Thin Layer Potential Scan Coulometry Determination of Metal Ions and of Halide Ions Using a MercuryCoated Platinum Electrode DONALD M. OGLESBY,' LARRY 8. ANDERSON, BRUCE MCDUFFIE,~and CHARLES N. REILLEY Department of Chemistry, Universify of North Carolina, Chapel Hill, N. C. A linear ramp potential excitation was applied to a thin layer electrolysis cell containing a solution of several electroactive substances. The integral of the current response constitutes a coulometric titration of the electroactive species present. The technique, potential scan coulometry, has been evaluated by electrolysis of solutions of copper, lead, cadmium, and zinc ions in a 1M KNO, medium and preBr-, and CI- ions cipitation of I-, with mercurous ion electrogenerated from a mercury-coated platinum electrode. The technique appears to be particularly suited to rapid analysis of mixtures and of very small amounts of electroactive substance.
S
RECENT reports of the applications of electrolysis in a thin layer of solution have cited the quantitative theory for chronopotentiometry and chronoamperometry in this finite boundary technique (8, 12, 19). In their discussion of the chronopotentiometric technique, Christensen and Anson (8) considered the transition time as the end point of a coulometric titration of the electroactive species entrapped in the solution layer. This presents the possibility of application of electrolysis in a thin layer to the many problems suitable for study by controlled current and controlled potential coulometry. The technique offers the advantages of small solution volumes (much less than a milliliter may be used) and rapid analysis time, This report concerns the extension of the coulometric technique by application of linear ramp potential and of step current excitation functions to a thin layer electrolysis cell equipped with a mercury-coated platinum working electrode. Scott, Peekma, and Connally (23) have discussed the application of linear ramp potential excitations to coulometric cells of more ordinary construction. Propst (20) in a similar study employed scan rates varied in proportion to the reciprocal of the Present address, Old Dominion College, Norfolk, Va. 23508. 2 On leave from State University of New York at Binghamton, N. Y. EVERAL
275 7 5
instantaneous current. Total elapsed time required for completion of a titration using these techniques is as short as seven minutes. When the analysis is carried out in a thin layer 10 to 30 microns thick, potential-scan coulometric determination of several components is possible in a time interval of two to three minutes. The thin layer technique has been tested and verified on a mixture of metal ions. In addition to the well known argentimetric methods for the determination of chloride, bromide, and iodide ions, the precipitation titrations of those ions have been studied using standard mercurous nitrate as the titrant (23, 17). Also, electrogenerated mercurous ion has been used (9, 21) to determine macro and micro amounts of halide ions. Thin layer coulometry is applied here to solutions of the halide ions and halide mixtures, precipitating the corresponding mercurous salts a t the mercurycoated platinum electrode. EXPERIMENTAL
All chemicals used were of ACS reagent grade. The metal ion solutions were prepared by dissolution of weighed amounts of each metal in a small amount of concentrated nitric acid, neutralization with sodium hydroxide, and volumetric dilution. Potassium salts were employed in preparation of the halide ion solutions. The supporting electrolyte was 1.0M KNOa in all cases, except with the 2 and 0.4m-%f halide solutions where 0.10X KN03 was used. Apparatus. The thin layer cell, equipped with a mercury-coated platinum working electrode, was described previously (19). Philbrick UPA-2 and chopper stabilized K2-W operational amplifiers were employed in a threeelectrode system to maintain potential control and measure the integral of the current. Generalized circuits of this type have been described by others (7, 29). Procedure. The total flow of charge, &, was recorded as a function of the potential applied to the working electrode. For the halides, a KNO, salt bridge to the S.C.E.reference electrode was used. Metal ion solutions were thoroughly deaerated prior to introduction into the cell. The poChemicals.
tential was preset a t 0.15 volt us.
S.C.E. and scanned cathodically until the thin layer was depleted of metal ions. Scan rates between 0.3 and 0.6 volt/minute gave well developed waves and acceptable background currents at solution thickness, I , of 20 to 30 microns. Deaeration was required in the case of halide solutions containing iodide ion. The potential was preset a t a sufficiently cathodic value and scanned anodically until precipitation of the halide ions was completed. A scan rate of 0.15 volt/minute yielded optimum separation of the halide waves. After completion of each scan, the potential was returned to its preset value, stripping the metals from the electrode or, in the case of halide precipitation, regenerating mercury metal. The analytical data are treated with reference to the theoretical equation for thin layer coulometry, Q = nFAlC", where A is the area of the working electrode and C" is the initial concentration. The effective area of the electrode, calculated from previous calibration data (19), was 0.283 sq. cm. or approximately 2% larger than the area calculated from the diameter of the electrode face. For each sample solution, a number of &-E curves were obtained, usually a t micrometer settings from 8 to 50 microns. Thicknesses up to 200 microns were used with some dilute solutions. Average Q / 1 values were determined in two ways. First, if the value of 1 was known from previous calibration, & / I was calculated directly for each run. Second, if the micrometer setting for zero thickness was not known, Q was determined a t several micrometer settings, and the least-squares best line yielded a value for the slope, Q / l . In both cases, & / E owas compared with nFA (27.3 X lo3 coul. cm.2/mole for a one-electron change) to obtain the per cent error. For routine analytical use, a better procedure would be t o use a Q-C calibration curve obtained a t a standard micrometer setting. For the cell used in this work, a solution thickness of 30 microns provides a volume element of suitable reproducibility. MIXTURES OF METAL IONS
A typical experimental curve for potential scan coulometry a t a mercurycoated platinum surface is shown in VOL 37, NO. 1 1 , OCTOBER 1965
1317
6
//zn
- S C A N 4 5
.-
4
0
x
0 . I
-aE . 3 u
electroactive substance, added to a given quantity of the sample, provides an internal standard for comparison with other waves observed. Only 8 single scan need be made to establish the concentrations of all species present. Alternatively, use of a standard addition method of calibration also eliminates the need for exact knowledge of the solution layer thickness and the area of the electrode. HALIDE IONS AND HALIDE MIXTURES
6 2
I
-0.4
0 POTENTIAL,
v o l t s vs.
Figure 1. Potential scan coulometry of solution 1.0 ions CU+~,Pb+2, Cd+2, and Zn+2 A.
-1.2
-0.8
S.C.E.
X 10-2M in each of the
Scan rate, 0.05 volt/minute
B. .%an rate, 1.20 volts/minute C. .%on rate, 12.0 volts/minute 1 .OM KNOa supporting electrolyte; thickness, 1 2.7 microns; effective electrode area, 0.283 sq. cm.
Figure 1A. The half-height potentials (CU+’ -0.03, Pb+2 -0.51, Cd+2 -0.70, Zn+2 -1.03 volt us. S.C.E.) are 30-130 mv. more negative than the half-wave potentials for these couples reported in the polarographic literature (Cuf2 +0.02, Pb+2 -0.38, Cd+2 -0.58, Zn+2 - 1.00 volt vs. S.C.E.) (18). Obviously, many other metal ions commonly analyzed a t the D.M.E. may also be studied with this technique. Table I summarizes the results obtained for a sample 10-2M in each of the ions Cu+2, Pb+2, Cd+2, and Zn+2, and 1.OM in KNOa. The potential scan of all four components required only three minutes. Analysis time with the thin layer technique is considerably less than
would be required to perform a similar controlled potential coulometric titration using a cell of more ordinary construction (9, 60). The results show precision and accuracy commensurate with our present thin layer electrode design. In coulometry, the total charge passed as the result of a potential or current excitation does not depend on the diffusion coefficient of the reacting species and, consequently, will be independent of such factors as temperature, ionic strength, and viscosity. For a given number of equivalents of reacting substance, the faradaic response will be independent of the identity of the substance. Thus, a known amount of an
Halide Pre-Wave. A significant anodic coulombic flow of transient nature was observed immediately preceding the mercurous halide precipitation waves. This pre-wave was more pronounced for iodide than for bromide or chloride (see Figure 2). When the applied potential ramp was halted in the pre-wave region and maintained constant for several minutes, no accumulation of product took place during the waiting period. A subsequent cathodic scan merely retraced the Q us. E curve. Had the anodic pre-wave been due to the formation of a crystalline mercurous halide precipitate of constant activity, a buildup of the precipitate would have continued throughout the waiting period, because of the diffusion of iodide ions into the thin layer a t the edge. Indeed, such a buildup was observed if the potential was maintained a t a potential on the main halide wave-Le., a t potentials more positive than the “starting” potential. The starting potential, E,, of each halide wave-Le., the potential a t which a reaction product of constant activity begins to form-was determined by application of a constant potential for several minutes, followed by a cathodic scan. Observed E , values were within 30 mv. of those calculated from the thermodynamic relationship
0.059 log [ X - ] Table 1.
Ions present c u +%
Potential Scan Coulometry of a Mixture of Four Metal Ions &/1c05 Ex tl. result &/1
C” pmole/cm.a 9.36
Average (pcoul./cm.)
x
anfstd. dev. (coul. cm.Z/mole)
Av. error,
10-8 x 10-a % 524. 56.0 f 2 . 2 +2.6 +7.0 546. 58.4 f 2 . 7 10.05 518. 51.5 f 2.3 -5.7 Pb +z -5.7 518.c 51.5 4~ 1 . 1 -0.5 9.05 491. 54.3 f 2 . 4 Cd +g 52.6 f 1 . 4 -3.7 476.c en += 8.91 447.b 50.2 f 1.2 -8.1 452.c 50.7 f 0 . 1 -7.1 & / E o= nFA; % error based on expected value of 54.6 X loa coul. cm.z/mole. b Average of 5 runs with Teflon collar slipped up past electrode face approx. 0.001 inch; 1 = 20.3 microns. c Average of 3 runs with Teflon collar slipped down past electrode face; 2 = 27.5 (1
microns. 1318
ANALYTICAL CHEMISTRY
using K’, values for the appropriate ionic strength (66). Two explanations have been proposed for the current preceding the main mercurous iodide precipitation wave. Biegler (3-5) suggests, on the basis of a.c. and d.c. polarographic studies, that this current is wholly nonfaradaic and is caused by the increased specific adsorption of iodide ions. On the other hand, Kolthoff and Okinaka (14) stated that this current is caused by formation of an adsorbed mercurous halide film. Our results indicate that the pre-wave current does not lead to the formation of a crystalline precipitate. The observed Q us. E behavior prior to E, is consistent
0.0
4
-
Figure 2.
Potential scan coulometry
of halide solutions
A. 5;OOmM CI8. 5.00mM BrC. 5.OOmM ID. Solution C, made 5mM in CI- and rescanned without moving the electrode Solution D, made 5mM in Br- and rescanned without moving the electrode 1 .OM KNOs supporting electrolyte; scan rote, 0.1 5 voit/min.; thickness, 34.6 microns; effective electrode orea, 0 . 2 8 3 sq. cm.; Teflon collar slipped up post the electrode face approximately 0.001 inch
E.
4-SCAU-
0.3
0.2 0.I P O T E N T I A L , volts
-0.1
0.0 VI.
either with a potential dependent adsorption of iodide ions or with the reversible formation of an electrode reaction product whose activity is potential dependent. An iodide ion stripped of its hydration sphere and located about 2 angstroms from the mercury surface may fit both of these descriptions (11). Individual Halide Ions. Analytical data for the halide ions and some halide ion mixtures are given in Table 11. The halide waves were meashred a t the half-height potentials, taking the initial slope parallel to the E-axis a t the point where a net anodic current began to flow and taking the final slope as best drawn from the post-wave plateau. At concentrations of 5mM, the individual halides can be determined to an accuracy of about 401,. This accuracy compares favorably with the results of Praybylowica and Rogers (21) for quantities comparable to the number of moles of halide contained in the thin layer volume element. At low concentrations the accuracy of the determination is impaired by the difficulty of correcting for background current in the presence of a relatively large pre-wave, amounting to as much as 30 pcoulombs. Direct subtraction of the curve run on the supporting electrolyte is not a valid correction; Shain and Perone (24) demonstrated that a layer of AgI on a silver microelectrode reduces the capacity of the electrical double layer. An analogous effect is apparently operative a t the mercury electrode. As the number of moles of halide ion becomes smallerLe., the concentration and/or the solution layer thickness are decreased these surface phenomena become more important. I n the special case of low concentrations of C1-, interference of the beginning of the mercurous ion wave with the top of the mercurous chloride wave causes additional uncertainty in measuring wave heights.
S.C.E.
At concentrations greater than 10 to 20mM, the mercurous halide film .becomes so thick that further precipitation of halide is inhibited. I n this condition, the electrode may still transfer electons, as shown by Kuwana and Adams' study of organic oxidations a t the mercurous chloride film anode (15). Those authors observed that an Hg2C12film 20 A. thick was sufficient to cause inhibition. From calibration data and the molar volumes of the mercurous salts, we have found inhibition of halide precipitation and of the final mercurous wave a t chloride or iodide film thicknesses of 20 to 40 A.
Table II.
Potential Scan Coulometry of Halide Ions
Q/lCoa Exptl. result No. of Average and std. dev. C" different Q us. E (ficoul./cm.) (coul. cm.2/mole) Av. error, pmol/~rn.~ 1-settings curves x 10-3 x 10-3 % INDIVIDUAL HALIDES Total No. of
Ion(s) I-
Br -
c1-
Halide Mixtures. The data of Table I1 indicate the existence of serious interferences in the thin layer potential scan coulometry of halide mixtures at the mercury-coated platinum electrode. The least interference (see Figure 2) is observed in the determination of I- in mixtures, where distinctly less error was observed than reported by Przybylowica and Rogers (21) in a more conventional coulometric titration procedure. Relatively low current densities (25 to 100 fia./sq. cm.) are used in the thin layer potential scan method, and the rate of mass transfer approaches homogeneous diffusional mixing. Thus, one might expect a close approach to equilibrium conditions in the thin layer precipitation of mixtures, approximating the technique of precipitation from homogeneous solution.
5.00 5.00 5.00 2.00 0.40 5.00 5.00 5.00 5.00 2.00
4 2 4 7 6 1 4 1 3 4
5.00 5.00 2.00 2.00 5.00 5.00 5.00 5.00 5.00
1
5
4
11
4
9
1
5
13 8 11 20 12 3 10 3 6 10
Q/1
141. 137. 145. -56.7* 11.3b 141. 137. 139. 126. 60.2b
28.2 f 1.0 27.4 f 1 . 0 29.0 f 1 . 0 28.4 f 1 . 6 28.3 f 2 . 0 28.2 f 0 . 7 2 7 . 4 f 0.9 2 7 . 8 =t 0 . 5 25.2 f 1.6 30.1 f 1 . 4
+3.3 $0.4 +6.2 $4.0 f3.7 +3.3 +0.4 f3.7 -7.7 +lo.
EQUIMOLAR HALIDEMIXTURES I-
c1Ic1Brc1IBrc1-
131. 112. 55.0b 44.8b 134.bpe 134. 134.O 126.c 112.c *so
26.2 =t 0 . 4 22.4 f0 . 6 2 7 . 5 =t 2 . 1 22.4 f3 . 3 26.8 f 1 . 8 26.8 f 1 . 7 26.8 f 1 . 3 25.2 f 1 . 5 2 2 . 4 =t 1 . 2
-4.0 -18. f0.7 -18. -1.8 -1.8 -1.8 -7.7 -18.
1 : 10 Ratio of I-: C1I5.00 1 4 135. 27.0 f 1 . 2 -1.1 c150.0 370. 7.4 f0.5 -73. a Q/lCo = nFA; % errorbase+ on expected value of 27.3 x lo3 coul. cm.z/mole. Slope of least-squares best line, from Q us. 1 plot. Q value for each halide quite dependent on method of measuring successive halide waves.
VOL 37, NO. 11, OCTOBER 1 9 6 5
1319
,
The Br--Cl- interference is probably caused by solid solution formation, as in the case of the silver halides where some improvement has been made by altering solution conditions (6). The mercurous halides have isomorphous, tetragonal structures (17),and mixed crystals of HgzClrHgzBrzhave been prepared by the addition of mercurous nitrate solution to solutions of various KC1 :KBr ratios (16). Apparently, HgzIzhas little tendency to form mixed crystals with HgzBrzor H g L L Extremely high concentrations of C1- or Br- in the presence of I- will tend to give soluble mixed complexes of Hg(I1) such as HgIzC12-2 or HgIBra-2 (16) whose anodic waves may not be well separated from the terminal HgCL-2 or HgBra-2 waves in such solutions. The chloride and bromide waves are more symmetrical if preceded by an iodide wave. This may be caused by adsorption of Br- or C1- on the HgJz surface a t potentials prior to E, for those halides, Potential scan of a solution 5mM in I- and 0.4mM in C1- resulted in a chloride wave showing 45% recovery a t 1 = 57 microns, 25% recovery a t 1 = 37 microns, and no detectable C1- wave (< 15%) a t 1 = 17 microns. As expected, the amount of substance adsorbed appears independent of 1, resulting in a greater percentage error in Q as 1 is decreased. A cell with twin working electrodes (1) might be used to advantage if the deposited product from a first reaction interferes with a subsequent reaction. In the above case of 5mM I- and 0.4mM C1-, one electrode could be used to collect the HgJZ film; then the chloride could be precipitated a t the facing electrode. A few chronopotentiometric studies were made on chloride and bromide solutions in the presence of oxygen because this would be the most economical method of applying the thin layer technique to the rapid analysis of small chloride or bromide samples. Well defined chronopotentiograms were obtained, and the results of the analysis are given in Table 111. Oxygen does not interfere, and a fraction of a milliliter of
Table 111.
Ion c1-
5
solution may be analyzed; only sufficient solution to contact the reference and auxiliary electrodes is required. DISCUSSION
Wave Shape and Separation.
If
both the oxidized and reduced species are soluble in the solution phase, the steady-state concentration of R in the thin layer after passage of a charge Q will equal C R O Q/nFAl where C E O is the initial concentration of R. Correspondingly, the concentration of 0 a t any time will equal Coo Q/nFAZ. The potential as a function of Q in the case of Nernstian behavior will then be
+
If the reduced form deposits on the electrode surface or forms an amalgam, this expression must, of course, be modified to account for the changing activity of the reduced form, R , at the electrode surface. The Q us. E curve will then deviate from the simple expression given in Equation 1 but will still maintain an approximate s-shape (Figure 1). Diffusion of the metal atoms into the electrode is restricted by the proximity of the platinum metal interface to the amalgam surface (10). The resulting increase in activity of the metal a t the electrode surface causes the half-height to be reached a t a more negative potential than in polarography. ZR drop across the face of the working electrode, uncompensated by the three-electrode system, would also cause the halfheight potentials to shift to even more negative potentials. These effects may account in part for the discrepancies already noted between the half-height potentials and the polarographic halfwave potentials. As 1 becomes smaller, the average time required for a molecule to diffuse across the solution layer becomes smaller, and fast potential scan rates are possible. Full advantage should be taken of the rapid mixing afforded by these thin solution layers in order to
Thin Layer Chronopotentiometric Determination of CI- and Br- with Electrogenerated Mercury(1)"
C" taken, moles/liter
Transition time, sec.
Q,
pcoulombs
C" found, moles/liter
5.59 x 10-3 5.31 X 5.15 X av. 5.35 X Br5.0 X 19.6 392 5.31 X 5.0 x 10-3 19.6 392 5.31 X 5.0 x 10-3 20.0 400 5.41 x 10-3 av. 5.34 X 1 = 27.5 microns; electrode area = 0.278sq. cm.; i = 20 m.; 1.OM KNOa supporting 5.0 x 10-3 5.0 X 5.0 X
electrolyte.
1320
ANALYTICAL CHEMISTRY
20.6 19.6 19.0
412 392 380
minimize contributions from secondary reactions and background currents (2). However, if the potential is changed too rapidly, the rate of mixing by diffusion is no longer sufficiently rapid, and the curves become badly distorted. Figure 1 shows the dependence of the wave shape on the rate of potential scan a t a 12.7-micron solution thickness. DeVries and Van Dalen (10) have investigated the current response upon application of a linear ramp potential to a thin mercury film containing a dissolved metal. Their results are useful in giving an order of magnitude estimate of the most suitable scan rate for a given solution thickness in potential scan coulometry. On the basis of their calculations, when l is 20 to 30 microns, the distance along the voltage axis between the bottom and top of the wave will not vary significantly from the equilibrium value until the scan rate exceeds 2 volts/minute. Experimentally, curve B in Figure 1 shows the beginning of distortion a t a scan rate of 1.2 volt/ minute. Of course, actual separation also depends on such factors as the magnitude of the residual current, irregularities in the geometry of the volume element, and ZR drop across the electrode face. Our experiments indica% that the separation of the waves for two-electron processes will not be good regardless of the scan rate if the halfwave potentials of the two waves do not differ by more than 200 mv. Application of a triangular wave excitation potential, instead of a linear ramp potential, would produce successive titration of the oxidized and reduced species-cyclic coulometry. By analogy to cyclic voltammetry, this technique would be useful for detection of irreversible electron transfer processes, detection and measurement of chemical reactions following electron transfer, and study of complex electrode reaction mechanisms. At slow potential scan rates the mathematical expressions for the dependence of Q on potential would be simpler than those encountered in cyclic voltammetry. Analysis of Errors. A significant factor in the accuracy and precision of the technique is the reproducibility of setting of the micrometer and of applying a fresh mercury surface t o the platinum electrode. With the present micrometer arrangement, these operations can be reproduced to approximately ~ k 0 . 5microns (19). When the operating distance between the parallel faces is of the order of 25 microns, a corresponding uncertainty of 2% is present. Another major source of error is background current, primarily that arising from edge effects. The cylindrical edge of the solution between the electrode and the glass plate is exposed to the bulk solution. Thus, a contribu-
tion (approximating semi-infinite diffusion) from the bulk into the cylindrical edge occurs as the electroactive species in the thin layer itself is depleted. The effect is evident in the plateau region. If the surface of the working electrode is perfectly flat, at a thickness of 10 microns the area of the cylindrical section exposed to semi-infinite diffusion is 1.75 X sq. cm. or 0.7% of the area of the electrode face. The flux per unit area a t the exposed edge (causing deviation from the simple model assumed for thin layer electrolysis) will always be larger than the flux per unit area a t the center of the electrode. An estimate of lyo,based on the ratio of the areas exposed to the two types of diffusion, would be very conservative. The error could easily be two to three times larger than this minimum. Because of slight rounding of the edge of the working electrode, which is brought about by the lapping process, some additional deviation is expected. The magnitude of the edge effect is related to the sum of the concentrations of all species being reduced a t the electrolysis potential. This becomes especially important if an ion of high concentration is reduced prior to an ion of low concentration. I n Figure 1, the concentration of the other metal ions reducible a t the zinc reduction potential is three times that of the zinc itself, causing greater error in the determination of the zinc concentration. An attempt was made to minimize the edge effects by slipping the Teflon collar down over the end of the micrometer spindle so that it projected slightly beyond the electrode face. While this arrangement seriously limited the versatility of the electrode assembly, it did succeed in shielding the perimeter of the working electrode from some of the semi-infinite diffusion. The background current was reduced by a factor of two with considerable improvement in the symmetry of the curve. However,
the increased I R drop resulting from forcing the shield against the bottom of the cup increased overlap of the waves for those ions reduced in the same potential region. Another potentially rewarding approach to diminution of the edge effect is removal of the electroactive species from the element of volume immediately surrounding the thin layer. This could be accomplished by encircling the working electrode with an independently controlled electrode maintained a t the same potential as the working electrode. Electroactive species diffusing into the thin layer a t the edge would be intercepted by this ring and would not contribute to the current flowing a t the working electrode. As an alternative arrangement, the inert barrier facing the working electrode could be replaced by a second electrode having a diameter slightly larger than the working electrode. By maintaining the potential difference between the two electrodes a t zero, the effective solution layer thickness would be halved, and the current flowing a t the working electrode would be freed of most error caused by the edge effect. CONCLUSION
The results of the titrations reported here show standard deviations of + 2 to 670, and an analysis of errors indicates that these values are within the expected capabilities of the present technique. Until it is possible to improve this accuracy by modification of the technique and cell design, the principal advantages of the thin layer techniques reported herein are in the speed of the analysis and in the small volume of sample material required. LITERATURE CITED
(1) Anderson, L. B., Reilley, C. N., J . Electroanal. Chem., in press, (2) Bard, A. J., ANAL. CHEM.35, 1125 (1963).
(3) Biegler, T., J . Electroanal. Chem. 6, 357 (1963). (4) Ibid., p. 365. (5) Ibid., p. 373. (6) Bowers, R. C., Hau, L., Goldman, J. A., ANAL.C H ~ M33, . 190 (1961). (7) Buck, R. P., Eldridge, R. W., Ibid., 35, 1828 (1963). (8) Christensen, C. R., Anson, F. C., Ibid., 35, 205 (1963). (9) DeFord, D. D., Horn, H., Ibid., 28, 797 (1956). (10) DeVries, W. T., Van Dalen, E., J . Electroanal. Chem. 8, 366 (1964). (11) Graham, D. C., J . Am. Chem. SOC. 80, 4201 (1958). (12) Hubbard, A. T., Anson, F. C., ANAL. CHEM.36, 723 (1964). (13) Kolthoff, I. M., Larson, W. D., J . Am. Chem. SOC.56, 1881 (1934). (14) Kolthoff, I. M., Okinaka, Y., Ibid., 83, 47 (1961). (15) Kuwana, T . , Adams, R. N., Anal. Chim. Acta 20, 51 (1959). (16) Marcus. V.. Acta Chem. Scand. 11. 8 i i (1957): ‘ (17) Matsuo, T., J . Chem. SOC.( J a p a n ) , Ind. Chem. Set;; 57, 811 (1954). (18) Meites, Handbook of Analytical Chemistr pp. 5-55 $. McGraw-Hill, New Yo& 1963. (19) Oglesby, D. M., Omang, S. H., Reilley, C. N., ANAL.CHEM.37, 1312
k.,
(1965). \ _ _ _ _
(20) PrApst, R. C., Ibid., 35, 958 (1963). (21) Przybylowicz, E. P., Rogers, L. B., Ibid., 28, 799 (1956). (22) Schwarz, W. M., Shain, I. S.,Ibid., 35, 1770 (1963). (23) Scott, F. A., Peekma, R. M., Connally, R. E., Ibid., 33, 1024 (1961). (24) Shain, I. S., Perone, S. P., ANAL. CHEM.33, 325 (1961). (25) Sillen, L. G., Martell, A. E., “Stability Constants of Metal-Ion Com-
plexes,” The Chemical Society, London, 1964. ~ .
.
~
(26) Vegand, L., 2.Physik 43,299 (1927). (27) Wyckoff, R. W. G., “Structure of
Crvstals.” 2nd ed.. Interscience, New Yo”rk, 1931.
RECEIVED for review February 8, 1965. Accepted July 23, 1965. Division of Analytical Chemistry, 149th Meeting, ACS, Detroit, Mich., April 1965. Research supported in part by the Advanced Research Projects Agency and by the Directorate of Chemical Sciences, Air Force Office of Scientific Research Grant NO. AF-AFOSR-584-64.
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