494 PROCEEDINGS [Vol. 86 Coulometric Methods in Analysis A Review” BY D. T. LEWIS (D.S.I.R., Laboratory of the Government Chemist, Clement’s Inn Passage, London, W.C.2) Modern applications of the principles of coulometry to analytical problems are reviewed. The types of electrolytic apparatus required for the electro- generation of reactant materials are described, special attention being paid to the various electrical indicator systems now being employed for titrimetric end-point determinations. Alternative chemical or photometric indicator methods receive general mention. The recent applications of oxygen and adsorption electrode devices are illustrated ; electrolytic hygrometry is discussed, and some examples are given of the use of coulometry for the quantitative analysis of pesticide residues on agricultural crops, the determination of oxide tarnish on metals and the determination of tin-alloy coatings on iron.The principles of the com- mercial “fuel cells” and their possible analytical applications are briefly indicated. 1. INTRODUCTION The general electrolytic principles governing the applications of coulometry to analysis have remained unchanged since their enunciation by Michael Faraday in 1833. These fundamental laws may be concisely represented by the equation- . Eit .. - - (1) w = E l t = - .. .. .. F where w is the weight in grams of an element formed by a primary electrode process produced by the passage of i amperes of current for a period of t seconds, E is the electrochemical * Reprints of this paper will be available shortly.For details, please see p. 556.August , 19611 LEWIS : COULOMETRIC METHODS IN ANALYSIS. A REVIEW 495 equivalent and is obviously the weight of the particular element produced by one coulomb, E is the gram equivalent weight of the element and F is the Faraday unit expressed in coulombs. The application of equation (1) to any analytical problem can only become possible if physical instrumentation is available that can measure in a precise quantitative manner the three connected variables, weight, current and time, or which will give related physical infomation from which the magnitudes of these variables may be determined. Detennina- tions that can often be made reproducibly to a precision of 0.1 per cent. and an equivalent accuracy will usually satisfy the demands of the most critical analyst, and, if modem techniques of measurement are employed, the coulometric method will invariably satisfy this criterion, not only in the macro range, but in the micro range as well.2. CHEMICAL AND ELECTRICAL STANDARDS The International System of 1908 defined the ampere as that current which would deposit 0.001118 grams of silver per second in a voltameter of special design. This definition became obsolete in 1948 when the Ninth General Conference of Weights and Measures decided that the more fundamental absolute units were becoming known with a certainty exceeding that attending the older “international units.” The theoretical re-definition of the ampere employing Neumann’s integral has resulted in the relationship- 1 International ampere = 0.99985 absolute ampere.From the analyst’s point of view, this change is of insignificant character, although the new value of the coulomb is also affected to a similar extent. The most recent physical measurements of the basic natural constants have yielded the following values1- (60) Avogadro’s Number (Chemical) = 6.02308 x atoms per mole. (45) Electronic charge = e = 1.60207 x e.m.u. (3) Velocity of light = C = 2.997929 x lofo cm per second. (26) Faraday =- = 9649.4 e.m.u. per gram equivalent = 96,494 coulombs per gram equivalent. Ne C The figures in parenthesis preceding the name of each constant give the probable errors in parts per million of the numerical factors. Since the value for e may be expressed as 1.60207 x 10-19 coulombs, it is obvious that an ampere of current is also associated with the transfer of 6.24 x l0ls electrons per second.Silver is employed quite widely in coulometry as an electrogravimetric standard. It is appreciated that it consists of two isotopes of atomic masses 106.950 and 108.949, present in amounts equivalent to 51.9 and 48.1 per cent., respectively. The migration velocities in aqueous solution of these two ionic forms must be exactly equivalent, because there have been no reports of isotopic enrichment during electrolysis.2 Such enrichment can occur during the electrolysis of fused salts at high temperatures. Shields, Craig and Diebeler2 at the U.S. Bureau of Standards, in a study of the absolute abundance ratio of silver to be used for the accurate electrochemical determination of the Faraday, have discussed the various conflicting results for the chemical atomic weight of this element, the 1957 International Value being Ag = 107.88.On the basis of their mass- spectrometric observations, these workers suggest that the chemical atomic weight (0 = 16) is more correctly given by Ag = 107-8731 0.0020, a result differing significantly from the usually accepted value. The position of silver in the electrochemical series makes it particularly useful as a coulometric standard. If we consider a neutral decimolar solution of silver nitrate of ionic strength 0.1 and of activity coefficient fAg+ = 0.77, we have, at 25” C, the following Nernst equation for the reduction Ag+ + e = Ag. At the inert anode, the evolution of oxygen proceeds according to the scheme- where aH+ x aOH- = K, = lO-l* in neutral solution, i.e.E, = EO, + 0.05915 log fAg+ CAg+ = 0.7990 - 0.0659 = 0.7331 volt. 20H- + &02 + H,O + 2e Eo, = Eoo, + 0.02957 log a20d- = - 0-402 + 0.02957 log = - 0.8159.496 LEWIS: COULOMETRIC METHODS IN ANALYSIS. A REVIEW [Vol. 86 The theoretical reversible decomposition potential of silver nitrate is thus quite small, ie., Moreover, if we consider the presence of 0.01 M copper as an impurity in our silver solution, fCUP+ = 0.5 when the ionic strength is 0.03, and the reduction potential of cupric ion is given by- Neglecting polarisation effects, the concentration of silver would have to fall to about 10-9 gram ions per litre before copper impurity became deposited on the silver cathode, i.e., when EAg+ becomes 0.2761 volt. Even lower concentrations of lead and tin would obviously be tolerated, because of their more positive oxidation potentials, and at a controlled-cathode potential, virtually pure silver is deposited.3. MEASUREMENT (a) MEASUREMENT OF CURRENT AND TIME- A precision stopwatch is used by many laboratories for the exact measurement of electrolysis time, the main objection to its use being that it is difficult to switch on the current and start the watch with complete simultaneity. For this reason, electrical or electronic timing units are generally preferred. They can form part of the electrolytic circuitry and give the advantage of being under the single switch control that also controls the current. Times accurate to one-hundredth of a second are possible with modern types of electric chronometers.For the accurate independent measurement of current, the preferred method involves the use of a calibrated resistor incorporated directly into the series circuit of the coulometric cell. The potential drop across the resistor is determined with a precision vernier potentio- meter. Such instruments are available in the United Kingdom and will measure from 2 volts to microvolts with an error of 0.002 per cent. If the electrolysis is carried out at constant current, the total number of coulombs consumed is given by q = it coulombs. If, however, an electrolysis is carried out at controlled potential, the current will usually decrease logarithmically with time according to the expression- where i, is the initial current, the total number of coulombs being given theoretically by the integral- Erev* = E,, + Eo, = 0.7331 - 0.8159 - 0.0828 volt.Ecua+ = 0.3441 + 0.02957 log f ~ u * + C ~ u z + = 0.3441 - 0.0680 = 0.2761 Volt. . . - - (2) .. * . . . i = i e-kt . . . . (3) It is obviously impossible to carry out an experiment to infinite time, and in practical analysis it will suffice if the electrolysis is followed graphically until the final observed current i is Time, t Fig. 1. Plot of current against time 1 Time, t Fig. 2. Plot of log, i = log, i, - ktAugust, 19611 LEWIS: COULOMETRIC METHODS IN ANALYSIS. A REVIEW 497 of the order of 0.1 per cent. of the original i,. This gives a curve of the type shown in Fig. 1, which may be integrated by counting the graphical squares or by cutting out the segment and comparing its weight with a square of the same graph paper of known area.Alternatively, MacNevin and Baker3 have plotted (Fig. 2) the linear equation log& = log,io - kt, and the intercept log& and the slope, -k, are found from the graph. A few points will establish the straight line, and the integral, equation (3), is then readily evaluated. The previous authors employed this method for determining the oxidation of the lower valency states of iron and arsenic by graphically following the coulometric titration over a period of only 10 minutes. (b) DIRECT MEASUREMENT OF A NUMBER OF COULOMBS- This method employs a standard chemical coulometer in series with the electrolysis cell and, provided the coulometric reaction proceeds with 100 per cent.efficiency, it will give an absolute integrated measurement regardless of any irregularities in the magnitude of the current. Silver and copper coulometers are widely employed, the increase in weight of the cathode being measured. Lingane4 describes a thermostatically controlled gas coulometer with potassium sulphate as electrolyte. Correcting for vapour pressure , atmospheric pressure and temperature, 16,811 ml of gas at S.T.P. = 1 Faraday. Many variants of electrolyte formulation are possible in such gas c~ulometers.~ p6 Ehlers and Sease6 have described the construction of a constant-potential coulometer for use in the 0 to 10 coulomb range. Copper is first deposited by the current to be measured from a copper sulphate solution, and the metal is then subjected to a quantitative anodic- stripping process.Lingane and Small7 make use of electrolytically generated acid or base to provide a coulometer accurate to 0.1 per cent. at 10 coulombs and to 1 per cent. at 1 coulomb, In addition to the chemical coulometers, many ingenious electromechanical and electronic devices have been described for determining the “q” function. Thus Booman* has developed an electronic potentiostat and integrator circuit with a 10-microsecond response to current changes and usable in the 10 pA to 10 mA range. Bett, Nock and Morrisg have described a low-inertia integrating motor whose speed of shaft rotation is a linear function of the applied voltage. This sytem has also been studied by Furman and Fentonlo who show that an empirical relation of simplifying character exists between the motor-calibration factor and the value of the series resistor that controls the voltage across the motor terminals.The rotation of the armature shaft is followed by a simple mechanical counter. Strip-chart recorders have been used to study coulomb changes, which are followed mechanically by ball-and-disc integrating systems.ll Coulometric devices of this nature are not commercially available in the United Kingdom. Potentiostats and automatically controlled cathode electrolysers may, however, be purchased, the cathode potential being pre-set and controlled automatically during the electrolytic deposition. These devices are also useful in polarographic measurements for the preliminary removal of large amounts of interfering ions by coulometric deposition.4. ANALYTICAL PRINCIPLES (a) PRINCIPLES OF ANALYTICAL COULOMETRY- In coulometry the electrode processes may obviously be carried out (a) at controlled potential or (b) at constant current, the voltage being applied from an external source, e g . , an accumulator. Such processes are examples of “external electrolysis.” In some unique instances quantitative electrode processes can occur without use of an external battery, e.g., by the short-circuiting through a resistor of a simple chemical cell. The applications in coulometric analyses of such systems are referred to under “Internal Electrolysis” (see Section 7). (b) ELECTROGRAVIMETRIC ANALYSIS- It is not proposed in this review to deal in any detail with external electrolysis of the electrogravimetric type involving the weighing of cathode deposits.The phenomena of “over-potential” and “concentration polarisation” are important in all applications of coulo- metry, hydrogen over-potential being greatest at mercury cathodes (0.8 volt) and oxygen[Vol. 86 over-potential being most pronounced for the noble metals (0.5 volt). Such phenomena permit the prior deposition of cadmium (EO == 0.402 volt), whose normal deposition would have been expected to follow that of the more reducible hydroxonium ion (H,O+). The electrogravimetric deposition of silver has already been discussed in Section 2. 498 LEWIS: COULOMETRIC METHODS IN ANALYSIS. A REVIEW (cj COULOMETRIC TITRATIONS AT CONSTANT CURRENT- Such titrations differ from volumetric titrations in that the titrant is generated electro- lytically, the electron being the standard reagent.The accuracy of these titrations is such that Tutundzic12 has suggested that the coulomb would be a preferable standard in titrimetric analysis, rather than the conventional chemical standards. The coulometric method is par- ticularly useful for studies in the microgram to milligram range and is capable of great accuracy. In primary coulometric titrations the substance to be determined reacts directly at the electrode. In secondary coulometric titrations, a reactive intermediate is first generated quantitatively by the electrode process, and this must then react directly with the substance to be determined. It is obviously a sine qua non consideration that the coulometric reactions must occur with 100 per cent.current efficiency, and this demands a completely inert electrode system, absence of reducible gases, such as oxygen, and also complete absence of electroactive solvents, impurities, etc. It is common practice to purge the atmosphere of the electrolyte cell system with pure nitrogen or argon. The stability of gold, platinum and palladium electrodes in strong oxidising solutions has been critically examined by Lee, Adams and Bricker,13 who conclude that none of these electrodes are truly inert. Various investigations have shown, however, that platinum anodes may be successfully used for the generation of halogen titrants according to the scheme- 2 C1- + C1, + 2e The classical papers of Szebelledy and Somogyi14 have described the internal generation of halogen and subsequent oxidation of thiocyanate, hydrazine, sulphite, etc., and this work has been considerably extended by Swift et Arthur and Donahue16 have also demon- strated that electrolysis of titanic chloride a t a gold cathode will produce titanous ions, which may be employed successfully as a reductimetric titrant.Tutundzic and Mladenovicl7 have similarly used a platinum anode for the generation of permanganate ion in an acidulated manganous sulphate anolyte. It is therefore obvious that noble metal electrodes can be employed under fairly adverse oxidising - reducing conditions. Two types of titrations are usually defined. (a) APPARATUS FOR CONSTANT-CURRENT TITRATIONS- Most titrimetric coulometry is carried out under constant-current conditions, particular attention being paid to the stabilisation of the current supply.A typical circuit is shown in Fig. 3, the switching on of the current being synchronised with the operation of an electric chronometer, although a stopwatch can obviously be used. A chemical coulometer can also replace both the precision resistor and the chronometer if this is preferred. With the circuit shown in Fig. 3, the constant current may be supplied from a 24-volt battery in series with a large resistance or, alternatively, the ax. mains supply may be employed via a constant-voltage transformer with full-wave rectification and appropriate stabilisation in the output circuit. Currents of 10 to 100 mA would generate from 1 x 10-7 to 1 x 10-6 equivalents of acid, base, metal ion, etc., per second during the electrolysis.The coulometric reaction can occur at either of the generating electrodes, and in general the cathode and anode compartments may have to be separated by a porous frit or agar gel, or both, to form an almost impermeable partition and prevent interaction of the electrode products. The electrolyte in either compartment may be agitated with a mechanical or a magnetic stirrer, and it is an advantage, particularly in controlled-potential coulometry, to keep the rate of stirring as smooth and constant as possible. The indicator-electrode system shown diagrammatically in Fig. 3 deserves special mention, because it is representative of those special devices employed in coulometry to denote the end-point of a particular titration. Such systems are described in detail in Section 4 (e).Sometimes, only one electrode or indicator half-cell is employed, this being coupled potentio- metrically with one of the working electrodes.August, 19611 LEWIS: COULOMETRIC METHODS IN ANALYSIS. A REVIEW 499 (e) INDICATOR SYSTEMS- In coulometric acid - base titrations, e.g., the liberation of hydroxyl radical at the segre- gated cathode of a potassium chloride electrolyte, the normal volumetric indicators, such as phenolphthalein, may be used to observe the end-point. Alternatively, in such instances, one could employ the normal glass-electrode system and find the equivalence point from pH observations. Conductimetric systems also have an obvious application in these instances.Spectrophotometric methods have also been widely used for end-point indication, the coulometric cell being suitably disposed in relation to a spectrophotometer and the,end-point A = Potentiometer B = Constant-current supply C = Rheostat E = Working electrodes e = Indicator electrodes or half-cells F = Permeable partition or frit I = Indicator meter, e.g., pH meter or M = Magnetic stirrer P = Potentiometric resistor R = Precision resistor S = Double-pole switch T = D.C. or A.C. operated timer microammeter Fig 3. Diagram of coulometric circuit noted photometrically at that wavelength at which excess of the generated titrant ion absorbs most strongly. For accurate work, measurements of the optical density are made at fixed intervals over the sensitive region of the titration.As an alternative to these preceding techniques, the so-called “amperometric” indicator- electrode system is much employed. A dry battery impresses through a suitable resistor a constant small potential across the two noble electrodes. The variation in current as recorded on a calibrated microammeter will yield a current - time graph showing marked inflexions in the end-point region. In experiments in the 10- to 100-pg range, the electrolysis occurring at the indicator electrodes must be of negligible order or it will interfere with the accurate determination of the amount of titrant generated at the working electrode. LeiseylS has shown that the determination of mercaptans in petroleum oil in alcoholic solution with electrically generated silver ion to precipitate the mercaptide may be fully automated by causing the current increase at the amperometric detector electrodes to energise a relay that stops both the current and an electrical timer. The widely known “dead-stop” indicator system of Foulk and Bawden has been much used for detecting the Fischer reagent end-point in water determinations. A related indicator system, depending on the rate of change of potential and known as the “derivative polaro- graphic method” has been introduced for redox titrations by Reilley, Cooke and F~rman.~e500 LEWIS: COULOMETRIC METHODS I N ANALYSIS.A REVIEW [Vol. 86 Two small platinum or gold electrodes are polarised with a minute constant current. The indicator electrodes show a varying potential difference during the progress of the deter- mination, the rate of change being particularly well marked at the titrimetric end-point.Such a system has been employed by Carson, Vandenvater and Gile20 in their study of the interferences produced by other substances during the reduction of plutoniumV1 with electro- generated ferrous titrant. They used a constant current of 0.1 pA produced by a 3-volt battery in series with a 30-megohm resistor. The value of the polarising current is critical in such applications and requires careful adjustment. Buck, Farrington and Swift21 have made use of a similar system for the titration of monovalent thallium with bromine. Potentiometric methods have been widely used for end-point detection in coulometric, acidimetric or redox determinations and their variations are so well known as to need no further comment.One recent interesting example, however, is given by the work of Mather and Anson,22 who utilised a non-aqueous solvent system consisting of an acetic anhydride - acetic acid mixture containing a perchlorate salt for the coulometric determination of milligram amounts of fluoride ion (error 0.3 per cent.) by titrating it as a base with electrogenerated perchloric acid. This acid was formed at a working mercury electrode according to the scheme- 2Hg + 2CH3COOH -+ Hg,(OOC.CH,), + 2H+ + 2e Most anions interfere, but for solutions of individual ions in acetic acid the method applies, e.g., nitrate or sulphate ions may be similarly determined. End-points were determined potentiometrically with a mercury - mercurous acetate electrode coupled with a glass electrode, sharp voltage inflexions being produced at the stoicheiometric end-point.Furman and ad am^^^ express the view that, for satisfactory end-point detection in the microgram range, pride of place must be given to the “Sensitive end-point method.” This involves the restoration of a pre-determined potential to an indicator cell system, the potential being itself determined by the end-point characteristics of the reaction being studied. This is essentially a null-point method, no current flowing ih the indicator circuit when this known potential is achieved. It is thus capable of great accuracy, and the previous workers em- ployed a high-sensitivity galvanometer as their end-point detector.They have applied the technique to the coulometric titration of p-methylaminophenol and hydroquinone with electrogenerated ceriumIv, the electrolyte consisting of a cerous sulphate solution in 2 M sulphuric acid. The indicator system was composed of a platinum - iridium anode coupled to a lead - lead amalgam - 2 M sulphuric acid half-cell. The potential of the anode may obviously be adjusted to any value by passing a constant generating current and allowing ceriumIv to form at the working electrode in the well stirred solution. The current is passed until the solution potential becomes equal to the indicator-electrode potential and no current flows in the indicator circuit. A known amount of the organic reductant is then added, the solution potential falls and is then again restored to the pre-set potential by electrogenerating ceric ions until zero current is observed in the indicator circuit.The number of coulombs employed to reach this stage can be most accurately determined. Ce3+ -+ Ce4+ + e 5. CONTROLLED-POTENTIAL METHODS If the coulometric electrolysis is carried out at controlled-potential, no indicating- electrode system may be necessary, the magnitude of the final current being sufficient indica- tion of the degree of completion of the reaction. S h ~ l t s ~ ~ has employed this method in the indirect determination of plutoniumv1 with excess of ferrous ion produced at a platinum electrode in sulphuric acid electrolyte, the excess of reductant being determined by coulometric back-titration.4H+ + PuO2,+ + 2Fe2+ --+ Pu4+ + 2Fe3+ + 2H,O. Methods of the controlled-potential type can suffer from the disadvantage of requiring long electrolysis times , but direct indication of the optimum eonditions for the successive electro- gravimetric deposition of cations can be obtained directly from the polarographic curves for the metal salts. Lord, O’Neill and Rogers25 have demonstrated the extreme sensitivity possible by the controlled-potential method and have determined amounts of silver in the millimicrogram range by first electro-depositing the metal and then subjecting it to an anodic strippingAugust, 19611 LEWIS : COULOMETRIC METHODS IN ANALYSIS. A REVIEW 501 procedure. The current - time curve was automatically produced by a recording potentio- meter of known chart speed and the area under the curve assessed with a planimeter (Section 3).A correction is applied for the background-current characteristics of the coulometer. 6. EXTERNAL GENERATION OF TITRANT One major difficulty attending the internal generation of a titrant in a solution is that other substances or impurities may be present which produce electrolytic interference. These difficulties have been neatly circumvented by Pitts et aZ.26327 and Bett, Nock and Morris,S who have described external generator cells wherein the titrant is formed externally and allowed to flow via capillary tubes into the solution to be titrated. Typical single-arm and bifurcate assemblies are shown in Figs. 4 and 5. Zinc anode /-L Generator Sodium chloride I Membrane i Copper sulphate Platinum (saturated) I 1 solution dish cathode Figs.4 and 5. External generators of titrant Chlorine and bromine may be produced at platinum electrodes Iodine is said to be best into reducing solutions of arsenites, etc. solution. which neutralises the alkali moduced at the cathode. in this way and passed generated in boric acid502 LEWIS: COULOMETRIC METHODS IN ANALYSIS. A REVIEW [Vol. 86 A most interesting application of the internal electrolysis technique is due to Hers~h,~2333 and this has been elaborated by KeideP into an automatic system for determining trace amounts of oxygen in inert gases. The apparatus consists essentially of the galvanic-cell system shown in Fig. 6. \ m Cadmium electroee Fig. 6. Coulometric oxygen meter The inert gas containing parts per million of oxygen is bubbled through a porous silver electrode into a 25 per cent.solution of potassium hydroxide containing a cadmium anode. The oxygen is quantitatively and instantaneously reduced and the cell current generated may be measured in the usual manner- 0, + 2H,O + 4e --+ 40H- (Reduction). Cd -+ Cd2+ + 2e (Oxidation). 2Cd + 0, + 2H,O + 2Cd2+ + 40H- (Cell reaction). If one accepts that one Faraday of current reduces 5603.6ml of oxygen at S.T.P., then, if the flow rate of inert gas containing C p.p-m- of oxygen is f ml per minute, it is readily deducible that the cell current, i, is given by- i = 0.287 f c P (?) PA where P is the pressure in atmospheres and T the temperature in degrees Kelvin of the inert gas under the conditions of the experiment.With a flow rate of 100 ml per minute and a temperature of 25" C, oxygen impurity equivalent to 1 p,p.m. would theoretically yield a current of 26.7 PA, and this is almost exactly the value obtained in practice. The method thus offers a most sensitive method for determining oxygen in nitrogen, helium, argon, etc., at levels well below 1 P.P.m., because current magnitudes of unit micro- ampere order are readily measurable. K ~ y a m a ~ ~ discusses the application of the Hersch cell system to other gases, e.g., carbon monoxide and carbon dioxide, and replaces the solution of potassium hydroxide in the galvanic cell by potassium hydrogen carbonate. It is obvious that if a de-oxygenated inert carrier gas is used to remove oxygen from liquids, then the Hersch method can also be applied to determinations in liquid media. Modifications of his original method have also been described by Hersch36 to determine traces of hydrogen in carrier gas.The gas stream is diluted with a known amount of pure oxygen and allowed to react at 500" C on silica wool, the excess of oxygen being measured galvanically. Other applications, e.g., studies of the corrosion of metals by acids, are referred to in the same paper.August, 19611 LEWIS: COUOLOMETRIC METHODS IN ANALYSIS. A REVIEW 503 8. ABSORPTION COULOMETRY Voorhies and Davis3' have recently described a constant-current coulometric method that involves the initial quantitative adsorption of the electroactive species to be determined on to a layer of compressed acetylene black.This adsorbent then forms one of the working electrodes of a generator cell in which the reducible adsorbed substances are subjected to a cathodic reduction process. Milligram amounts of anthraquinone and cupric ion have been determined in this way after adsorption from solutions. Acetylene black may be obtained in a state of high purity, it possesses a low redox blank and exhibits a high over-voltage property for both hydrogen and oxygen. Moreover, I kg weight 1 Fig. 7. Adsorption electrode its contamination by adsorbed atmospheric oxygen is consilered of negligible order. It is probable that organic impurities in gaseous systems may be isolated from the gas phase and determined in this manner. The general design of the working acetylene black electrode is shown in Fig.7. 9. COULOMETRIC HYGROMETRY The electrolysis of water in the presence of any suitable acidic electrolyte proceeds in accordance with Faraday's law, oxygen and hydrogen gases being produced, following the consumption of 2 Faradays, according to the scheme- 2H+ + 20H-+H,(g) + +O,(g) + H,O (liq.). Since the dissociation constant for water, k, = lO-l*, the thermodynamic equation for the reversible decomposition potential at 25" C of an electrolysis cell giving these gases is- log k: = -0.403 - 0,826 = -1.229 volts. 0-059 E=E:,+ - 2 In practice, because of polarkation effects, the decomposition potential as measured experi- mentally is usually about 0.5 volt higher for molar solutions. Wexler and Keide13g have developed an hygrometer based on the principle that, when a water vapour-air mixture is contacted with solid phosphorus pentoxide in an electrolysis cell composed of the inert plastic Teflon, the wet solid becomes electrically conducting.The pentoxide film is contacted with two spirally wound platinum-wire electrodes, and the absorbed water is quantitatively decomposed by a measured current. The magnitude of this resultant electrolysis current permits the determination of water vapour in the p.p.m. range in air.[Vol. 86 At a flow rate of 100 ml per minute of air through the Teflon cell under normal room conditions, 1 p.p.m. of water vapour produces an electrolysis current of about 13 micro- amperes. The instrument responds in a few minutes to humidity changes of the order of 50 to 100 per cent.of the original value. 504 LEWIS COULOMETRIC METHODS I N ANALYSIS. A REVIEW 10. COULOMETRIC APPLICATIONS OF PARTICULAR INTEREST (a) The extent to which foodstuffs are contaminated by residues of toxic agricultural pesticides is a matter of world-wide interest, and in some countries, e.g., the U.S.A., legislation restricts these residue levels to the p.p.m. range. Normal methods of analysis are time- consuming, but Coulson et have recently developed a method for determining BHC, aldrin, dieldrin, DDT and other chlorinated organic pesticides in 1 hour. This method depends on a gas-chromatographic separation of the pesticide followed by a combustion, the effluent gases yielding chloride ions, which are absorbed in water and coulometrically titrated with silver.The method is applicable to mixtures of chlorinated pesticides and to the thiophosphates. Schwabe and Seide14* have also examined the direct determination of gamma-BHC by controlled electrolysis. (b) Reilley and Porterfield41 have employed the electrogenerated complex ion of the soluble mercuric salt of ethylenediaminetetra-acetic acid to titrate milligram concentrations of calcium, lead, zinc, manganese, etc., in strongly ammoniacal solution. The reaction sequence is as follows, the complex ion being produced by reduction at a large mercury cathode : 2e + HgE2- -+ Hg + E4- Ca2+ + E4- -+ CaE2- A pre-titration is necessary to find the blank value due to contaminating ions, the end-points being observed with a potentiometric system. The method is undoubtedly applicable to microgram amounts also.(c) Devanathan and Fernando42 describe an unusual coulometric method wherein a multivibrator circuit gives constant pulses of electrolysing current to a titration cell, these pulses being accurately counted via a relay operating a Post Office mechanical counter. Minute amounts of reagent may be quantitatively produced in this way, and the method is considered superior to the constant-current method when the amounts to be determined are of the order of 10-4g or less. (d) Wilson and othersm have employed the method of controlled-potential reduction to study the number, n, of electrons involved in the reduction stages of the aminoacridines. They make use of a time factor, t+, determined graphically, which represents the time for the initial current to fall to half its original value. The total number of coulombs passed during the reduction is given by q=o.693 id, a n d n = - qM Fw where w is the weight or reducible compound of molecular weight M.( e ) Kunze and Willey44 have examined the anodic dissolution of tin and tin alloy, FeSn,, from tinplate anodes immersed in a decinormal hydrochloric acid electrolyte, a graphite rod being used as cathode. A high-speed recording potentiometer was used to determine the potential differences between the anode specimen and a silver - silver chloride indicator electrode. Steps in the potential - time curve correspond to the dissolution of pure tin and tin alloy. (f) Campbell and Thomasg5have employed the coulometric method to determine T, the thickness of oxide tarnish (in Angstrom units) on a metal film reduced slowly with a small measured current.The cathode potential rises sharply to the hydrogen discharge potential when reduction is complete. The following equation applies- lo5 itM T=- A nFd where i is expressed in milliamperes, t in seconds, A is the film area in sq- cm, d is the density of the film and M is the molecular weight of the oxide composing the film.August, 19611 LEWIS : COULOMETRIC METHODS IN ANALYSIS. A REVIEW 505 Similar methods have been described by the Tin Research Institute46 for the deterrnina- tion of the relative amounts of stannous and stannic oxides on a tinplate surface. (g) Gierst and Mechelynck4’ have made a unique mathematical and experimental study of constant-current coulometry as applied to unstirred, homogeneous solutions and claim that certain determinations can be carried out in times of less than 1 minute with a precision of the order of 0-2 per cent,.An equation is developed, based on the laws of electrolysis and of ionic diffusion, which relates the extent of the electrode reaction to a function called “transition time,” which is indicative of the time interval between the establishment of a capacity charge on the stationary electrode and the f a l l to zero of the concentration of electro- active substance in its vicinity. A detailed schematic diagram of the electronic “transito- meter” coulometer is given by the authors. (12) Considerable international commercial interest is being shown in the development of “fuel cells,”48 which are essentially coulometric devices for the direct conversion of chemical into electrical energy with consequent improvement in the thermodynamic efficiency.Typical of these devices is the Sondes Place cell, which operates at 500” to 700” C and has porous electrodes of zinc oxide and metallic silver, which are contacted with fused carbonate electrolyte. These electrodes, when contacted with air or oxygen and combustible sludge gas, respectively, produce electrical current according to the scheme- Air electrode: 0, + 2C0, + 4e -+ 2CO;- L 5 2 Fuel electrode: 2CO;- -+ + CH, + -CO, + H,O + 4e The corresponding Bacon cell utilises porous nickel electrodes and employs hydrogen as fuel; it operates at a temperature of 200” C and at a pressure of 400 lb per sq.inch.49 These fuel cells suggest an application of coulometry that has not yet been fully explored in the analytical field. There are obviously possibilities of utilising such systems for deter- mining combustible impurities in inert gas phases, e.g., as laboratory indicator cells for gas-chromatographic effluent gases. It is agreed that for such purposes it would be advan- tageous to develop a fuel cell that would operate satisfactorily at room temperature, but some cells are already known that can function at approximately 100” C, and it may be possible by employing catalytically active porous electrodes to lower this temperature yet further. I express my sincere thanks to Mr. W. H. Scates of the Laboratory of the Government Chemist, who has kindly drawn all the diagrammatic illustrations included in this review.1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. REFERENCES Kaye, G. W. C., and Laby, T. H., “Tables of Physical and Chemical Constants,” Twelfth Edition, Shields, W., Craig, D., and Diebeler, V. H., J . Amer. Chem. SOC., 1960, 82, 5033. 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