g of sample mg/100g are mixed with 40 ml of oxalic (EQ1−B)∗ T ∗M∗F1 Ascorbic acid [mg/100g] = acid solution (100 g/l) and 1 ml W ∗F2 of sodium acetate solution (100 g/l). 40 ml water is added EQ1: Consumption titrant [ml] until the after 5 minutes and titrated with equivalence point B: Blank value of the solvent DCPIP (Fig. 72). T: Exact concentration of the titrant M: Molar mass of ascorbic acid The following titration (176.12 g/mol) parameters are recommended: W: Weighed sample standard/sample  Linear titration to an F1: 100 (conversion l – ml, g - mg, equivalence point reference to 100 g)  Step size: 0.05 ml F2: 1  Measuring speed: fixed waiting time 7 s  no damping  Titration end: 1 EQ, slope value 80

mV 310.0

300.0 2.78ml 292.3mV 290.0

280.0

270.0

260.0

250.0 ml 0 0.375 0.75 1.125 1.5 1.875 2.25 2.625 3.0 mV/ml dmV/dml

Fig. 72 Titration ascorbic acid in a drink

132 133 Titration guide 6.4 Dead Stop Titrations The Dead Stop titration can be used when reversible redox pairs occur. An important Indication example is the titration with iodine. The detection with a double platinum electrode proceeds much faster than the potentiometric detection with a platinum redox electrode. At the endpoint of the titration, both iodine and iodide ions are present in the solution. Two anions of iodide migrate to the anode and release two electrons there. At the cathode, the iodine absorbs two electrons and reacts to form two iodide ions. With an applied (low) voltage (approx. 100 mV) a current flows, which is detected (Fig. 73). + -

- 2 I I2

Fig. 73 Reversible redox reaction of iodine

132 133 Titration guide Direct iodometric determination of vitamin C The iodometric titration of ascor- The following titration bic acid is usually performed as parameters are recommended: a Dead Stop titration. It is the  Dead Stop Titration usual titration for many drinks. As  linear step: 0.02 ml sulfite ions can also be present  Pre-titration: 0.1 ml in drinks, they must be converted  Dosing speed: 20 % with glyoxal.  Titration direction: increasing 50 ml of sample and 2 ml of  Measuring speed: glyoxal solution (40% in water, fixed waiting time 1 s adjusted to pH 7 with NaOH)  Polarization voltage 100 mV are placed into a beaker. After  Delta endpoint: 2.0 µA 5 minutes, 5 ml of 25% sulfuric  Titration end: 2.5 µA acid are added and titrated with  Endpoint delay: 5 s 0.01 mol/l iodine solution. The content is calculated as acorbic acid mg / l. Formula for ascorbic acid mg/l

In our example (Fig. 74), the Ascorbic acid [mg/l] = ascorbic acid content of a fruit (EP1− B)∗T ∗ M∗ F1 juice was determined. The iodo- V ∗ F2 metric determination offers - de- spite the lower selectivity - some EP1: Consumption titrant [ml] until the advantages over the titration endpoint B: Blank value of the solvent with DCPIP: T: Exact concentration of the titrant M: Molar weight ascorbic acid Iodine solutions are significant- (176.12 g/mol) ly more titer-stable than DCPIP V: Volume sample [ml] solutions, additionally iodine F1: 1000 (conversion g – mg) F2: 1 standard solutions are available in various concentrations.

134 135 Titration guide

µA

3.5 3.0 µA 0.909 ml 3.0

2.5

2.0

1.5

1.0

0.5

0.0 ml

-0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 µA/ml

Fig. 74 Titration curve ascorbic acid with iodine

Determination of the SO2 content in wine Wine is protected from oxidation The titre of the iodine solution

by adding SO2. Free and bound can be determined with thio-

SO2 are therefore differentiated. sulphate solution (Fig. 75). If additionally ascorbic acid is

The free SO2 is determined by present in the sample, the sum adding 3 ml sulfuric acid 10%, of all reductones is titrated in

30 mg Na2EDTA and 10 ml this application. The ascorbic KI solution (5%) to the 50 ml acid can be determined after sample in a beaker and titrating the addition as described in the immediately with iodine. The section "Direct iodometric deter-

total SO2 is determined by mination of vitamin C" according adding 8 ml 4 mol/l NaOH to to the reaction of SO2 with glyoxal. a 50 ml sample and waiting 5 minutes. Then 10 ml of 10% sulfuric acid are added and titrated immediately with iodine.

134 135 Titration guide

The following titration Formula for SO2 in mg/l parameters are recommended: (EQ1− B)∗ T ∗ M∗ F1 SO [mg/l] =  Linear step: 0.02 ml 2 V ∗ F2  Pre-titration: none EP1: Consumption titrant [ml] until the  Dosing speed: 20 % endpoint  Titration direction: B: Blank value of the solvent increasing T: Exact concentration of the titrant

 Measuring speed: M: Molar weight SO2 (64.06 g/mol) fixed waiting time 1s V: Volume sample [ml] F1: 1000 (conversion g – mg)  Polarization voltage 100 mV F2: 1  Delta endpoint: 1.0 µA  Titration end: 2.0 µA  Endpoint delay: 5 s

µA 3.0

2.625

2.25 2.0 µA 1.581 ml 1.875

1.5

1.125

0.75

0.375

0.0 ml 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 µA/ml

Fig. 75 Titration curve SO2 in wine 136 137 Titration guide 6.5 Complexometric titration Complexometry enables the At high pH values, the hydroxide determination of numerous formation is a competitive metal ions. Chelate complexes reaction. Work is often done in have higher stability than com- ammoniacal solutions. plexes with several smaller ligands for two reasons: The detection of the titration is carried out with ion-sensitive  One molecule instead of indicator electrodes (ISE) and a several small ligands reacts (usually separate) Ag/AgCl refer- with a central atom ence electrode, preferably with (entropy effect) a platinum diaphragm.  If a bond is free, the metal central atom still remains bonded

Na2EDTA, di-sodium-ethylene- diamine-tetra acetic acid is often used. The stability of the complexes there depends on the pH. The higher the pH value, the more stable the complex. In acidic solution, the less dissociated acid provides less complexation possibilities. The pH dependence of the complex stability can be exploited during the titration. Stable complexes can still be titrated in acid, while less stable complexes require a high pH value.

136 137 Titration guide Calcium and magnesium in drinking water In drinking water, calcium and If the pH value decreases, magnesium form the permanent the Mg complex becomes less hardness of the water as cations. stable and the Ca jump more The determination of water hard- pronounced. The first derivation ness is an important parameter shows to peaks of an approx- of water chemistry. Calcium and imately same height. If the pH magnesium can be determined value is too low, Mg can no next to each other with Na2EDTA longer be detected, but the and a calcium-sensitive electrode. Ca complex also becomes less stable, the potential jump will be Two potential jumps occur flatter. during titration (Fig. 76). Their form can be influenced by the In practice, one titrates at a pH pH value and the addition of value of about pH 8-9. Acetyl- auxiliary complexing agents. At acetone and TRIS are added as a very high pH value, the weaker auxiliary complexing agents. Mg complex is also stable and the difference between the Ca In the titration of tap water, and Mg complex in the potential 100.00 ml of the sample are is very low. This means that first pipetted into a 150 ml beaker. the stronger Ca complex forms, 15 ml TRIS/acetylacetone buffer but that the Mg jump follows (20.4 g TRIS and 12 ml acetyl soon. acetone to 1000 ml) are added and titrated with 0.05 mol/l EDTA. The first derivation therefore shows only a flat first jump A Ca-ISE indicator electrode and for the calcium. Only after the an Ag/AgCl reference electrode magnesium, if no other metals with a platinum diaphragm are are present, comes a strong used as electrodes. jump.

138 139 Titration guide

The following titration M: Molar mass of CaO parameters are recommended: (56.08 g/mol) V: Volume sample [ml]  Dynamic titration F1: 1000 (conversion g – mg)  Dynamics: flat F2: 1  Dosing speed 100%  Measuring speed: Formula for magnesium oxide Measurement time 4 s Drift 5 mV/min [mg/l] Min time 5 s (EQ1−EQ2)∗ T ∗M∗F1 Max time 12 s MgO [mg /l] = V ∗F2  no damping  Titration end: 2 EQ, EQ1: Consumption titrant [ml] until the  slope value 120 first equivalence point EQ2: Consumption titrant [ml] until the Formula for calcium oxide [mg/l] second equivalence point B: Blank value of the solvent (EQ1−B) ∗T ∗M ∗F1 CaO [mg /l] = T: Exact concentration of the titrant V ∗F2 M: Molar mass of MgO EQ1: Consumption titrant [ml] until the (40.32 g/mol) equivalence point V: Volume sample [ml] B: Blank value of the solvent F1: 1000 (conversion g – mg) T: Exact concentration of the titrant F2: 1

mV 40,0

20,0

0,0 2.48 ml ml -15.1 mV

-20,0

-40,0

-60,0

-80,0 3.18 ml -100,0 -84.8 mV

0 0,375 0,75 1,125 1,5 1,875 2,25 2,625 3,0 3,375 mV/ml dmV/dml Fig. 76 Titration curve drinking water 138 139 Titration guide Total hardness in drinking water If the total hardness is to be The following titration determined, it often makes parameters are recommended: sense to have only one jump in  Dynamic titration the titration curve (Fig. 77).  Dynamics: flat In this case, the sum of  Dosing speed 100% all metals is determined.  Measuring speed: A Cu-ISE indicator electrode Measurement time 4 s (solid-state electrode) and an Drift 3 mV/min Ag/AgCl reference electrode Min time 5 s with a platinum diaphragm is Max time 12 s used as indicator electrode.  no damping So that all metals can be detect-  Titration end: 1 EQ, slope ed, Cu(NH4)2EDTA 0.1mol/l is value 120 mV/ml added as indicator. With very small contents (< 0.1 °dH), a Formula for water hardness blank value must be determined. [mmol/l] (EQ1−EQ2)∗ T ∗M∗F1 Water hardness [mmol/l]= Almost all divalent metal ions can V ∗F2 be titrated in the same manner. The water hardness is nowadays EQ1: Consumption titrant [ml] until the given mainly in mmol/l alkaline equivalence point earth ions. From this it is easy to B: Blank value of the solvent T: Exact concentration of the calculate the water hardness in titrant [mol/l] other units such as °dH or °fH. M: 1 V: Volume sample [ml] 5 ml of ammonium chloride/am- F1: 1000 conversion g – mg monia buffer pH 10 are added F2: 1 to a 100 ml sample and 1 ml of indicator Cu(NH4)2EDTA 0.1 mol/l is added, then one titrates with

Na2EDTA 0.05 mol/l.

140 141 Titration guide

120.0

100.0

80.0

60.0

40.0

20.0 0.71 ml 0.0 13.6 mV ml

-20.0

-40.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 mV/ml dmV/dml

Fig. 77 Titration curve drinking water

140 141 Titration guide 6.6 Determination of molecular weights by titration Titration is usually a method for The formula indicates the acidity the quantitative determination in % of a salicylic acid solution of known samples. The method having a molecular weight of can also be used for the deter- 138.12. However, if the content is mination of substance sizes if the known very accurately (because content of a sample is clearly and a pure compound is present), precisely known. the molecular weight can becal- culated from the consumption: The simplest case is a reversal of W ∗F2∗[%] the calculation formula for the Molar mass [g/ mol]= EQ∗T ∗ F1 determination of salicylic acid: W: Volume EQ ∗T ∗M∗F1 [%]: Content in % Salicylic acid [%]= W ∗F2 EQ: Consumption titrant [ml] until the equivalence point EQ: Consumption titrant [ml] until the T: Exact concentration of the titrant equivalence point [mol/l] T: Exact concentration of the titrant F1: 0.1 (conversion l-ml and %) [mol/l] F2: 1 M: Molar weight [g/mol] W: Volume If a compound is thus prepared F1: 0.1 (conversion l-ml and %) in pure form, its molecular weight F2: 1 can be determined in this manner. The most common application is certainly the determination of the crystal water of a molecule, as the molecular weight changes significantly with crystal water.

142 143 Titration guide

6.7 Determination of pKs values

Further substance-specific para- At the point on the titration curve meters can be determined from where HAc and acetate ions have

the titration curve: pKs value the same concentration, the pH is

(acid strength), pKb value (base equal to the pKs value: strength), complex stability pH = pK constants, solubility products, s stability constants and extraction This point, the half neutralization equilibria. point (HNP), can be read from the titration curve (Fig. 78). As an example, a simple possibility serves for the determination In methods for determining the of the pK value: s pKs value, the equivalence point is thus determined first. The pK HAc + H O ↔ H O+ + Ac- s 2 3 value is then determined from Here, the HAc acetic acid is an the titration curve suring the con- example of a monobasic acid sumption EQ/2 ("y at x"). This is which dissociates in water to also possible with several jumps a hydronium ion and acetate and EQs in a first approximation. anion to a small extent. The concentration of water is considered constant in diluted solutions and is included in the equilibrium constant. [H O+]∗[Ac−] K = 3 s [HAc] The negative logarithm of the equation is: [Ac−] pK = pH−log s [HAc]

142 143 Titration guide

However, the pKs values thus Special software (for example obtained are still subject to small Hyperquad) is used for the eval- errors. In order to accurately uation. determine the pKs value of an acid, other factors must be considered, for example:

 Electrode properties (Slope, zero point, deviation from the theoretic behavior in acid and alkaline)  The ion activities instead of the concentrations  Evaluation of a larger curve area instead of an individual data point

Acetic acid with sodium hydroxide 9

8 Titration degree = 1

pH Titration degree = ½

At titration graph 1/2: pKs = pH 5

3 0 5 10 15 20 25 ml NaOH

Fig. 78 Graphic representation of the pKs value from the HNP point

144 145 Titration guide An interesting variant is the rep- The advantage of this represen- resentation of an acid profile. tation is evident in applications The pH value of a titration curve where several acids or acid is plotted on the x-axis and the centers are present in a molecule. quotient dml/dpH on the y-axis, In all cases, it is sensible to have similar to the gradient of the more data points in the flat part titration curve, only transferred of the titration. Dynamic titration

to the normal pH-y axis. The pKs is therefore unsuitable and linear value can be recognized as the titration is the method of choice. maximum (Fig. 79).

16 Proﬁle acid strength acetic acid

dml/dpH 8

0 3 4 5 6 7 8 9 10 pH

Fig. 79 Graphic representation of the acid strength with pKs value as maximum

144 145 Titration guide 6.8 pH Stat titrations The titration is divided into phases; an setting phase in pH Stat titrations can cover very which the starting pH must first different applications. Even an- be reached, at which the reac- alog potentials of other sensors tion proceeds optimally and a can be kept constant. Stat phase in which a defined pH value or measured value Typical applications are: must be maintained (Fig. 81).  Enzymatic titrations in which The following can be consulted protons are released. as the result:  Extraction reactions, e.g. of soil samples from which alkaline  The total consumption [ml] acid components are released  The consumption of the Stat for 24 hours by an acid. phase without setting phase  Stability studies of e.g. [ml] concrete at very low pH values,  The gradient of the Stat phase in order to get an idea of the consumption per time [ml/s] corrosion behavior. or [mmol/s]  Crystal growth, in which the ions, which are removed by The duration of the stat phase crystallization from the solu- starts when the pH value of the tion, are supplied continuously reaction is reached. Two different in order to always obtain the times can be set as time variable; same concentration. the total duration of the titration  Neutrality reactions over a lon- and the interval for the docu- ger period of time. mentation. The total duration is the period during which the pH In the pH Stat titration, one often value is kept constant. The time works under nitrogen at an accu- interval defines the number of rately set temperature to prevent measurement points for the the influence of CO from the air. 2 documentation. One also titrates between these intervals and the pH is kept constant.

146 147 Titration guide

If a titration takes 24 hours, that Time NaOH pH value are recorded every five minutes. [s] [ml] [pH] 288 value triplets with consump- … … … tion [ml], time [s] and pH value 44.013 3.509 6.905 [pH] are obtained. 46.014 3.574 7.116 48.016 3.624 6.984 Fig. 80 shows a data section of 50.018 3.724 6.977 52.02 3.759 6.987 the pH Stat titration from Fig. 81 54.021 3.857 6.957 with a recording frequency of 56.023 3.874 7.043 two seconds. A pH value around 58.024 3.974 6.874 pH 7.00 is kept constant. 60.025 4.024 7.073 62.026 4.106 6.867 The pH value is kept very 64.028 4.174 7.089 constant on average between … … … the documented time and volume values. Fig. 80 pH-Stat table with an interval of 2 s

pH is kept constant 10 Duration8

9 7 8 6 7 5 6 ml ml NaOH 5 4 pH pH Continuous addition, gradient = 4 reaction speed 3 3 2 2 NaOH is added, until the starting pH value is reached = setting phase 1 1

0 0 0 50 100 150 200 250 Dauer [s]

Fig. 81 pH-Stat titration curve with the phases of the pH Stat titration 146 147 Titration guide 6.9 Gran titrations (and the highest value is scaled to 1), the green straight line in The Gran titration is led back to Fig. 82 is obtained. The "Gran" two publications by Gunnar Gran values do not reach the value [7], [8]. It is based on a lineariza- "0", but they become very small. tion of titration curves. If a straight line is now placed through the Gran function The basis is the Nernst equation: until just before the equivalence R ∗ T a E = E0 + ∗ln ox point, the Gran line will intersect ∗ ze F a red the x-axis exactly at the equiva- E Electrode potential lence point. The values can also E° Standard electrode potential be extrapolated linearly, the R Universal or molar gas constant titration does not have to reach R = 8.314 J mol−1 K−1 T absolute temperature this point then. The advantage (=Temperature in Kelvin) is of course that "later" distur- ze Number of electrons transferred bances are not included. (also equivalence number) F Faraday constant, Analogously, the excess of F = 96485.34 C mol−1 a Activity of the respective redox hydrochloric acid can be calcu- partner lated back to the last equivalence point with the Gran function, in The acid/base equilibrium is that the pH value is used as a contained in the equation in a negative exponent in the Gran logarithmic form. An exponential equation: notation thus leads to a linear- ization of the titration curve. (Start volume+ Thus if, taking into account the titration volume) *10-pH volume correction, a titration of a base with a strong acid is cal- This Gran function can be seen culated according to the formula as an orange function in Fig. 82. In order to detect no further bas- (Start volume+ es or acids, the straight line area titration volume) *10pH must not be placed too close to the equivalence point.

148 149 Titration guide This opens up the possibility  Acid samples in which acid/ of a number of applications. base titrations falsify metals Whenever the endpoint or by hydroxide formation at the equivalence point is disturbed equivalence point. by other effects, Gran titration is an alternative. Examples are:  The pH value of the equivalence point must not be  Determination of the acid reached because a subse- capacity in waters where quent reaction is then no other acids (humic acids, longer possible. phosphates) than carbonic acid interfere with the usual endpoints.

1.2

10 0.8

8 ]

H 0.6 p [ Gran scaled 6 0.4

4 0.2

2 0 0 10 20 30 40 50 60 70

HCl [ml]

pH Gran base 10^pH Gran acid 10^-pH

Fig. 82 Gran function at a titration of NaOH with HCl

148 149 Titration guide A widely used application is the The titration is carried with HCl determination of alkalinity in up to a value of pH 3.0 . For a seawater [9]. range of pH 4.0 to 3.0, a Gran evaluation takes place. The standards In Fig. 83, the classic titration ISO 22719:2008 [9] ASTM curve is shown in dark blue. The D3875 - 08 [10] ASTM D1067 - evaluation range of the Gran 06 [11] ASTM D513 - 06 [12] titration is marked with dark describe methods for determin- blue dots. The light blue first ing the hydrogen carbonate or derivation shows how difficult the alkalinity for various waters. it would be to calculate an Even in wooded areas, a simple equivalence point or endpoint. endpoint titration is often not The Gran function is represent- possible due to humic acids [13]. ed in red and orange. For the evaluation range between pH The determination of the alka- 4 and 3, the Gran straight line linity should be picked out here. is marked with red dots. The

The CO2 equilibrium has a large extrapolation of the Gran influence on our climate. A straight line with the x-axis gives multiple of the CO2 content of the alkalinity. the atmosphere is dissolved in seawater. If the pH value The excess of hydrochloric acid decreases and/or the tempera- is calculated back to the last EQ ture increases, less CO2 dissolves by means of the Gran evaluation. in the seawater. The change of As a result, disturbances in the the pH value is called acidifica- area of the EQ have no influence tion. Instead of a pH value of 8.3, on the result. nowadays only a pH 8.1 is usually reached.

150 151 Titration guide

Alkalinty

pH values Selection Gran (^-pH) Gran (^pH)

Gran pH 3-4 Derivation Linear (Gran pH 3-4)

1.000

8.00 0.900

0.800 7.00 0.700

0.600 6.00

H 0.500 p

y = 1.7463x - 2.1402 Gran R² = 0.9998 0.400 5.00 0.300

4.00 0.200

0.100

3.00 0.000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ml HCl

Fig. 83 Gran titration of sea water

150 151 Titration guide SECTION 7 PHOTOMETRIC TITRATIONS

Classic titrations usually work  Acid / base titrations in aque- with an optical indicator, in order ous and organic solvents to display the end of a titration  Complexometric titrations (also see section 2.5 “Manual  Redox titrations titration”). Many standards there-  Precipitation titrations fore still require the use of optical indicators nowadays. The use of Tyical application examples for a photometric sensor to detect photometric sensors are: the endpoint offers several advantages:  Determination of chondroitin sulphate sodium according  Objective evaluation of the to Ph.Eur. and USP. colour change  Determination of carboxyl end  Possibility of method automa- groups in PET according to tion ASTM D7409  Low-maintenance sensor  TAN/TBN according to ASTM  Inert against most solvents D974  Simple operation  Titration of sulphate (indicator  Long lifetime thorin)  Complexometric determina- As optical indicators exist for tion of the total hardness almost all titration applications, a photometric sensor also has a correspondingly broad application range for:

152 153 Titration guide 7.1 The OptiLine 6 The OptiLine 6 electrode offers the possibility to select between six different wavelengths (Fig. 84). The shaft material shaft consists of titanium, whereby a maximum compatibility with the different solvents is ensured. Power is supplied through a USB interface, via which the measured values are also transmitted to the TitroLine titrator (digital sensor). The setting of the titration parameters, such as wavelength and intensity, is performed directly in the titration software. In addition, the sensor has an analog DIN/BNC interface, which allows you to connect the OptiLine to any titrator with a corresponding input.

Shaft diameter 12 mm Shaft length 132 mm Minimum immersion depth 25 mm Shaft material Titanium Cable Fixed cable Connections USB interface A, BNC interface, with BNC-DIN adapter Current supply via USB Measurement range 0 – 2000 mV Temperature range 0 – 50 °C pH range 0 – 14 Adjustable wavelengths 470, 520, 570, 590, 605, 625

Fig. 84 OptiLine 6 electrode, technical data 152 153 Titration guide 7.2 Measurement principle During a photometric determi- The wavelength should be nation, the change in intensity selected so that the absorption is measured, which is caused by difference between the start and the colour change of the indica- the end of the titration is greatest. tor used. Due to the colour of the In order to determine the cor- solution, the light emitted by the rect wavelength, you could use sensor is absorbed. The change a photometer to record a spec- in absorption that is caused by trum at the start and at the end the colour change of the indica- of the reaction. The maximum or tor, is measured as a change in minimum of the difference spec- intensity on the detector is used trum shows the optimal wave- as a regulating parameter for the length for this determination. titration. The wavelength closest to this wavelength can now be selected During a precipitation titration, for the determination. either turbidity is generated during the titration, which reaches its maximum at the end of the reaction or the occurrence of turbidity indicates the end of the reaction. In both cases, the turbidity causes a dispersion of the light emitted by the sensor, which in turn causes the change in intensity on the detector.

154 155 Titration guide 7.3 Error sources 7.4 Applications Air bubbles Determination of the

In particular in aqueous media, alkalinity KS 4,3 air bubbles may form on the A general description of the OptiLine. These lead to alkalinity can be found in refractions of light, whereby no the section "Titration of KS 8,2 and stable signal can be measured. KS 4,3". The indication takes place Therefore, one should work with by means of methyl orange degassed water if possible. The (0.2 % in H2O). degassing of the water can take place via a vacuum or boiling. Furthermore, the sensor should be aligned in such a manner that the optical range of the sensor points against the flow direction so that any air bubbles in the sample are removed.

Ambient light As optical electrodes are light dependent, in certain circumstances, strong ambient light may interfere with the measurement leading to erroneous readings. As such, it is important to consider the location when performing photometric titrations.

154 155 Titration guide a) Titer determination Approx. 120 mg TRIS (Tris-(hy-  Waiting time: 10 s droxylmethyl)aminomethane)  Pre-titration: 8.5 ml are weighed in for the deter-  Wavelength: 520 nm mination of the titer. The deter-  Titration end: 1 EQ mination takes place at 520 nm  slope value: steep (Fig. 85).  Intensity: 30 %  Smoothing: average The following titration parameters are recommended: Formula for titer in mol/l  Measured value: mV (E) W ∗F2 cHCl [mol /l] =  Linear titration to an (EQ1−B)∗M∗F1 equivalence point  Linear step: 0.05 ml EQ1: Consumption titrant [ml] until the equivalence point  Measuring speed: B: Blank value = 0 Measurement time 3 s M: Molar weight of TRIS Drift 10 mV/min (121.14 g/mol) Min time 5 s W: Weighed sample TRIS [g] Max time 12 s F1: 1 F2: 1000 (conversion g – mg)

1140.0

1120.0

1100.0 10.00 ml 1106.2 mV 1080.0

1060.0

1040.0

1020.0

1000.0

980.0 ml 0 1.25 2.5 3.75 5.0 6.25 7.5 8.75 10.0 mV/ml dmV/dml

Fig. 85 Titration curve of a photometric titer determination with 0.1 molar HCl

156 157 Titration guide b) Sample measurement To determine the alkalinity of  Pre-titration: none drinking water, 100 ml of sample  Wavelength: 520 nm are placed in a 150 ml beaker.  no damping Depending on the alkalinity,  Titration end: 1EQ the sample amount must be  slope value: steep adjusted (Fig. 86).  Intensity: 30 %  Smoothing: average The following titration

parameters are recommended: Formula for KS 4.3 mmol/l  Measured value: mV (E) (EQ1−B)∗ T ∗M∗F1 K [mmol /l] =  Linear titration to an s4,3 V ∗F2 equivalence point  Linear step: 0.05 ml EQ1: Consumption titrant [ml] until the  Measuring speed: equivalence point B: Blank value = 0 Measurement time 3 s T: Exact concentration of the titrant Drift 10 mV/min [mol/l] Min time 5 s M: Molar weight = 1 Max time 15 s V: ml presentation F1: 10 F2: 0.01

1300.0

1250.0

1200.0

1150.0

1100.0 3.71 ml 1050.0 1084.8 mV

1000.0

950.0

900.0 ml 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 mV/ml dmV/dml

Fig. 86 Titration curve of a photometric Alk. 4.3 determination of drinking water

156 157 Titration guide Photometric determination of acids in oils (TAN) A description of the optical in- The following titration dication of the acid titration in parameters are recommended: oils can be found in the ASTM  Measured value: mV (E) D974. 0.05 mol/l KOH in ethanol  Linear titration to an is used as titrant. The solvent equivalence point consists of a mixture of 500 ml of  No damping toluene, 495 ml of isopropanol  Linear step: 0.05 ml and 5 ml of dist. water. Indicator  Measuring speed: is p-naphtholbenzein (1% solu- Measurement time 3 s tion, dissolved in the solvent). Drift 10 mV/min Min time 5 s a) Titer determination Max time 12 s  Waiting time: 10 s The determination of the titer is  Pre-titration: 4 ml carried out in the aqueous at a  Wavelength: 520 nm wavelength of 520 nm by means  Titration end: 1 EQ of potassium hydrogen phthalate  Slope value: steep and phenolphthalein as an  Intensity: 30 % indicator. Approx. 50 mg of  Smoothing: average potassium hydrogen phthalate are weighed in and after Formula for titer in mol/l the dissolving, 50 µl is added W ∗F2 (Fig. 87). cKOH [mol /l]= (EQ1−B)∗M∗F1

EQ1: Consumption titrant [ml] until the equivalence point B: Blank value = 0 M: Molar weight of potassium hydrogen phthalate (204.22 g/mol) W: Weighed sample potassium hydrogen phthalate [g] F1: 1 F2: 1000 (conversion g – mg)

158 159 Titration guide

mV 1200.0

1050.0

900.0

5.26 ml 750.0 821.2 mV

600.0

450.0

300.0

150.0 ml 0 0.625 1.25 1.875 2.5 3.125 3.75 4.375 5.0 5.625 mV/ml dmV/dml

Fig. 87 Titration curve photometric titer determination 0.05 molar KOH

158 159 Titration guide b) Blank value of the solvent To 100 ml of the solvent,  Wavelength: 625 nm 0.05 ml of indicator is added and  No damping the titration is carried out. The  Titration end: 0.3 ml max. measurement is carried out at dosing volume 625 nm (Fig. 88).  Intensity: average  Smoothing: average The following titration parameters are recommended: Formula for blank value  Measured value: mV (E) Blank value [ml] = EQ1  Linear titration to an equivalence point EQ1: Consumption titrant [ml] until the  Linear step: 0.02 ml equivalence point  Measuring speed: Measurement time 4 s Drift 20 mV/min Min time 10 s Max time 40 s

2000.0

1800.0

1600.0

0.10 ml 1400.0 1491.1 mV

1200.0

1000.0 ml 0 0.05 0.1 0.15 0.2 mV/ml dmV/dml

Fig. 88 Titration curve of a photometric blank value determination of a solvent mixture (toluene/IPA/water) 160 161 Titration guide c) Sample measurement The weighing in of the sample  Wavelength: 625 nm depends on the acid number of  Titration end: 1 EQ the oil. The sample is dissolved in  Slope value: steep 100 ml of the solvent (Fig. 89).  Intensity: average  Smoothing: average The following titrationparame- ters are recommended: Formula for FFA in mg KOH  Measured value: mV (E) (EQ1−B)∗ T ∗M∗F1 TAN [mg KOH / g] =  Linear titration to an W ∗F2 equivalence point  No damping EQ1: Consumption titrant [ml] until the  Linear step: 0.04 ml equivalence point  Measuring speed: B: Blank value of the solvent T: exact concentration of the Measurement time 4 s titrant [mol/l] Drift 20 mV/min M: Molar weight KOH (56.1 g/mol) Min time 10 s W: Weighing in the sample [g] Max time 40 s F1: 1 F2: 1

2000.0

1900.0

1800.0

1700.0 0.53 ml 1600.0 1702.8 mV

1500.0

1400.0

1300.0

1200.0 ml 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 mV/ml dmV/dml

Fig. 89 Titration curve of a photometric TAN determination of an insulating oil 160 161 Titration guide Determination of carboxyl end groups in PET The determination of carboxyl b) Blank value of the solvent end groups in PET pellets For the determination of the (polyethyleneterephthalate) is blank value, the solvent is treated described in the ASTM D 7409. as described above, but no Bromophenol blue (0.5% in sample is added. The blank value ethanol) is used as indicator, is boiled under reflux just as long 0.05 molar ethanolic KOH as as the sample needed to titrant. A blank value determina- dissolve. The titration is carried tion of the solvent is carried out out after adding the indicator (Fig. 90). (0.04 ml).

Approx. 1 g of the pellets are The following titration parame- weighed in for the determina- ters are recommended: tion. 20 g o-cresol is added to the sample. The sample is  Measured value: mV (E) boiled under reflux until it has  Linear titration to an completely dissolved. An adjust- equivalence point ment of the sample and solvent  Linear step: 0.004 ml amount is necessary if e.g. pre-  Measuring speed: cipitations result. After cooling, fixed waiting time: 20 s the mixture is mixed with 35 ml  Wavelength: 605 nm of chloroform. For the indication  Titration end: 0.1 ml max. dos- 0.04 ml bromophenol blue are ing volume added (Fig. 91).  Intensity: 50 %  Smoothing: high a) Titer determination Formula for blank value The titer determination can be Blank value [ml] = EQ1 determined photometrically, as described in the part "Determi- EQ1: Consumption titrant [ml] until the equivalence point nation of the alkalinity KS 4,3".

162 163 Titration guide

900.0

850.0

800.0 0.02 ml 813.1 mV 750.0

700.0

650.0

600.0

550.0

500.0 ml 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 mV/ml dmV/dml

Fig. 90 Titration curve of a photometric blank value determination of a solvent mixture (o cresol/chloroform)

162 163 Titration guide c) Sample measurement The implementation of the mea- Formula for R-COOH in mmol/kg surement is described in the (EQ1−B)∗ T ∗M∗F1 general method part. R− COOH [mml/kg]= W ∗F2

The following titration parame- EQ1: Consumption titrant [ml] until the ters are recommended: equivalence point  B: Blank value of the solvent Measured value mV (E) T: exact concentration of the  Linear titration to an titrant [mol/l] equivalence point M: Molar weight = 1  no damping W: Weighing in the sample [g]  Linear step: 0.1 ml F1: 1 F2: 1000 (conversion g – mg)  Measuring speed: fixed waiting time: 20 s  Wavelength: 605 nm  Titration end: 1 EQ  Slope value flat  Intensity: 50 %  Smoothing: high

mV 975.0

900.0

825.0

750.0

675.0

600.0 0.54 ml 620.7 mV 525.0

450.0

375.0 ml 0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 1.125 mV/ml dmV/dml

Fig. 91 Titration curve of a photometric carboxyl end group determination of PET pellets 164 165 Titration guide SECTION 8 KARL FISCHER TITRATION 8.1 The Karl Fischer reaction and reagents The Karl Fischer titration serves to The oxygen of the sulphate ester determine the water content of a comes from the water molecule. sample. It has the advantage of The examinations of the mech- faster determination compared anism show a change of the to the drying method and is also stoichiometry when working in more selective. The exact mech- other solvents. The addition of anism of the Karl Fischer reaction other solvents should therefore has been controversial for a long not exceed 50 % by volume. time. Even the stoichiometry of In addition to water, four compo- the reaction was not clear for a nents (an alcohol, sulfur dioxide, long time. In principle, a titration a base, iodine) participate in the would not be possible therewith. reaction; these must be present In more recent times, there have so that the reaction takes place. been some investigations of the mechanism, which have resulted With the classic KF titration, all in the following reaction equa- components are offered as a tion: combined reagent and are available in sufficient stability with ROH + SO + RŃ → [RŃH]SO R 2 3 suitable bases and alcohols. In H O + l + [RŃH]SO R + 2 RŃ → addition, 2-component reagents 2 2 3 are also offered nowadays, in

[RŃH]SO4R + 2 [RŃH] which the solvent component Wherein: contains an alcohol, a base and SO . ROH An alcohol, e.g. methanol, 2 ethanol, ethylene glycol mono- ethyl ether RŃ A base, e.g. imidazole (previously often pyridine)

164 165 Titration guide The titration solution then con- The KF titration is largely selec- sists of an iodine solution in an tive for water under the given alcohol. This reagent has the circumstances. However, there advantage of pH buffering and are of course limitations for a a higher concentration of all number of secondary reactions. components on the left side These can be divided into the of the reaction equation. The following types: reaction is clearly faster and the reagents last clearly longer.  Reactions which generate water  Reactions which require water With the one-component rea-  Redox secondary reactions of gent (Fig. 92), it is possible to iodine adapt the solvent to the solubility  External water of the sample.

1 component reagent 2 component reagent

Sample Titrant Sample Titrant

• Methanol • Alcohol • Alcohol • Iodine • Base • Base

• SO2 • SO2 • Iodine

Fig. 92 Schematic of 1 and 2 component reagents

166 167 Titration guide The best known water-producing Aldehydes can also form a bisul-

reaction is the formation of phate addition with SO2 under acetals or ketals. The alcohol certain conditions. This reaction necessary for the reaction and should be largely suppressed used as a solvent reacts with with a correctly set pH value. carbonyl groups (C = O) while This reaction also requires water forming water. This water is also and could pretend in this way a detected by the titration. The water content that is too low. titration does not seem to stop. A high permanent “drift” results. Further reactions with water formation are the reaction of However, acetal or ketal forma- carbonyls with amines to form tion can be avoided by using Schiff's bases, the formation of special reagents for aldehydes enamines and the esterification and ketones. A second possibil- of acids with the alcohol of the ity is the mode of operation with solvent. The risk is reduced when reduced temperature. One works using methanol-free solvents. at temperatures below 0 o C. The ionic KF reaction proceeds in External water is the most com- a virtually unaffected manner, mon error source in KF titration. while the acetal and ketal forma- It can reach the titration cell tion is significantly slowed down. through various possibilities. The lower temperature limit is First, the solvent or the presenta- determined by the viscosity of tion component must of course the solvent and the crystallization be dry-titrated. This procedure of secondary components. is called conditioning. If External water still gets into the titration cell, this is assigned to the sample as External water. External water reaches the titration cell in the following manners:

166 167 Titration guide The titration cell is not tight. The KF titration is strongly pH- Foreign particles can for exam- dependent (Fig. 93). At values ple hang between the ground below 5.5 pH, the reaction speed joints. Another possibility is slows by up to a factor of 1000. defective O-rings on the screw connections of the titration cell. Secondary reactions can occur in the alkaline range. But this also  While the titration cell is implies that in the KF titration opened to add the sample, air of acids, bases must be added humidity enters. and in the titration of bases (e.g.,  The septum for the addition of amines), acids must be added. liquid samples is leaking and worn.  Acidic samples: add imidazole  The molecular sieve in the or methyl imidazole drying tube for pressure equal- ization is used up and must be  Alkaline samples: add benzoic dried. acid oder salicylic acid  Humid air is present in the pump system. The air for adding the solvent must also be dried with the molecular sieve.

k Reaction speed

Slow area Prohibited KF area area

pH value 5.5 7.5

Fig. 93 Dependence of the reaction speed from the pH value 168 169 Titration guide 8.2 The detection of the KF titration and titration curves The KF titration uses a double However, the current curve does platinum electrode for detection, not give any information about to which a voltage of 20-200 mV the course of the reaction. There- is applied. The titration is titrated fore, a representation is usually with an iodine solution. The chosen in which the time is iodine reacts directly to iodide plotted on the x-axis and the in the KF reaction. No current consumption on the y-axis. First, can flow at the double platinum the reagent is added quickly and electrode of the detection sys- a steep increase results. Then, tem. However, as soon as the one titrates slower and more first drop of an iodine solution carefully, because the titrator de- is present in excess, a reversible tects the approaching endpoint. redox system of iodine and The smaller reagent additions iodide is present. A current flows, make the titration curve increas- which is measured and indicates ingly flatter until no more reagent the end of the titration. is added and the titration runs parallel to the x-axis (Fig. 94).

3 Bend which is not too acute 2.5 Flat curve,

2 parallel to the x-axis

1.5 Consumption [ml]

1 Steep increase, fast reaction 0.5

0 0 20 40 60 80 100 120 Titration duration [s] Fig. 94 KF titration curve 168 169 Titration guide If a secondary reaction is present 8.3 Sample handling during the titration, e.g. because The samples must be com- ketones are present and two pletely dissolved for the safe moles of water are formed per total determination of the water mole of ketal, a continuous in- content. Not all samples dis- crease can be seen, the drift does solve in methanol or the solvent not go down and the titration component of the 2-component does not stop when there is no reagent. In these cases, the time limit. Fig. 95 shows an exam- one-component reagent is pre- ple for a titration with secondary ferred and the methanol is treat- titrations. ed with a solubility enhancer. For polar samples, formamide is often used. For non-polar samples chloroform, xylene or long-chain alcohols are used.

0.9

0.8

0.7

0.6

0.5

0.4 Consumption [ml] 0.3

0.2

0.1

0 0 20 40 60 80 100 120 140 160 180 Time [s] Fig. 95 Titration curve with secondary reaction

170 171 Titration guide Even a sample that does not The possibilities are often limit- release the water immediately ed by the water content and the would show a continuous in- type of the sample. Thus, ex- crease. Different ways exist to ternal extraction is unsuitable if optimize the water release: the water content of the sample is significantly lower than the  Adaptation of the solvent, water content of the solvent. where possible (Fig. 96)  Heating of the solution (to For some samples, however, approx. 50 °C) by means of a drying oven is required for a heatble magnetic stirrer, sample preparation. An exam- or a double jacket vessel and ple are plastic samples that are a water bath virtually insoluble, at least not in  External sample preparation/ a solvent that is suitable for KF extraction titration. However, the oven can  Use of a homogenizer only be used to a limited extent  Use of a KF oven if the samples decompose before they release the water or if volatile components outgas and condense in the colder part of the oven.

Polarity

Duration Methanol and formamide

Dissolving trials Polarity of the solvent Methanol

Temperature Methanol + chloroform

Fig. 96 Dissolving trials with the KF titration

170 171 Titration guide 8.4 The coulometry The volumetric reagent addition At the cathode, hydrogen is is preferably replaced by coulo- generated by reduction. The metrically generated iodine with amount of iodine generated low water contents. is calculated from the titrator according to Coulomb's law: Coulometry is based on the M∗Q m = same chemical reaction, but z∗F the iodine is not dosed by a burette but generated in situ m mass of the water to be determined at the anode of a generator M molar mass electrode by oxidation of iodide Q measured charge amount (Fig. 97). z valency F Faraday constant (96,485.3 Coulomb/Mol)

VOLUMETRY COULOMETRY

Iodine generation Indication Iodine dosing

- + -

- 2 I I2 - 2 I I2 I2 From KF reagent KF reaction Fig. 97 Comparison KF coulometry and volumetry 172 173 Titration guide

Coulometry is an absolute Only with very small amounts of method; a titer determination water, difficult samples and very is not necessary and also not high demands of the accuracy, possible. KF volumetry and electrodes with diaphragms are coulometry are the same except used. Then suitable reagents for the iodine addition (Fig. 98). are available for the cathode Nowadays, a generator elec- chamber. trode is mostly used, which dis- penses with a diaphragm.

Coulometric Volumetric

KF titration KF titration

Switch on titrator Switch on titrator

Carry out the first filling

Fill the solvent into the titration cell Fill the solvent into the titration cell

Start the method

Condition the solvent Condition the solvent

Start the titration Start the titration

Place the sample into the titration vessel Place the sample into the titration vessel

next next titration Weighing in and designation Weighing in and designation titration

The titration is running The titration is running

The results are issued The results are issued

Pump off the solvent

Fig. 98 Workflows for the coulometric/volumetric KF titration 172 173 Titration guide In a direct comparison, the cou- Both methods complement each lometric KF titration is simpler, other and one can rarely be com- as there is automatically condi- pletely replaced by the other. tioned in the background, so Coulometry has its advantages the titration cell is kept dry. With in the ease of operation and volumetric titration, condition- the determination of very small ing is added, which is necessary amounts of water, while volume- for each sample prior to titration try can be used far more flexibly. (Fig. 98 and 99).

Property Coulometry Volumetry

WWaterasse contentrgehalt uandnd • • Psampleroben mamountenge • •

• • Sample types • • •

• • • • PSamplerobezu additiongabe und • • andVorb preparationereitung • • •

• • Operation • •

• μ • AWorkingrbeitsb erangereich • 10 μgμ to 5 mg water • 200 μgμ to 50 mg μ water

• • Correctness water amounts > 400 μg

400 μμg water, RReproducibilityeproduzierbarkeit

Fig. 99 Comparison use of coulometric and volumetric KF titration

174 175 Titration guide SECTION 9 VERIFICATION OF THE TITRATION 9.1 Overview An important prerequisite for In principle, all devices and meth- the correctness of titrations is the ods must be validated in the correctness of the concentration laboratory so that traceability can of the titrant. The titration is an be guaranteed. absolute method, that is, the consumption is directly attributable Definition of the validation to the chemical conversion. according to (DIN EN ISO 8402, 1994): As many titrants cannot be weighed in directly or their "Confirmation by examining and concentration does not always providing an objective evidence remain the same, the current that the special requirements for content must be checked and a special, intended use are ful- documented again and again. filled... This happens by means of the Verifiable information based on titer determination of the titrant. facts obtained by observation, measurement, test or in another Usually secondary reference manner." materials according to NIST are used nowadays. These are pro- For the validation, a comparison vided by the manufacturer with between the requirements and a certificate of the exact content, their fulfillment must always un- uncertainty and durability. All derlie according to ISO 8402. titrations whose titers have been This is verified with the execu- set with such a standard can be tion of a validation process. traced back to NIST. Titer determinations are described in detail in section 4.

174 175 Titration guide 9.2 Qualifications The qualification of a titrator happens essentially by check- ing its correct volume (the measurement unit of the titration) according to ISO 8655. For use in the laboratory, however, the device additionally has to be qualified by a series of processes (Fig. 100). IQ and OQ can usually be carried out by the manufacturer.

After the qualification, the device can be used in the laboratory for the routine. An additional validation is necessary for the methods. This takes place with the same scheme for all analysis methods and is described in detail in the literature [14, 15] for many methods.

176 177 Titration guide

Qualiﬁcation Description What has to be done? Aids/documentation

The DQ specifies the functional ● Describe the usage purpose ● Manuals, operating instruc- Design and operational qualifications ● Select the instrument tions of an instrument. ● Evaluate the manufacturer ● Standards and quality qualification guidelines (DQ) ● Conformity guidelines ● Manufacturer documents

The IQ ensures that an ● Check delivery scope ● Operating instructions instrument in the delivery state ● Set up ● Device support Installation corresponds to the ● Start up ● Support of the manufacturer qualiﬁcation speciﬁcations of the order. It ● Carry out a test ● IQ document (IQ) also documents the installation of the selected work environment.

Within the scope of the OQ, it is ● System suitability test ● OQ forms Operational verified that an instrument in ● e.g. linearity with standard ● Standards ● Certificates qualification the selected work environment ● Determination of the functions in correspondence standard deviation ● Training certificates (OQ) with the operational ● Calibration specifications. ● Training

The PQ verifies that an ● Adapt analysis methods ● Log book Performance instrument continuously ● Validate the methods ● Application support qualification delivers the performance ● Seminars (PQ) according the specifications ● Standards during normal use. ● SOPs

Maintenance The MQ describes and ● Cleaning and care ● Maintenance contracts ● Re-qualifying ● Technical customer service qualiﬁcation documents the necessary maintenance. ● Maintenance ● Test means monitoring (MQ) ● Titer checks

Fig. 100 Qualifications of a titration measurement place

176 177 Titration guide 9.3 Validation The extent of the validation depends on how much of a product is contained in a sample and how the influence of the sample matrix is. Fig. 101 repro- duces the validation scheme according to USP (United States Pharmacopoeia). In practice, the focus is on precision and linearity, as they give characteristics such as area, determination and detection limit.

Category I Category II Category II Category III Characteristic (Content (Limit (Quant. (Quant. determination) check) determination) determination) Precision + - + + Correctness + (+) + +

Veriﬁcation limit - + - +

Determination limit - - + +

Selectivity + + + +

Range + (+) + +

Linearity + - + +

Robustness + + + +

Regulations of the USP XXII for validation: • Category I: Main components • Category II: Secondary products • Category III: Performance parameters (substance release)

Fig. 101 Validation elements according to USP 178 179 Titration guide 9.4 Check of the correctness of a titration It shall be shown at an example that the small additional effort of a linearity test compared to a simple multiple determination provides a great number of information.

A relative standard deviation (RSD) of almost 12% is the result (Fig. 102, a). The linearity now shows that a negative consumption of 0.3 ml results from a 0.00 ml sample. This indicates a defective sample amount.

The used pipette was examined according to ISO 8655 and the found volume error was inserted into the data as correction. At 0.2%, the RSD is in the expected order of magnitude after the correction. The linearity shows a correlation coefficient of 1,000. The straight line passes (almost) through the zero point (Fig. 103).

178 179 Titration guide

ml sample ml result “content”

Fig. 102 Linearity of the titration results shows a serious error

ml sample ml result “content”

Fig. 103 Linearity after the correction of the volume error 180 181 Titration guide For a simplified validation, only The curves are analysed and a few characteristics have to be the results are represented in a checked and only a few titrations graph: are required. In the example  x-axis = sample amount (Fig. 104 and 105), five titrations  y-axis = consumption. are performed, the average value and the relative standard The RSD is very low at 0.02 %. deviation RSD are calculated. For a titer determination, values up to approx. 0.5% would be routinely accepted. The average value is also exactly where you expect it.

Titer determination NaOH 0.1 mol/l

No. Weighted sample [g] Consumption [ml] Titer NaOH 1 0.1189 5.8445 1.0060 2 0.1576 7.7489 1.0057 3 0.2090 10.2722 1.0061 4 0.2578 12.6710 1.0061 5 0.3045 14.9631 1.0063 MW titer 1.0060 SD titer 0.0002 Fig. 104 Result of a titer determination RSD titer 0.0218

y = 49.128x + 0.005 Linearity R² = 1.000 16

10 8 6 4 Consumption [ml] 2 0 -2 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 Weighted sample [g] Fig. 105 Linearity representation of the titer determination 180 181 Titration guide The titration curve is a very It is important that sample important element for the preparation is taken into account evaluation of the titration result in the various titrations. It is not (Fig. 106). permissible to take several partial amounts of a prepared sample. The criteria are as follows: Fig. 107 shows an example of a  Calm titration curve without validation of a KF coulometer. “dents” and “fluctuations“ A volume test is not possible due  Steep 1st derivation to a lack of burette, but the linear-  Even form of the derivation ity test can also prove the correct  Only one peak, no secondary function of the device here. By peaks means of the linearity test and a reference substance, the correct- If the titration curves are correct, ness of the water determination the linearity is examined. is verified according to specified criteria. The characteristics are as follows:

 Correlation coefficient better than 0.99(9)  Interface with the y-axis (x = 0) smaller than a drop of titrant (0.05 ml)  The factor of the slope is examined if necessary

Some parameters such as the correctness have not been examined. This could be checked by adding a standard that can be recovered at 100%.

182 183 Titration guide

pH 11.375

10.5

9.625 10.13 ml 8.568 pH 8.75

7.875

7.0

6.125

5.25

4.375

3.5 ml 0 1.25 2.5 3.75 5.0 6.25 7.5 8.75 10.0 pH/ml dpH/dml

Fig. 106 Exemplary curve of a titer determination

Test protocol of manufacturer test TL KF Trace

KF Reagent:

Reference Material:

Linearity Specified value 1.000 [mg/g]

]

No. Sample Weight [g] Result [µg] Found [%] g µ [

e t a W Mean 100.220 RSD 0.241 Weight [g]

Fig. 107 Check of a KF titrator with the help of a linearity test 182 183 Titration guide 9.5 Measurement uncer- The variables are quantified and tainty converted into equal measuring units. Then the relative errors can Today, the accuracy of a method be plotted as shown in Fig. 109. is no longer specified, but the The uncertainty "u" of a titer uncertainty "u" is estimated. For determination then essentially this, a method is examined by depends on the correctness of means of a cause-effect diagram the volume. (Fig. 108) for all parameters that have an influence on the The uncertainty is multiplied by calculated result. In the titration, a factor k = 2 and added as an all factors are evaluated that are expanded uncertainty to an directly or indirectly contained in analysis value, such as e.g. can the calculation formula. be seen on the certificates of the reference materials.

Volume expansion water Volume expansion Linearity cylinder Sensitivity Titration parameter Repeatability Electrode properties empty weight

Repeatability gross weight purity NaCl Deviation EQ turning point

Titration speed temperature weighing

Volume

Concentration mass NaCl

Repeatability Uncertainty chloride Weighing Uncertainty sodium Volume Temperature

Mass NaCl

Fig. 108 Cause-effect diagram of a titration 184 185 Titration guide

1 00 7 00 5 00 33 00 29 00 0 0 0 . . 0 0 . . 0 . 0 0 0 0 0 Result Relative standard Uncertainty u(x)/x

1 - l Highest uncertainty

o l g

m 3 m

g 3 00 5

00 29 1 0 00 1 . 0 0 . . 0 0 . 0 03 8 0 Standard uncertainty 0 0 0.12 . 0 0.1 0

- l

l m g

m g

4 0.08 2 1 1 88 8 6 1 .

Value 3 2 . 8

) 2 0 1 1 . - 4 l 0 o 2 0.06 m

m (

) i x . 0.04 y ( u 0.0 2 Description 0.00 ) ) ) T ) P ( H) P V H H P H K K ( K ( ( M Repeatability Weight of KHP Purity of KHPs Molar mass of KHP Volume of the NaOH during KHP titration P m

c( N a O Repeatability

KH P KHP KH P T rep m P M V

Fig. 109 The uncertainties of a titration in comparison according to GUM [15] 184 185 Titration guide BIBLIOGRAPHY

[1] Schulze, Simon, Martens-Menzel, Jander Jahr “Maßanalyse: Theorie und Praxis der Titration mit chemischen und physikalischen Indikationen”, Walter de Gruyter, Berlin/Boston, 18. Auflage, 2012

[2] DIN EN ISO 8655-3:2002-12 Volumenmessgeräte mit Hubkolben — Teil 3: Kolbenbüretten (ISO 8655-3:2002)

[3] PTB-Mitteilungen 112 (2002) Heft 2, S. 139-149

[4] Gernand, K. Steckenreuter, G. Wieland „Greater analytical accuracy through gravimetric determination of quantity“, Fresenius Z. Anal. Chem. (1989) 334:534-539

[5] pH-Fibel, SI Analytics 2014

[6] DIN 38409-H7 Summarische Wirkungs- und Stoffgrößen (Gruppe H) — Teil 7: Bestimmung der Säure- und Basenkapazität

[7] Gran, G. Determination of the Equivalence Point in Potentiometric Titrations, Acta Chimica Scandinavica (1950) S. 559-577

[8] Gran, G. (1952) Determination of the equivalence point in potentiometric titrations — Part II, Analyst, 77, 661-671

[9] ISO 22 719 First Edition, 2008-03-15, Water quality — Determination of total alkalinity in sea water using high precision potentiometric titration

[10] ASTM D3875 - 08 Standard Test Method for Alkalinity in Brackish Water, Seawater, and Brines

[11] ASTM D1067 - 06 Standard Test Methods for Acidity or Alkalinity of Water

186 187 Titration guide

[12] ASTM D513 - 06 Standard Test Methods for Total and Dissolved Carbon Dioxide in Water

[13] Handbuch Forstliche Analytik (4. Ergänzung 2009), C 2.1.1-3

[14] S. Kromidas, Handbuch Validierung in der Analytik, 2014 Wiley-VCH Verlag, ISBN-13: 978-3527329380

[15] ISO/IEC Guide 98-3:2008: Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in measurement

[16] Küster, Thiel, Ruland, „Rechentafeln für die Chemische Analytik“, Gruyter; Auflage: 105., aktualis. A. (16. Oktober 2002)

186 187 We express our core competence, namely the production of analytical instruments, with the name SI Analytics. SI also stands for the main products of our brand: sensors and instruments.

As part of the history of SCHOTT® AG, SI Analytics has more than 80 years experience in glass technology and in the development of analytical equipment. As always, our products are manufactured in Mainz with a high level of innovation and quality.

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