Analyst, May, 1973, Vol. 98,pp. 313-324 313 Precise Coulometric Determination of Acids in Cells Without Liquid Junction Part II.* The Silver - Silver Bromide Auxiliary Anodic Reaction? BY E. BISHOP AND M. RILEY: (Chemistry Department, University of Exeter, Stocker Road, Exeter, EX4 4QD) The solubilities of silver halides in solutions of their respective halides have been examined. The anodic deposition of silver bromide on silver electrodes has been studied, and mass-transfer limited current densities determined. The resistance of silver bromide films has been investigated, and the critical thickness at which the resistance suddenly rises was found to be inversely proportional to current density. The thickness of films in terms of coulombs per square centimetre and of micrometres was determined, and the specific resistance of various films measured. The magnitude of the “silver error” arising from solubility of silver bromide in bromide solutions and anodic stripping of silver ions to form a precipitate in the bulk of the solution has been established and found to be unacceptably high for precise work, although it can be reduced to less than 0-01 per cent.for less critical work. The behaviour of anodically deposited silver bromide films is explained on the basis of a porous deposit that becomes non-porous at the critical thickness. Conditions are chosen for determinations of 0.05 mol of a mono- basic acid a t high total currents that are well within the capacity of the silver anode. THE complexity of coulometric cells for high-precision work, and the degree of simplification achieved if the auxiliary electrode can be immersed directly in the test solution, have been mentioned in Part 1.l The requirements for this simplification were examined and found to be very restrictive; however, in one important determination, the cathodic assay of acids, it is possible to use a non-protolytic anodic auxiliary reaction of low potential.This reaction, which was first used by Szebellkdy and S ~ m o g y i , ~ ~ ~ involves the deposition of halide on a silver anode- i c is (equations are numbered in sequence from Part 11) where X- is chloride or bromide; iodide is not generally suitable as it tends to produce hard, non-porous films.* The limitation of this device is that the silver halide has a small but significant solubility in the supporting electrolyte, and its reduction to silver at the cathode competes with, and reduces the current efficiency of, the desired reduction of hydrogen ions and water molecules.Moreover, if the anodic current density exceeds the mass-transport limited current density of the halide ion, silver ion is anodically stripped and forms a precipitate with the halide in the bulk of the solution; the precipitate adheres to the cathode where it is reduced, thus further increasing the loss of current efficiency. The combined effect is hereafter called “the silver error.” Thus when the silver - silver halide auxiliary anode has previously been used in high-precision coulometric acidimetry, it has been kept isolated in a separate compartment .5 ~ 6 Szebellddy and Somogyi used chloride deposition in the determination of hydrochloric2 and sulphuric3 acids, but Lingane and Small’ preferred the use of the less soluble bromide, as did Carson and Ko8 for the determination of nitric acid. Lingane further used bromide in automatic determinations of hydrochloric acid,g as did Bishop and Shortlo in determining perchloric acid and in the micro-determination of perchloric and acetic acids. Results for .. - . (7) AgX + e + Ag + X- . . .. * For Part I of this series, see p. 305. t Presented a t the Second SAC Conference, 1968, Nottingham. @ SAC and the authors. Present address : Electronic Instruments Limited, Hanworth Lane, Chertsey, Surrey.314 BISHOP AND RILEY : PRECISE COULOMETRIC DETERMINATION [Analyst, Vol.98 the solubility of silver halides in solutions of their respective halide+ are presented in Fig. 1, which suggests that little advantage exists for bromide over chloride. The minimum solubility of silver chloride in chloride media occurs at chloride concentrations of between and 10-3 M, and of silver bromide in bromide media at bromide concentrations of between 10-3 and M. The solubility of silver bromide exceeds that of silver chloride when the respective halide concentrations become greater than 0.1 M, while silver iodide is more soluble in iodide media than the other halides in their respective media at all halide concentrations. 0 -2 -4 -6 Log,, IKXI Fig. 1. Solubilities of silver halides in solutions of the corresponding potassium halides. A ( x - - - x ) , X = Cl-, 25 "C; B (0-O), X = Br-,25"C; andC(0-.-0), X = I-, 20 "C.[KX] is measured in moll-1 Increase in solubility at high halide concentrations arises from complex formation. Assuming that the latter does not proceed beyond AgX,- formation, the reactions can be represented, together with their formation constants, as follows- KO .. .. * * (8) -k x- Agxsolid .. If So is the concentration of undissociated silver halide in the solution, and Ks is the solubility product of the silver halide, then .. .. .. .. . . (11) 1 KO = - KS and .. .. .. .. . . (12) SO KS K1 =- If no complexes higher than AgX2- are formed, then the solubility of the silver halide is12 S = - Ks + So + KIK,Ks[X-] . . .. . . (13) [X-I When the halide concentration [X-] is high (K, being small) the solubility of the silver halide increases linearly with [X-1.Forbes and Cole13 derived a similar equation for silver chlorideMay, 19731 OF ACIDS IN CELLS WITHOUT LIQUID JUNCTION. PART I1 315 in chloride media, and obtained values for So, representing the minimum, “intrinsic solu- bility” of silver chloride, of 6.1 x 1 0 - 7 ~ in hydrochloric acid and 6.3 x 10--7~ in sodium chloride solutions. The rate of dissolution of the silver halide may also be important in controlling the amount of dissolved silver in the cell electrolyte. This rate may be expected to depend on the surface area exposed to attack, that is, the particle size or film porosity, or both, of the halide, but, apart from work on photographic emulsions showing that the dissolution rate depended on both particle size and halide concentration,l4 no quantitative information is available.For the present purpose, the halide concentration must be kept low so as to avoid formation of soluble silver species, and yet sufficiently large to maintain the mass-transfer limited current above the working current so as to prevent formation of precipitate particles in the bulk of the solution: a large electrode area, with correspondingly reduced current density, is an obvious aid. For a variety of reasons, including reduced light sensitivity, the silver bromide system was chosen, and the purpose of this work was to establish conditions that involve the passage of 5000 C at a generating current of 2 A, which give the minimum “silver error,” and to examine possible means of further reducing the error.EXPERIMENTAL The equipment used has been previously described.l The coulometric cell and circuit are shown in Fig. 2. The salt bridge leads to an S.M.S.E., the platinum-gauze cathode was the large 72020 and the cell electrolyte consisted of a potassium bromide solution containing the aDDroDriate amount of suhhuric acid to simulate the acid. A kllelectrode potentials ’ire given with reference Clock r-3 Si I ,ver I anode to conditions for a determination o’f the standard hydrogen electrode -Platinum cat1 ,Stirrer bar lode Fig. 2. Coulometric cell and circuit for the study of the silver - silver bromide auxiliary anode system. V = Sangamo Weston S82 multirange voltmeter; and PSU = Solartron AS 1411 thyristor power supply unit, 2 A, 40 V RESULTS ANODIC OXIDATION OF SILVER IN BROMIDE~MEDIA- Tests were made of the electrolysis of potassium bromide solutions 0.08 M in sulphuric acid at 2 A by using silver anodes of areas 20 to 50 cm2. At bromide concentrations large316 BISHOP AND RILEY : PRECISE COULOMETRIC DETERMINATION [A%&?ySt, VOl.98 enough to support the anodic mass transport, the cell resistance rose rapidly until the output voltage limit of the power supply was exceeded and constant-current operation was no longer possible. At lower bromide concentrations the cell resistance remained relatively low, but the mass transport of bromide ions could not sustain the current and the potential of the silver anode rose rapidly to over + 1-8 V ; evolution of oxygen was observed and silver bromide was precipitated in the bulk of the solution. A potential - time curve plotted on the fast recorder is shown in Fig.3. At a current density of 70 mA cm-2 in 0.08 M bromide solution, after the initial almost instantaneous rise the potential rose slowly for about 10s as some silver bromide was deposited on the anode and some was precipitated in the solution. The potential of the anode then rose rapidly to a steady value governed by the evolution of oxygen [equation (4), Part I]. Repetition with a large silver anode of area 220 cm2 gave an initial rise of 30mV and then the potential of the silver anode rose steadily at about 1 mV s-1 for 500 s. > 1.5 > w. 5 0 p. in 0 ’ I +-- Chart travel Fig. 3. Anodic oxidation of silver a t 70 mA cm-2 0-05 M potassium bromide - 0.08 M sulphuric acid 0.2 0.4 0 6 Potential versus S.H.E./V Fig.4. Current - potential graphs for a silver anode: A, in 0.08 M sul- phuric acid; B, in 0.0038 M potassium bromide - 0.08 M sulphuric acid; and C , in 0.0067 M potassium bromide - 0.08 M sulphuric acid The limiting current for the discharge of bromide ion at the anode is15 nFDB,Ar [Br-IB I&. = -- .. .. .. . . (14) (l - tBr)aX E + + m &Is -+o where DBr 1 cm-1 s-1 is the thermal diffusion coefficient of bromide ion and 6% cm is the diffusion layer thickness. Subscripts S and B refer to concentrations at the plane of closest approach to the electrode surface, and in the bulk of the solution, respectively. The apparent electrode area is A cm2, the roughness factor is r and the transport number of bromide ion is tBr.A value of DBr = 2.06 x 1 cm-1 s-l was calculated from the Nernst expression16 . . (15) .. .. . o RT Z F 2 D = 10-3 - & . . where z is the charge number of the ion and A, IR-1 cm2 equiv-1 is the limiting conductance at infinite dilution. If a value of 6x = 3 x 10-3 cm in a well stirred solution17 is taken, then from equa$ion (14) the limiting current density for bromide ions at a bulk concentration of 0.01 M is 6.6 mA cm-2. Badoz-Lamblingls reports a value of 0.75 mA cm-2 in 0.001 M bromide solution, which is in fair agreement. Typical current - potential scans for a silver anode of A = 250 cm2 are shown in Fig. 4. Limiting current densities were proportionalMay, 19731 OF ACIDS IN CELLS WITHOUT LIQUID JUNCTION.PART I1 317 to bromide concentration: a mean value of 6.3 mA cm-2 in 0.01 M bromide solution is in good agreement with the calculated value. The calculated values for Fig. 4 are 2.5 and 4.4 mA cm-2 as against the measured values of 2.4 and 4.2 mA cm-2. The concept of 8% in well stirred solutions is a fiction, and the mass-transfer rate constant15 calculated from equation (15) can be used with some confidence in the selection of conditions; THE RESISTANCE OF ANODICALLY FORMED SILVER BROMIDE FILMS- A low film resistance is necessary to keep the over-all cell resistance within the limits of the power supply, and, in the interests of good current regulation, rapid changes in cell resistance must be avoided. At known constant currents, the cell resistance was monitored by means of the voltmeter, V, in Fig.2. Readings were taken at intervals of 20 to 200s and corrected for known resistance in the circuit. Electrolyses were performed at various current densities in solutions 0.3 M in bromide and containing 0.025 mol of sulphuric acid. Relatively small anodes of apparent area, A, 15 to 30 cm2 were used, so that large changes in total bromide concentration were avoided: the current densities of 4 , 7 , 10,20 or 40 mA cmW2 were calculated on the basis of the initial electrode area. The graphs of cell resistance versus film thickness in coulombs per square centimetre (means of several replicate runs in each instance) are shown in Fig. 5, and display a characteristic pattern. There is first a slow steady rise to approximately five times the initial resistance, followed by an accelerating increase to more than fifty times the initial resistance, and this rapid increase occurred at a critical film thickness that was inversely proportional to the current density.Similar curves were obtained at current densities of 10 to 40 mA cm-2 in 0.15 M bromide solution. The sharp rise coincided with the appearance of yellow patches or stripes on the previously dull green silver bromide film. The yellow areas, less than 1 per cent. of the total area, formed at places where the current density would be expected to be least, that is, at places most remote, or screened, from the cathode. The yellow deposit was softer than the green deposit, and dissolved very rapidly in the 1.0 M cyanide cleaning solution.Further, the cell resistance tended to show large irregular fluctuations during the rapid rise, suggesting that occasional cracking o€ the film occurred. On dissolution of the film in cyanide, a black, loosely adherent deposit remained on the electrode. The deposit dissolved rapidly in 1 + 1 nitric acid solution and was chemically identified as silver. Values for the critical film thick- ness were estimated by extrapolation of the two straight portions of the curves shown in Fig. 5 to a point of intersection. These values are plotted against the reciprocal of the current density in Fig. 6 and show a good fit. Estimates were made of the dimensional thickness of the films by direct measurement ILim. = - Kmass Br nFA [Br-IB. and by calculation. Direct measurements were made by micrometer gauge of the diameter Film thickness/[: cm-* Fig.5. Cell resistance v e w m film thickness graphs for the anodic formation of silver bromide at current den- sities of 40 (A), 20 (B), 10 (C), 7 (D) and 4 (E) mA cm-2318 BISHOP AND RILEY : PRECISE COULOMETRIC DETERMINATION [APUdySt, VOl. 98 I I I I 0.10 0.20 (Current density)-' /mA'-' cm2 Fig. 6. Variation of critical film thickness with current density of film formation of the coated rod and of the diameter after removal of the film; portions of the film removed from the anode were also measured; and such films after drying out were sandwiched between two thin glass plates, and the thickness of the glass plates was measured with and without the portion of film between them. Calculations were made on the assumption that no signifi- cant dissolution of the film occurred during its formation and that the density of silver bromide was 6.47 g cm-3.Results for films formed at a current density of 7 mA cm--2 are shown in Table I. The measured values were always 20 to 30 per cent. greater than the TABLE I THICKNESS OF SILVER BROMIDE FILMS Thickness/ p m 1 15.6 47 61 16.4 49 64 ThicknesslC cm-2 Calculated Measured calculated values, so the density of the deposit is less than the bulk density, thus supporting the contention that the deposited films are porous. B b 1 I 1 I I 40 80 120 F i I m t h ic kness/p m Fig. 7. Specific resistance of anodically formed silver bromide films at different current densities of formation. A, 20mAcm-2; and B, 4mA cm-2May, 19731 O F ACIDS I N CELLS WITHOUT LIQUID JUNCTION.PART I1 319 The calculated value for film thickness was used in conjunction with the appropriate value for cell resistance, corrected by subtraction of the cell resistance at zero time before any deposit had formed, in order to obtain estimates of the specific resistance of the films. The values were found to be in the region of lo4 to lo5 SZ cm and to vary as the film thickness increased. The variation for two films formed at different current densities is shown in Fig. 7. Attempts were made to measure the specific resistance of pre-formed films in potas- sium sulphate solutions of various concentrations. The output voltage of the source was measured with an anode current density of 5 mA cm-2, passed for the shortest possible time, before and after deposition of the film.Results are shown in Table I1 for the specific resistance of films pre-formed in 0.3 M bromide - 0.08 M sulphuric acid solution, measured in 0.2 and 0.02 M potassium sulphate solutions. The electrodes were immersed in turn in the two solutions, starting with the more dilute solution, and the process was repeated with fresh potassium sulphate solutions. The figures for the 30-pm film show that the specific resistance depends on the electrolyte concentration, again indicating that the films are porous. The 47-pm film was above the critical film thickness and caused the voltage limit of the power supply to be exceeded, so that it switched over to the constant-voltage mode; the current was rather unsteady, so that exact values could not be obtained.TABLE I1 SPECIFIC RESISTANCE OF PRE-FORMED SILVER BROMIDE FILMS, MEASURED I N POTASSIUM SULPHATE SOLUTIONS Specific resistancela cm Film thicknesslpm in 0:2 M K,SO, in 0.02 M SO, 30* (q 2.60 x 104 3-41 x 104 (2%) 2-73 x 104 3-28 x 104 47 > 4.5 x 106 > 4.5 x 106 * Estimated uncertainty of results = k0.13 x lo4 M cm. To check performance during a full acidimetric assay, the cell resistance was measured during the passage of 6000 C at 2 A by using a silver anode of area 255 cm2 in a 0.25 M potas- sium bromide solution containing 0.025 mol of sulphuric acid. A typical graph is shown in Fig. 8. The resistance increases steadily until a rapid rise occurs near the end-point, when the cathodic reaction switches from reduction of hydrogen ions to reduction of water molecules [equations (1) and ( 2 ) , Part 11] with consequent increase in the back e.m.f.of the cell. There- after, the cell resistance increases steadily at an enhanced rate, but is always well within the voltage output of the supply unit. In a similar full-scale experiment with a silver anode 10-3 OK Fig. 8. Cell resistance during the anodic formation of silver bromide a t 7-9 mA cm-a in a solution initially 0-25 M in potassium bromide and 0.08 M in sulphuric acid320 BISHOP AND RILEY PRECISE COULOMETRIC DETERMINATION [AIzdySf, VOl. 98 of area 263 cm2 in 0.1 M potassium bromide solution, the cell potential and the potential of the silver anode were measured. As shown in Fig. 9, both relationships are similar: the initial steady rise is followed by a more rapid rise as the limiting current density for the residual potassium bromide concentration is exceeded. The subsequent irregular behaviour indicates fracture of the anodic film. The magnitude and behaviour of the anode potential prior to breakdown of the film indicate an increasing overpotential due to film resistance.The measured anode potential was independent of the distance between the anode and the termination of the salt-bridge connection to the reference electrode, thus confirming that the IR drop between the working electrodes is caused by the resistance of the silver bromide film. Fig. 9. Silver anode poten- tial uersus S.H.E. (A) and power supply unit output voltage (B) during electrolysis a t an anodic current density of 7.6 mA cm-8 of a solution initially 0.1 M in potassium bromide and 0.08 M in sulphuric acid THE MAGNITUDE OF THE “SILVER ERROR”- The silver error was measured by chronopotentiometric anodic stripping, which will be described in Part 111, in order to ascertain its magnitude and the dependence on bromide concentration.Large anodes, of area 260 to 290 cm2, were used, and the acid determinand was about 0.025 mol of sulphuric acid. Most electrolyses were continued to the end-point, but some were of shorter duration in an attempt to discover whether the initial rate of dissolution of the halide film was greater than the average rate on account of the initially high but continuously decreasing bromide concentration. After the electrolysis, a visible film of silver black was present on the platinum cathode.The cathode was removed, carefully drained, washed by immersion in several successive portions of water so as to prevent loss of silver, and then transferred to a fresh cell for the determination of the silver error. This determination was carried out in an electrolyte consisting of 0.1 M potassium nitrate - 0.001 M nitric acid solution, at a current of 3 to 5 mA to a potential of +O.S V. The results in Table 111 show that the silver error is significant, being as high as 0-08 per cent., and is strongly dependent on the initial bromide concentration. The minimal error was attained with a low initial bromide concentration with subsequent addition of increments of potassium bromide at regular intervals so as to maintain the concentration at a level necessary to support the mass transport by bromide ions at the current of 2 A.The results also confirm that the rate of dissolution of the silver bromide film is higher than the average rate during the early stages of the electrolysis.May, 19731 OF ACIDS I N CELLS WITHOUT LIQUID JUNCTION. PART I1 TABLE I11 THE MEASURED “SILVER ERROR” 321 Quantity of electricity Initial [KBr]/mol 1-1 passed/C 0.33 4840 4750 0.25 4500 4500 1500 1010 Silver error/ C 3.63 3.28 1-48 1.48 0.57 0.47 Silver error, p.p.m. 750 690 330 330 380 470 0.22 4500 1.00 220 0-10* 4500 0.43 95 * KBr (10 mmol) added to cell electrolyte after each 500 s (1000 C ) of electrolysis. The results indicated that unacceptably large errors would arise in the assay of acid, even if the minimum initial bromide concentrations were used with periodic replenishment (0.0095 per cent.).Attention was turned to the cathodic reaction, and means of maintaining the cathode at a more positive potential during the determination, thus decreasing the silver deposition current. Saturation of the solution with oxygen so that reaction (4) (Part 11) would dominate without loss of cathodic current efficiency and the use of an “emerging” cathode were examined, The latter device was used by Hersch,lS who found that the electro- dissolution current of oxygen at silver cathodes was enhanced as much as twenty-fold by partially withdrawing an initially submerged electrode from the solutioq so as to expose a narrow band to the air. Chart travel - Fig.10. The potential of the platinum cathode in the vicinity of the end-point in the determination of 0.025 mol of sulphuric acid in 0-25 M potassium bromide solution. A, immersed electrode, solution exposed to air ; B, immersed electrode, solution saturated with oxygen; and C, “emerging” cathode, solution saturated with oxygen A series of three comparative experiments was performed in which the potential of the platinum-gauze cathode was recorded throughout an electrolysis that involved the passage of about 5500 C through a solution that was initially 0.25 M in potassium bromide and con- tained 0.025 mol of sulphuric acid. The area of the silver anode was 250 cm2, and the ceramic plug termination of the salt-bridge connection to the reference cell was replaced with a Luggin capillary placed very close to the cathode.The first experiment was performed with the solution exposed to the atmosphere (A in Fig. lo), the second with oxygen bubbling rapidly through a fine porosity sintered-glass disperser (B in Fig. 10) and the third with the top 3 to 5 mm of the cathode above the surface of the solution through which oxygen was322 BISHOP AND RILEY : PRECISE COULOMETRIC DETERMINATION [Analyst, VOl. 98 bubbled as in the second experiment (C in Fig. 10). The curve obtained with the “emerging” cathode was not significantly different from that obtained when purging with oxygen. In the first aerated solution, the cathode potential, initially about -0.4 V, decreased steadily to -0.7 V, then rapidly (as reduction of water molecules replaced reduction of hydrogen ions) to -1-5 V in the vicinity of the end-point of the neutralisation reaction. With the oxygen purge the curve was very similar, but the potential was about 0.1 V more positive throughout and the sharp drop occurred slightly later in the electrolysis.Purging with oxygen therefore had the desired effect qualitatively, but was disappointing quantitatively. Current - potential curves were prepared in oxygen-saturated and oxygen-free 0-05 M per- chloric acid - 0.1 M potassium bromide solutions. A Luggin capillary and a silver anode of area 240 cm2 were used, and the curves obtained (shown in Fig. 11) indicate identity at currents above 0.8 A, while at lower currents the presence of oxygen gives potentials that are rather more positive, but the difference is not more than 70 mV even at a current of 50 mA.DISCUSSION The distinct green colour of the anodically formed silver bromide films, together with the loose residue of silver black after treatment with cyanide, attest the migration of bromide into the silver metal, and that of silver atoms through the film to the liquid interface, a common occurrence. Indira and Doss20 later found silver to chlorine ratios to be as high as 1-1: 1 in chloride films formed at 10 to 20 mA cm-2, but thought that the excess of silver might be present in the form of interstitial silver ions, which involves the presence of an equal number of trapped electrons (presumably solvated) , and consequently that absorption in the visible region produced a colour different from that of the normal halide.However, such a colour would be brown, not green, and such a large accumulation of separated charge in a conducting and porous film is very unlikely. I - 0 5 -0.3 -0.1 Potential versus S.H.E./V Fig. 11. Current - potential curves for a platinum cathode in 0.05 M perchloric acid - 0.1 M potassium bromide, de-oxygenated (A) and saturated with oxygen (B) Porosity readily explains the characteristic shape of the cell resistance versus film thickness curves. Growth of the film reduces the effective surface area of exposed silver, and the more restricted mobility of electrolyte solution in the pores will lead to exhaustion of bromide ions and stripping of silver ions, which migrate to the film- liquid interface, depositing normal silver bromide in the pores.Hence the yellow colour appears in parts of the film that retain high porosity. Final blockage of the pores leads to an essentially non-porous film and a rapid rise in resistance. The values found for the specific resistance in potassium sulphate solutions further confirm that silver bromide films are porous until the critical thickness is exceeded. Although this finding conflicts with the results obtained by Jaenicke, Tischer and Gerischer,21 who found the specific resistance of silver chloride films to be inde- pendent of electrolyte concentration for thicknesses even as small as 3 pm, Briggs andMay, 19731 OF ACIDS I N CELLS WITHOUT LIQUID JUNCTION. PART I1 323 Thirsk22 considered such films to be porous, and calculated that if the total capillary area were only 0.1 per cent.of the electrode area, then 99 per cent. of the current would be carried by the liquid in the capillary pores in a 0.1 M potassium chloride solution. K ~ r t z ~ ~ first observed that anodically formed silver halide layers had specific resistances ten to one hundred times less than that of the solid crystallised from the melt; the value for solid silver bromide is about lo7 Q C I T L . ~ ~ The values found in the present work, 5 x lo4 to lo5 Q cm, agree with those found by Lal, Thirsk and Wynne- Jones,24 and Jaenicke et aZ.21 obtained curves similar to those in Fig. 7 for silver chloride films. In all three instances, the calculated values for specific resistance increased with decreasing current density of film formation.The higher conducti- vity of anodic silver halide films has been explained by Kurtz23 in terms of porosity, while Briggs and Thirsk22 thought that the silver chloride film was a crystalline material of specific resistance equal to that of the solidified melt, in parallel with a capillary network of pores. Jaenicke et aL21 concluded that silver chloride films were non-porous, while Indira and Doss20 ascribed the higher conductivity to a high concentration of interstitial ions. The inverse proportionality between critical film thickness and current density of formation (Fig. 6) parallels the work of La1 et u Z . , ~ ~ who observed a change of slope of about two-fold in the overpotential versus time for anodic formation of silver chloride. The calcu- lated film thickness at the point of change was approximately inversely proportional to current density of formation and was independent of chloride concentration in the electrolyte, as is demonstrated here for bromide films.It is clear that the structure of anodically formed silver halide films is strongly dependent on the current density of formation, and so also, therefore, is the coulombic capacity of the reaction. The small effect of oxygen on the cathodic reaction indicates that the charge-transfer overpotential for the reduction of oxygen on platinum, either clean or covered with a film of silver, is very large under the conditions used. CONCLUSIONS The results presented provide a basis for the selection of suitable values for the current density and bromide concentration for the auxiliary electrode reaction at given values of generating current and total quantity of electricity required.An anode area of 300 cm2 is chosen; at a current of 2 A the current density will be about 7 mA cm-2, the capacity of the anode for silver bromide formation will be about 9000 C and, even after ten determinations of 0.05 mol of a monobasic acid, the capacity should still be in excess of 6000 C. A residual bromide concentration at the end of a determination has been chosen to be 0.03 to 0.05 M, for which the limiting current density is 20 to 33 mA cm-2; when added to the amount of bromide consumed in the reaction, the initial bromide concentration should be 0.20 to 0.22 M. The “silver errors” are significant and attempts to minimise them were only partially effective.A means of correction for the silver error is necessary for work of the highest accuracy, and will form the subject of Part 111, but it is possible to make the error tolerably small for less critical work. One of us (M.R.) expresses deep gratitude to the Charitable and Educational Trust of the Worshipful Company of Scientific Instrument Makers for financial support in the form of a Research Studentship. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. REFERENCES Bishop, E., and Riley, M., Analyst, 1973, 98, 306. Szebelledy, L., and Somogyi, Z., Z. analyt. Chein., 1938, 112, 323. Bishop, E., and Dhaneshwar, R. G., Analyt. Chem., 1964, 36, 726. Taylor, J. K., and Smith, S. W., J . Res. Naha. Bur. Stand., 1959, 63A, 153. Eckfeldt, E. L., and Shaffer, E. W., Analyt. Chem., 1965, 37, 1534. Lingane, J . J., and Small, L. A., Ibid., 1949, 21, 1119. Carson, W. N., and KO, R., Ibid., 1951, 23, 1019. Lingane, J. J., Analytica Chim. Acta, 1954, 11, 283. Bishop, E., and Short, G. D., Analyst, 1964, 89, 587. Linke, W. F., “Solubilities of Inorganic and Metal Organic Compounds,” Fourth Edition, Volume 1, Laitinen, H. A., “Chemical Analysis,” McGraw-Hill, New York, 1960, pp. 114-116. Forbes, G. S., and Cole, J. I., J . Amer. Chem. SOC., 1921, 43, 2492. James, T. H., and Vanselow, W., J . Phys. Chem., 1958, 62, 1189. I , Ibid., 1938, 112, 332. -__ Van Nostrand, Princeton, 1958.324 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. BISHOP AND RILEY Bishop, E., Chemia Analit., 1972, 17, 511. Kolthoff, I. M., and Lingane, J. J., “Polarography.” Volume I, Second Edition, Interscience Publishers Inc., New York, 1952, p. 52. Bishop, E., Dhaneshwar, R. G., and Short, G. D., in West, P. W.. Macdonald, A. M. G., and West, T. S.. Editors, “Analytical Chemistry 1962,” Elsevier, Amsterdam, 1963, p. 241. Badoz-Lambling, J., Bull. Soc. Chim. Fr., 1959, 792. Hersch, P., in Reilley, C. N., Editor, “Advances in Analytical Chemistry and Instrumentation,” Volume 111, Interscience Publishers Inc., New York, 1964, p. 198. Indira, K. S., and Doss, K. S. G., J . Electroanalyt. Chem., 1968, 17, 145. Jaenicke, W., Tischer, R. P., and Gerischer, H., Z . Elektrochem., 1955, 59, 448. Briggs, G. W. D., and Thirsk, H. R., Trans. Faraday SOL, 1952, 48, 1171. Kurtz, L. J., Dokl. Akad. Nauk SSSR For. Lang. Edn, 1935, 2, 305. Lal, H., Thirsk, H. R., and Wynne-Jones, W. F. K.. Trans. Faraday SOC., 1951, 47, 70. NOTE-Reference 1 is to Part I of this series. Received December 121h, 1972 Accepted January lst, 1973