------..,

Journal of Research of the National Bureau of Standards-A. Physics and Chemistry Vol. 63A, No. 2, September- October 1959 Precise Coulometric of Acids and Bases

John K. Taylor and Stanley W. Smith 1 (i\fay 25, 1959)

Apparatus and techniques a re dc ~c rib ed for t he t itration of acids a nd. bases by co nstant­ current coulometry. The precision nnd accuraey of t he method aI~e JndLcated by tl traLlons of benzoic acid, potassium acid pMhalate, adLpiC aCld, hy droc~ l o l'l c aCid, ~nd sod ium eal'­ bonate. Standard deviations of ± 0.003 p er cent have been obtaIned which LndlCatp. that the reli abili ty of the method is equal to or exceeds t hat of classIcal analytlcfLI procedures.

1. Introduction 2. General Considerations In coulom etri c anal),sis, the laws of clcctl'o!ysis arc 2.1. Classification of Methods applied Lo analytical cbemistry. The matel'Jal Lo be C'oulomeLric li trations ma r be classified according analyzed is placed in a n clectrolytlc. cell and IS neu­ to wh ether Lhe process direc tl.\Tor indirectly tralized, oxidized, reduced, 01' preClpl Lated, a~ .the influ ences the composi tion of . the solu tion . Acidi­ case may be, by a meas'ured quantity of clectncLty. meLrie Litrations in which hydrogen ion is reduced From t his measurement, Faraday's laws arc used. to aL Lhe cathode are examples of Lhe former type, determine the amount of chemical subs Lance ong­ while Lhe precipiLation of halide ion by coulometl' i­ inally present. call)T ge ll erated silver ion is an example of the laLter IV-hile this technique has been lI sed onl y for the type. . past 20 years, and parlieularl y in Ute pasL decade , A flll"L hel' classificalion mar be made on the baslS numerous procedures have been developed, especially of the type of cUl'l'enL con Lrol. Co n trolled-pote ntwl in microchemical analysis, wh ere cO lilomelly. has coulomeLry cOll si ts in mainLain ing Lil e elecLrode definite experimenLal advantages over co nve n LlO lJ al potenLial 'at a seleeLed value LbaL produces only a volumetric method s [1 , 2, 3).2 desired electrode reacLion. J n Lili s case, l he cUl'l'enL With the evah lation of the farada)- co nstan t decreases co n tinuou sly and exponen liaHy durin g tb e with ever-increasing precision , by pmcly ph)'sical eleeLrol ysis a nd asymptoLically approaches zero or methods coulom.e Lry ofl'ers Lhe attractive possibilit)­ some sni.all ~o ll sta nt value. The current is in tegrated of permi'tling chemlcal sLandardizaLions to be made during the course of t he eleetrolysis, and is clisco n­ directly with reference to fundamenlal clectncal LinlLed when iL docs 110L differ s i g nifi canLl~r from Llus constanLs. In faet, a proposal has been made to the terminal value. International Union of Pure and Applied Chem.istr)' Constant-current coulomeLry is based on t he to accept the electron as a fundamental chemical main te nance of an accuraLely mea ured cunen Land standard (4). Lhe determin ation of the time )'equired to complete The K ational Bureau of Standards has had a con­ the desired reaction. Jntegl'aLion is not required, tinuing in Lerest in developing a n al yti ~al I?-ethods of but the must be disco ntinu e~l at Lhe en.d the highe t accuracy for the deterill~natlOn of the point of the desired reaction. End-polllt determi­ purity of materials suitable for cheilllCal s.tandards. nation may be made by co nvenLional method~ uch Because they differ so much from conventlOnal pro­ as potentiomeLric, colorimetric, . amperorneLnc, .or cedures, the preeision and accuracy. of coulometnc thermometric techniques, dependlng on the par t IC­ methods are being extensivel)' investLgated. A pre­ ular reaction. liminary report Oil t his program was pr esenLed. to the National Academy of Sciences at ItS meetll1g In 2.2. Advantages of Coulometric Washington in November ] 956 (5). The present paper is a detailed accounl of the. apI?ara~u s and te~h­ In addition to the possi.bility of making detenui­ niques developed for coulometnc tltl:aLl?nS of lugh. nations based on physical sta ndards, coulomeLric precision. It is shown Lhat the rehablllLy of the measurements have several obvious advantages. results obLain ed is equal to or exceeds that of the Electrochemical reactions may be co nsidered as most cal'cful determinations made by classical anal)'t­ Litrations with electrons, a uni.versal "reagent." ical m ethods. This reagent may be added uniformly at any desired rate by methods more convenient than those re­ quired to eli pense conven tional chemical s ub sta~ces. U ncertainties in composition of standal'd solutlOns 1 Present address: Delco·Rerny Divisi on, General Motors Corporation, An- are eliminated as are volumetric errors. The high derson, Ind. '1 d f th O 2 Figures .i n brackets indicate ille litcJ'atw'e references at t le en 0 IS paper. precision with wmeh electrical measurements can be 153 made is a distinct advantage in co ulometric methods. Methods for the control of electrical cir cuits are well­ developed, so that coulometric titrations are espe­ p-iall y adaptable for automatic operation.

2.3. Sources of Error It is of prime importance that the stoichiometry of the electrode process and any of its indirect reactions be completely defined. Any uncertainty in the current-chemical reaction relationship will result in a direct error in the determination. In general, 5 , S2 reactions which proceed with less than 100-percent current efficiency are not useful. In many cases, the reverse of the desired reaction occms at the second electrode, or the product of the reaction at this electrode may interfere with the reaction of primary interest. Accordingly, it is frequently necessary to isolate the second electrode in a separate compartm ent that is in electrolytic contact with the electrolysis chamber. In such cases, A it is necessary to minimize losses due to diffusion or FIGURE 1. Coulomel1'ic titration cell. to bulk transfer of the solution. A further source of error may arise from ionic migration from the electrolysis chamber. The familiar technique of addition of a supporting electrolyte will minimize from a sheet of silver 7.6 by 15 by 0.065 cm in thick­ this error. ness. This is corrugated and placed as far as possible Errors, both accidental and systematic, can arise from the connecting port, to assure large current in the determination of the end point as in conven­ capacity and good current distribution. Such an tional titrations. Errors can arise from faulty cali­ electrode has a capacity of more than 1,5 00 coulombs bration of the apparatus used for the measmement and can be regenerated by electrolytic reduction of the current and the time. of the silver chloride. More conveniently, however, the electrode may be renewed by chemical solution 3 . Apparatus and Procedure of the chloride in ammonia. The actual compartments are 400-ml beakers of 3.1. Apparatus the electrolytic type, without lip. They are con­ nected by a 35-mm tube, approximately 125 mm in The acidimetric titrations to be described were length, in which are sealed sintered glass disks as made by the method of constant-current coulometry. shown in the figure. Sintered disks 1 and 2 are of The cell consists of a platinum cathode and a silver medium porosity while 3 is of fine porosity. For anode, with an alkali chloride solution as the support­ convenience, tills bridge is made from commercially ing electrolyte. The cell reaction results in the available "sealing tubes." Each of the center com­ reduction of one equivalent of hydrogen ion (libera­ partments has a tube attached to permit emptying tion of one equivalent of hydrogen gas) at the and filling under nitrogen pressure as will be de­ cathode, and the formation of one equivalent of scribed. A plug of agar gel, P (3 percent agar-agar silver chloride at the anode for each faraday of in 1 N potassium chloride) is placed at the anode . side of disk 3 to prevent liquid transfer into or Because of the small but finite solubility of silver from this compartment. chloride in the electrolyte, a small amount of silver The circuit used for the maintenance of the con­ is reduced and deposited on the cathode when a stant current is shown in figure 2. A storage single compartm ent cell is used. To overcome this battery, B I , of 48 v serves as the cmrent somce. somce of error, the titration cell shown in figme 1 It permits a illgh-resistance circuit so that small was designed. The cathode chamber, 0, contains changes in cell resistance (voltage drop across the the platinum-gauze cathode and also the glass and cell) dming the course of the electrolysis will have a calomel to indicate the end point pH proportionally smaller effect on the current. A of the solution. An encapsulated magnet bar is voltage dropping resistor, R I , is immersed in an oil used to stir the solution. A tube is provided to bath to aid in heat dissipation and stabilize its re­ admit nitrogen to the cell to remove carbon dioxide. sistance dming a measmement. The combination, The compartment is sealed with a rubber stopper and RsR6' consists of a fL'{ed resistance and a carbon­ a bubble trap to exelude air. compression resistor in parallel. It has an overall The anode compartment, A, contains a silver variation of about 20 ohms and is adjusted continu­ anode of large area so that the anode reaction re­ ously during the measurement to maintain the sults only in the precipitation of silver chloride on current constant. R esistance R j is used for coarse its surface, no acid being formed. It is fabricated adjustment of the current. 154 occasionally with NBS standard time signals to ~I-~ -- -- -I check its performance. It is capable of an accuracy of one part in a milli.on, and has never difI'errd from j j ." the time signal by this amount. The pH measurements, on which the end point (2) deLermination is based, ar e made with conventional D------< 1-- 'I-- 52 8 2 TO TI M glp.ss electrodes and a line-operated indicator. A suitable re istance is eonnected in series with the Io me ler of Lhe insLrument and the voltage drop across (I) lllis is measured (14.5 mv per pH unit). This efI'ec­ Li\rely expands Lh e cale of Lhe instrument since this oltage ean be r eadily measured Lo a few hundredths of a millivolt with a n ordinary potentiometer. The stability of the pH m eLer duri.ng the period of a determination of the end point is suffLeient to war­ rant this procedure. All apparatus for making the eleeLrieal measm e­ ments, including standard eells, standard r esistors, and potentiometers, was calibrated by the electrieal division of this Bureau. The value for Lhe far aday eonstant used was 96,495.6 coulombs [7]. FIG URE 2. ELectricaL ci1' cuit diagram f or c01tlometric titrations. 3.2. General Procedure

A variable resistor, Rz, is adjusted to have, within A 1 N solution of potassium chloride is added Lo narrow limits, the same resistance as the cell. The Lhe anode compartment of the eell. A weighed por­ switch 8 2 when in position (1), permits the current tion of solid potassum chloride is placed in the to flow t hrough tllis "dummy" resistor for pre­ caLhode compartmen t and, after flushing with nitro­ liminary adju tment. Ammeter.fl is used to facili­ ge n, freshly boiled dis Lilled water is added in suffieienL tate the iniLial adjustment of the current. Switch quanti.ty to make the resulting solut;on 1 N. Pure S2, when thrown to position (2), causes the currell t nitrogen is then introduced through the connecting to flow tluough Lhe cell and simultaneously triggers Lube and into the solution to r emove di.ssolved carbon the timing device. dioxide. To insure that the elec trolyte is sufficiently The current is m easured by the voltage drop acid to facili ta Le Lhis operation, a few drops of acid across the standard resistor, R., a 5- or a 10-ohm are intentionally add ed to bring the elee trolyte to a precision resistor, depending on the value of the pH of 5. current. These resistors are placed in a constanL­ After purgi.n g is eomplete, the added acid is temperature oil bath. Saturated standard cells, neutralized as follows. S Lopcocks SI and S2 arc suitably thermostated, serve as the primary reference opened to the atomsphere Lo permit the solution to of voltage. The voltage drop across Rs is compared flow into tbe eonneet;ng tube to a depth of abouL 2 with the voltage of the standard cell, any difference mm. A curren t of 10 ma is passed un til Lhe glass being measured by potentiometer P . elee trode indieates a pH value of 7.0 .3 Nitrogen is then admitted into the side tube to " blow" the co n­ During a titration, the current is maintained con­ tents baek into the eathode eompartment. This stant by manually adjusting it in the following procedure is repeated until no further change in pH manner. By preliminary trials, it is possible to results on mixing and the pH remains at 7.00 . adjust the value of the dummy resistor to approxi­ By appropriate manipulti, tion of the stopcocks, the mately that of the cell. Accordingly, when the connecting tube is then fiJled with lleutralized swi tch. is thrown to the "electrolysis" position, eatholy te. The stopper is momentarily r emoved Lo potentIOmeter P can be adjusted quickly to corre­ in troduce the aeid to be titra ted . spond to the cell current. The potenLiometer key The curren t is then adjusted to a value of 200 ma is t hen locked in the closed posiLion . Any change and the olution is eleetrolyzed until the oIass elec­ in the c urrent causes the galvanometer to deflect trode i.ndicates a value very dose to Lhe end point. from the null position, and this is immediately At this rate of eleetrolysis, Lhe aeidity of the elec­ corrected by adjustment of res istor R5. trolyte in the vicinity of Lhe ell d poin t changes more Initially, the time in terval was determined by rapidly Lhan Lhe glass elec trode can respond. Ac­ means of an elec Lric clock, driven by a tuning-forI ;;: eordingly, some experience may be required to insure regulated eonsLant-freql.lency device, capable of a that the end point is not overrun. Nitrogen pressure precision of one p l1rt in it hundred thousand. To is then used to push the eon ten ts of the eonneeting secure higher precision in timing, and to eliminate tube into the cathode compartment for mL'(ing. errors due to clutch slippage in the clock, a quartz crystal-controlled time-interval meter (TIM) was 3 )10 appreciable error is incurred by assuming the neutral point of the solution used in la ter experiments. The meter is compared to be that of pure water.

155 The connecting tube is then filled with electrolyte while point B indicates the final pH value for the to a depth of 2 mm, as previously described, and the solution, after rinsing was completed. The corrected solution is electrolyzed at a current of 10 ma to end point is then time 0+ (time A-time B ). within about 0.5 pH unit of the end point. At this current, the glass electrode follows the change of pH 4. Titration of Potassium Hydrogen Phthal­ very closely so that there is little danger of over­ ate running the desired value. Electrolysis is then carried out, stepwise, for con­ 4.1. Procedure venient time intervals and the pH is recorded for The potassium hydrogen phthlate used in these each interval. From these data, a conventional experiments was NBS Standard Sample 84d. Small differential potentiometric plot is constructed to amounts (15 to 20 g) were crushed in a mortar and determine the end point. The connecting tube is dried at 120 0 C for 2 to 3 hr. The samples were then flushed several times with catholyte until no stored in a desiccator until used. further change in pH results. From the change in After removal of carbon dioxide from, and neu­ pH resulting from this flushing, and the titration tralization of the supporting electrolyte, the rubber curve, a small correction is made to the end-poin t stopper was removed momentarily, and the acid time already determined. (2 g), weighed to 0.01 mg, was dumped into the cell A typical end-point determination is shown in from a weighed platinum boat. Reweighing of the figure 3. Curve P represents the plot of the poten­ boat gave the amount of acid introduced into the cell. tial of the glass electrode indicator as a function of The acid was then electrolyzed at a current rate the elapsed time. Curve D is the differential plot of 200 ma and finally at a rate of 10 ma, as described used to locate the end point, identified as point O. above. The tolerance limits for the location of the end point 4.2. Results that would correspond to an error of ± 0.002 per­ cent in the titration are indicated. Point A repre­ The results ob tained for a number of titrations of sents the time at which electrolysis was discontinued, standard sample 84d are given in columns 2 and 3 of table l. The values given represent the purity

56 -, found for the sample on the basis of an equivalent weight of 204.216. The electric clock was used for 0 54 ±.OO2 "1o measurement of time in the case of the first group

0 0 while the time-interval meter was used in the second 51 senes.

0 0 40.0 Although separated by a period of time of about 0 50 38.0 1 year, and determined by slightly different tech­ 0 36.0 niques, the agreement of the averages for the two E 48 0 34.0 series is excellent and shows the high precision of ~ 31.0 coulometric titrations. 46 30.0 > On the basis of very careful titrations by conven­ 18.0 E tional methods, sample 84d was indicated originally 44 16.0 as having an of 100.04 percent. Subsequently, 14 .0 Bates and Wichers [6] compared this material with 11.0 specially purified benzoic acid by differential ti tra­ 10.0 tion and reported an assay of 99.987 percent (CT = 40 18.0 1.10 1.25 1.30 1.35 1.40 1.4 5 1.50 1.55 1.60 0.002). The agreement of the values of table 1 with COU LOMB S ADD ED AT 10 ma this latter value is confirmation that the coulometric FIGURE 3. Typical end-poinl determination. method is one of high accuracy.

T ABLE 1. Summary of results

Potassium Potassium Benzoic Benzoic Hydrochloric Adipic Adipic Sodium hydrogen hydrogen ac id a. acid b acid a c acid a d acid b 6 carbonate a Determination number pbthalate' phthalate b assay assay assay assay assay assay assay assay

% % % % % % % % L . . ... _...... 99.976 99.9i9 99.985 99.991 99.982 99.935 99. 985 99. 909 2_...... _...... _.. _... 99.980 99.976 99.991 99.993 100.004 99.937 99. 987 99.901 3 _._ ... __ ...... _. . _. __ .. 99. 978 99.981 99. 989 99.996 100.014 99.937 99. 980 99. 915 4 _... _.•.•... _... _.•••• _.. 99. 970 99.976 100.001 99.991 100.003 99.947 99.981 99.9lO 5_.. . _...... __ ..... _... .. _ 99.974 99.9i4 99.985 99.986 100.002 99.942 99. 989 99. 920 6 _. _.. _.. __ .. _.. _... __ ._. __ ...... _...... __ ...... 99. 998 99.999 99.955 7_.. __ .. _... __ ...... ___ ...... _...... _...... _.... _._ ..... _... 99.990 99.951 8 __ .... _...... _...... _...... ______.... __ .. ______...... _._ . ______. __ . ... ____ .. ___ _ 99.948 J'vf ean __ .... __ .. ____ ...... 99.976 99.977 99.990 99. 994 99.999 99. 945 99.984 99.91 1 Standard deviation ._ ... . 0. 004 0.003 0. 006 0.004 0.010 0. 007 0.004 O.OOi

• Timed by electric clock. d Once recrystallized from melt. b Timed by time interval meter. e 'rwice recrystallized from melt. o Assay based on calcnlated acidity by the pressure-d istill ation mcthod. 156

L ______-_._--- 5. Titration of Benzoic Acid 6.2. Results

5.1. Procedure The results of seven coulometric titrations of this acid are given in column 6 of table 1. The reported The benzoic acid used wa prepared at NBS for valu e is Lhe "puriLy" of the acid on the basis of its use as a calorimetric standard. The acid was a calculated concentration from pressure-distillation coarse,. crystalline material and has been bown by datft. Expre sed in other terms the solution was other InVestIgators [5) not to take up waLer under found to have a concentration 'of 0.114850 milli­ ~ondition s pr?vailing in this locali ty. Accordingly, equivalents per gram, as compared with the calcu­ It was used WJtho:ut further purification or drying. lated value of 0.114852 indicated in section 6.1. I ' . After preparatlOn of the cell as described pre­ While the agreement with the calculated value is vlOusly, a 1-g sample was weighed in a platinum boat satisfactory, the preci ion of the determination is and transferred to the cathode compar tment. A disappointing. On the basis of uncertainty of the penod of about 30 min was allowed before starting end point, a reproducibility of at least 1 part in the electrolvsis, to permit a substantial amount of 100,000 would be expected. Undoubtedly, some of the ~c~d. to dissolv.e. Ad~itional acid dissolves during the error IS that inheren t in th e dispensing of liquid the lnItIal reductlOn pertod. When the reaction is samples. In order to estimate the magnitude of approximately 98 percent complete, the current is such errors, a series of m easuremen ts were made in dIs c o~lill uC' ? , the connecting' tube is blown dry, and which 50-g samples of water wC're dispensed from" a sufiicLCn t t [me IS allowed for the solution of the wC'ight buret into tared weighing bottles. The remai .lldC'~· of the sample (about 20 to 30 min). The difT"erence between the wC'igilt of water dispensed tltratlOn lS then completed with a current of 10 ma and the contents of the weighing bottles sbowecl a as already described. A final rinsing of the cell walls variation of 3.6 parts in 100,000. Tf all of this were a~d stoppC'r is accomplished with 15 percent, carbon reaected in the uncertai n t:v of the weight of the dlOxlde 11"('e ethanol, to insure solulion of residual sample, the larger average deviation found in these traces of the acid. measurem.ents would be partially explained.

5.2. Results 7. Titration of Adipic Acid The results obtain ed in two independent series of 7.1. Procedure measur~ment s with different timing techniques are The adipic acid used was reagent grade material shown In columns 4 and 5 of table l. The values which had been further purified by filtration and reported represen t the a say of the acid 0 n the basis crystallization from the melt by Delmo Enagonio of of an equivalent weight of 122.112. the Bureau. The material was estimated to have By the di~erenti al method already referred to , an assay of 99.9 + percent. The titration procedure Bates and Wlchers [6) found the assay of this acid used was the same as that followed in the case of to be 99.996 percent (CT=O.OOl). poLassium acid phthalate, and the results are reported merely to show the adaptability of the method to a 6 . Titration of Hydrochloric Acid variety of acids. 7 .2. Results 6.1. Procedure The results of a series of titrations to determine Lhe ~ . solu~io~ of hydrochloric acid was prepared by purity of this sample of adipic acid are given in wClght dllutlOn of constant-boiling acid. Based on column 7 of table 1. The material was further re­ the pressure during the distillation of the startin" crystallized and the purity was found to be higher, material and the dilution data, the acid was calcu~ as recorded in column 8. The smaller value for the lated to have a concentration of 0.114852 milli­ standard deviation indicated that the homogeneity equivalents per gram of solution [8). of the sample was also improved by the second ~ftcr the usualyreparation of the cell, 50 g of the purification. aCld was add.ed from a weight buret. Electrolysis was started nrunedlately and continued to about 8 . Titration of Sodium Carbonate 99 .8 percent of completion. The connecting tube was then rinsed and the neutralization was completed 8.1 . Procedure at th~ 10-ma rate as described previously. In this case, It was not necessary to prepare an end point These experiments were performed to extend the curve, due to the rapid change in pH at the end method to the titration of bases. The sodium car­ point. Thus, a difference in pH of 0.1 unit at the bonate was reagent grade material which had been end point corresponded to 0.005 coulombs (0.5 sec heated in a platinum dish for several hours at a at the 10-ma rate). It was only necessary to attain temperature of 350 0 to 400 0 C. The assay was not the su:m~ end point obtained in the preliminary determined by an independent method. condit1Ol1lng of the cell, a value ea ily determined The electrolyte used was 1- 1\1 sodium sulfate within 0.02 pH 1.mits. . since chlorides' would be oxidized at the anode if 157 I I present in the solution. The agar plug was also accomplished by drawing large quantities of hot I i made with 1- 1\11 sodium sulfate. distilled water through the frits. The effectiveness The solu tion was preconditioned as described of the cleaning procedure can be checked when the previously. Aftcr addition of the base, the platinum solution is brought to neutrality at the start of a electrode was made the anode and electrolysis was titration. Prolonged downward drift of pH on stand­ continued until approximately 99 percent of the base ing and continuing change of pH on rinsing the had been ncutralized. The titration was completed connecting tube indicate the presence of acid in the at the 10-ma rate as before. Sufficient time must be frits. Should this situation arise, it is necessary to allowed near the end point for the removal of carbon discard the solution and to rinse the cell further with dioxide. hot distilled water. Errors associated with the electrical measurements 8.2. Results are easily made much pmaller than other errors. The results of a series of five titrations of this ma­ Standard resistors, certified to a few parts in a terial are given in column 9 of table 1. The precision million, are readily obtained, and normal tempera­ obtained is comparable to that found with the acids ture control is all that is required to assure main­ determined by this method. tenance of their calibration to this accuracy. Cali­ brated potentiometers permit measurement of the voltage drop, and hence the current, to better than 9. Discussion one part in ten thousand. For current measuremente of the highest precision, the arrangement used here This invcstigation shows that the coulometric is preferred, in which the potentiometer measures method is capable of a high degree of precision. In only the difi'erence between the volta,ge drop across view of the results obtained for benzoic acid and the resis tor and that of a saturated standard cell. potassium acid phthalate, for which the assay is This differential method permits measurements with known, there is su bstantial evidence that the method a precision of a few parts in a million. is also capable of a high degree of accuracy. No difficulties have been experienced in maintain­ The attainment of precision and accuracy of the ing the current constant to better than one part in order indicated by the data requires careful control a hundred thousand. The galvanometer used to over several sources of error. These may be dis­ indicate potentiometric balance had a sensitivity of cussed best by a division into errors of procedure and 0 .3 J.Lv /mm. Accordingly, a defiection of 3 mm from of measurement. the null position corresponded to only ]J.LV , or 1 ppm Errors may arise as a result of the pretreatment of with refcrence to variation in the current. the acid to be determined, in its introduction into the It was possible to maintain b alance within a few cell, and as a result of losses during the titration. millimeters throughout a determination, provided Errors associated with the preparation of the the variable resistor used for current control had a sample are frequently overlooked. In the case of smooth response. In this connection, a carbon com­ the phthalate, for example, the procedure for drying pression resistor, spring-lo aded and mounted verti­ the sample is critical. It is important that only cally, is much superior to multituI'll potentiometers small quantities be. crushed preliminary to drying, in which have a tendency to become "noisy" wit,h use. ~rder to release mlCroamounts of entrapped mother liquor from the crystals. Furthermore, the crushing For aecurate measurements, it is imperative to ll!.ust be done gently, to avoid generation of appre­ insure that the current tluough the stand.ard resistor cIable heat in localized areas which might result in is actually that through the cell. While this may decomposition of a part of the sample. Also, the seem an obvious condition, the possibilities of extrane­ sample should be spread out to facilitate the drying ous connection to ground ("ground loops"), even process. though of high resistance, must be considered. To minimize errors associated with the transfer of Timing errors should not seriously affect the pre­ the sample into the cell, it has been found advan­ cision or accuracy of coulometric titrations. For tageous to stop the fiow of nitrogen during this samples of the order of about 10 milliequivalents, process. This assures that fine spray will not deposit approximately 1,000 coulombs are needed, requiring on the platinum dish to cause an errol' in weight and about 5,000 sec at the 200-ma rate of electrolysis. also preven ts spray losses of material from the Electric clocks, driven by frequency-controlled power cathode compartment. supplies, are inexpensive timing devices which pro­ After the sample has been introduced into the cell vide measurements reliable to a few parts in a it can be lost only through transfer of solution i n t~ hundred thousand. Perhaps the largest source of the al~ode compartment, or escape as spray through error associated with their use is the so-call ed clutch the mtrogen eXIt tube. The former is effectively errol' involved in starting and stopping, which may prevented by the agar plug in the connecting tube. amount to a few hundredths of a second per opera­ The l atte~' is minimized by maintaining only sufficient tion. The crystal-controlled elec tronic time interval fiow of mtrogen during the titration to guarantee a meter used here is reliable to a part in a million. positive pressure of nitrogen in the cell. Both techniques require that the timing switch oper­ It is very important to remove residual amounts ate in close synchronization with the current switch. of strong acids from the cell such as would be Errors arising from the determination of the end introduced during a cleaning' operation. This is point depend on the slope of the pH curve in this 158 region, as well as the sensitivity of the pH indicating dependent upon the manipulative skill of the analyst device. In the case of the weak acids used in this than arc classical methods. The method has the investigation (pK values, 4.5 to 5.5), the uncer­ further ad van tage of being absolute in the sense tainty of the end point is about 8 millicoulombs, that the results arc based on electrical standards corresponding to elTO ["s of less than 10 PPl"P. Fo r etHel no ass umptions as to the purity of chemical strong acid the end point error is much smaller primary standards are involved. Titrations reliable than this, due to the greater slope of the end poinl to a (ew hundredths of a percent for both strong curve, and depends largely on the rnliabjJ. ity of the and weak: acids can be readily obtained. The method pH indication. is equally well-adapled to the titration of bases. Errors in accuracy arise from th e cleviaLion of the inflection point in a poten tiometric titration from the stoichiometric cquivalence point. According to 11 . References Roller's equations [9], errors from this source should be less than 0.001 percent. There is some evidence [I] .T . .T. Linga ne, ElecLroanalytical Chemistry (I nLc rscience to indicate that the experimefltal deviations are Publishers, Inc., New York, N.Y., 1 95:~ ) . somewhat greater than the calculated values [6]. [2] J. J. Lingane, Anal. Chem. 30, ]7J6 (1958). [3] F. Cu ta, Anal. Chim. Acta 18, 45 (J 958). However, insufficient work has been done to justify [41 P. S. Tutundzic, Anal. Chim. Acta 18,60 ( 19.58) . the assignment of corrections to the values reported [5] .T. Ie T aylor' and S. W. Smith, Science. 124,940, ( 1956). in this paper. [6] R. G. Bates and E. vVichers, J. Research NBS 59, 9 (1957) RP2769. 10. Summary [7] E. R. Cohen and J. W. Du Mond, Phys. R C\·. L C'Lte rs 1 , 283 (J 958). [8] C. W. Foulk and M . Hollings worth. J. Am. ChC'm. Soc. This investigation has shown that co ulomelri c 45, 1220, (1923). acidimetric titrations can be made with a precision [9] P . S. Rolier, .T. Am. CI1('111. Soc. 54, 3-[85 (1932). and accuracy equal to or exceeding that obtainable by the most careful conventional chemical methods of analysis. Furthermore, reli able results arc less , VASHINGTON, D.C. (Paper 63A2- 8)

159