1871
V O L U M E 28, NO. 1 2 , D E C E M B E R 1 9 5 6 Table IV.
Reproducibility of Method for Phosphorus in Silicon Sample G. P/G. Si No. ( x 109 1 8 28 2 7 75 3 7 87 7 so 7 72 7 93 7 89
4
5
6
.Iverage Standard erior 2 401,
laboratory in performing many of the radiochemical separations. The silicon samples described were analyzed by the spectrographic section of Metal Hydrides, Inc., Beverly, Mass , under AF contract A F 19(604)-1416. LITERATURE CITED
(1) (2) (3) (4) (5) (6) (7)
(8) merit the folloA ing evidence is cited. I n the determination of galiium, indium, thallium, and bismuth, no activity whatsoever Kas found in the final counting form (Table 11). This is prima facie evidence that in these cases a t least, no contaminating activity could have been present. I n the case of phosphorus, iron, copper, zinc, silver, and antimony sufficient activity n-as found to be able t o characterize the half life with a precision a t least within 10%. Errors from this source are considered to be no more than 10% (standard error). 5 . ERRORS RESULTING FROM STATISTICAL VARIATIONS IN THE PROCESS. The standard error of a disintegration rate is given by where N is the total number of events recorded. I n all cases a sufficient number of counts was taken t o give a Standard error of no more than 10%. I n cases of high activity the standard error p a s approximately 1%. The over-all error of the method is estimated as approximately 50% for the absolute method and 10% for the comparative method.
a,
ACKNOWLEDGMENT
(9) (IO) (11)
(12) (13) (14) (15) (16) (17) (18)
(19) (20)
~
(21) (22)
The authors nish to express their thanks for the valuable assistance given by Lester F. Lon-e and Elinor hi. Reilly of this
Boyd, G. E., ANAL. CHEY.21, 335 (1949). Bron-n, H., Goldberg, E., Science 109, 347 (1949). Cohn, W.E., - 1 3 - 4 ~ .CHEX 20, 498 (1948). Friedlander, G., Kennedy, J. W., “Introduction t o Radiocheniistry,” Wiley, S e w York, 1949. Glendenin, L. E., Nucleonics 2 , 12 (1948). Goldberg, E. D., Brown, H., ANAL. CHEM.22, 308 (1950). Gordon, C. L., Ibid., 21, 96 (1949). Hevesy, G., Levi, H., Kgl. D a n s k e V i d e n s k a b . Selskab. Math.F y s . M e d d . 14, 5 (1936); 15, 11 (1938). Hudgens, J. E., Jr., Cali, J. P., . ~ N A L .CHEM.24, 171 (1952). Hughes, D. J., “Pile Seutron Research,” Addison-Werley Publishing Co., Cambridge, Nass., 1953. Kant, .irthur, Cali, J. P., Thompson, H. D., “Detailed Radiochemical Procedures for the Determination of Several Elements by Xeutron Activation Analysis,” Air Force Cambridge Research Center, Bedford, Mass. lleinke, W.W.,“Chemical Procedures Used in Bombardment Work at Berkeley,’’ U. S. -1tomic Energy Commission, Rept. AECD-2738 (19491. XIeinke, W.W:,Science 121, 177 (1955). Meinke, W.W., Anderson, R. E., AI^.*^. CHEX.25, 778 (1953). Morrison, G. H., Cosgrove, J. F., I b i d . , 27, 810 (1955). Satl. Bur. Standards Circ. 499 (September 1950). Soyes, A. X.,Bray, IT. C., “System of Qualitative Analysis for the Rare Elements.” AIacinillan. Kea York. 1948. Scott, W. W.,“Standard Methods of Chemical Analysis,” Van Sostrand, Kew York, 1939. Tobias, C. rl., Dunn, R. IT.,Science 109, 109 (1949). Vogel, rl., “Quantitative Inorganic ..inalysis,” Longmans, Green 6- Co.,-London, 1961. Wahl, A . C., Bonner, S . A,, “Radioactivity Applied to Chemistry,” lt‘iley, New York, 1961. Welcher, F. J., “Organic Analytical Reagents,” Van Nostrand. Sew York, 1947.
RECEIVED for review September 24, 195.5. Accepted October 2, 1956.
Amperometry with Two Platinum Electrodes with the Cu prous-Cu pric, Bromine-B romide System JAMES J. LINGANE and FRED C. ANSON Department of Chemistry, Harvard University, Cambridge 38, Mass.
The behavior of the indicator current observed with two polarized indicator electrodes during coulometric titration with bromine or cuprous copper in acidic cupric bromide solutions has been critically examined. The interpretation of the indicator current, and the relation between the observed minimum current and the equilibrium constant of the reaction 2Cu++ 7Br- = 2CuBri Bri, given by prebious authors has been shown to be inadequate. Correct relations for this system have been derived; these lead to an apparent equilibrium constant more nearly in accord with the value deduced from the observed formal potentials of the half-reactions involved. However, because the bromine-bromide couple does not behave with the thermodynamic reversibility demanded by the correct treatment, the apparent equilibrium constant from the amperometric measurements is considerably larger than the true value. Two-electrode amperometry, although very useful as an empirical means of end point detection in titrations, is not appealing as a technique for measuring equilibrium constan ts.
+
+
A
S ORIGINALLY demonstrated by Foulk and Bawden (6),
the change in current between two platinum indicator electrodes subjected t o a constant, small applied voltage can be used t o recognize titration end points. During the past decade this technique has been applied very successfully (albeit empirically) for end point detection in divers types of coulometric titration, particularly by Swift and his collaborators. The principles and applications of the method are reviewed in the monographs of Lingane (9) and Delahay (3) and in articles by Duyckaerts (4), Bradbury (I), and Kolthoff (7). Our interest here is with the application of amperometry \\-ith two polarized platinum electrodes to end point detection in the particular case of coulometric titration with bromine and cuprous copper as dual intermediates, as originally used by Buck and Swift (3) for slom bromination reactions. The titration cell is essentially as indicated in Figure 1. The electrolyte contains relatively large concentrations of bromide ion and cupric ion, and is acidified with sulfuric acid. By appropriate selection of the polarity of the generator electrode in the test solution bromine can be generated via anodic oxidation of bromide ion, or cuprous copper (CuBrz-) can be generated by cathodic reduction of cupric ion. Starting Fith either excess bromine or excess cu-
ANALYTICAL CHEMISTRY
1872 prous copper, and generating the other with strictly constant current, a plot of the resulting indicator current against generation time produces a V-shaped titration curve whose extrapolated point corresponds very closely to the equivalence point, as shown in Figure 2. Farrington, Meier, and Swift (6) recognized that the magnitude of the minimum current not only depends on the geometrical characteristics of the indicator electrodes and cell, and the value of the constant voltage applied across the indicator electrodes, but is also a function of the equilibrium constant of the reaction
2Cu++
+ 7Br-
= 2CuBrp-
+ Bra-
K = (CuBrp-)*(Bra-) _ _ _ (Cu +)*(Br -)'
(1)
~
+
Farrington, Meier, and Swift derived a relation betneen the minimum current, the slopes of the two branches of the titration curve, and K , and used it to evaluate K . The average value which they obtained (1.4 X 10-18) is about 100 times larger than the value deducible from the standard potentials (as quoted by Farrington, Meier, and Swift) for the half-reactions involved. This prompted the authors to examine more closely the derivation of Farrington and associates, and this study leads to the conclusion that certain of their basic assumptions are not valid under the experimental conditions which they employed. The possible reactions a t the indicator electrodes that can contribute t o the observed indicator current are Br3Cu-+
+ 2e = 3Br-
+ 2Br- + e
(3)
(cathode)
= CuBrp-
( 4)
(cathode1
and
+ 2e (anode) + 2Br- + e (anodej
3Br- = Br3CuBrz- = C u t +
(5) (6)
With excess bromine present, virtually all the current results from Reactions 3 and 5, and there is very little contribution from Reactions 4 and 6. Conversely, in the presence of excess cuprous copper, Reactions 4 and 6 so greatly predominate that Reactions 3 and 5 become insignificant. However, a t the indicator current minimum all four reactions contribute to the observed current. That this is true is evident from the individual anodic and cathodic current-electrode potential curves shown in Figure 3.
M Figure 1. Cell for coulometric titration with amperometric end point detection by two polarized electrodes
20
12
n
811 electrodes of bright platinum, lower pair indicator electrodes and upper generator electrodes. A constant small voltage E. is maintained across t h e indicator electrodes and t h e indicator current is observed with microammeter M . T h e solution is stirred efficiently
E p -
4
E
O
5-
-4
W
n n
5
-12
-20
I
6 700
I 600
I
I 500
I
I 400
Evs SCE,rnv
Figure 3. Individual cathodic and anodic currentelectrode potential curves 1. Excess bromine 2. Excess cuprous copper 3. Solution adjusted t o amperometric minimum current Solution composition same a s for experiments of Figure 2
0 0
5
10
15
20
G E i i E R A T I O N TIME. s e c
Figure 2. Amperometric titration curves with various voltages applied across indicator electrodes Solution (volume 150 00.) consisted of 1F sodium bromide, 0.067F cupric sulfate and 0.33F sulfuric acid. Generator electrode area was 5 sq. cm. a n d odnstant generating current was 12.7 ma. Area of each indicator electrode mas 3 sq. cm.
The curves in Figure 3 rrere obtained with a single platinum indicator electrode (area 3 sq. cm.) in a solution containing 1F sodium bromide, 0.067F cupric sulfate, and 0.33F sulfuric acid. The potentials of the indicator electrode were measured against an external saturated calomel reference electrode. Curve 1 rras obtained after generating a small excess of bromine, curve 2 in the presence of excess cuprous copper, and curve 3 after adjusting the solution composition by appropriate generation of bromine and cuprous copper until the minimum in the titration curve with two identical platinum electrodes (at 60 mv. applied) %-as precisely reached. For all three cases the final unlimited increase in cathodic current (upward) results from C u + + -c CuBrz-, and the final unlimited increase in anodic current (at a potential above about 650 niv.) stems from Br- + Bra-.
V O L U M E 2 8 , NO. 1 2 , D E C E M B E R 1 9 5 6
1873
Suppose, nox-, that two identical platinum electrodes are placed in the solution corresponding to curve 2 in Figure 3, and subjected to an applied e.m.f. of 60 mv. (the value used by Farrington and associates). The currents a t the indicator cathode and indicator anode are equal, because each is simply the observed indicator current. Hence the potentials adopted by the indicator cathode and indicator anode are such as to correspond to equ:~Icathodic and anodic currents as indicated by the shaded sections of curve 2 . Because with excess cuprous copper (curve 2) the concentration of bromine (or tribromide ion) is vanishingly small, the cathodic current results practically entirely from reduction of cupric ion, even though the cathode potential corresponds to the limiting current region of bromine reduction. As the potential adopted by the anode (ca. 490 mv.) is well below the value a t Tvhich oxidation of bromide ion is significant, the anodic current results almost entirely from oxidation of the cuprous bromide complex to cupric ion. An exactly similar interpretation applies to curve 1 (excess bromine), except that in this case the only significant reactions are reduction of bromine a t the cathode and oxidation of bromide ion a t the anode. With excess cuprous copper (curve 2 in Figure 3) the potential adopted by the indicator anode is far below the limiting current section of the anodic curve. I n other words, the observed indicator cuirent is much smaller than the limiting anodic current corresponding to the extant concentration of cuprous copper in the solution. Similarly, with excess bromine (curve 1) the observed indicator current is much smaller than the limiting cathodic current for bromine reduction. I n the “minimum solution” the potentials adopted by the cathode and anode are smaller than corresponds to the limiting cathodic and anodic currents, and in addition there are appreciable contributions to the current from reduction of cupric ion and oxidation of bromide ion. These latter contributions evidently will be greater the greater the voltage impressed across the indicator electrode pair, which is the chief reason the net minimum current increases viith increasing applied voltage (see Figure 2). The treatment of Farrington and associates rests on the assumption that at any stage of the titration the indicator current will be given by an equation of the form
i
= kl(CuBrZ-)
+ k4(Br3-)
(3)
where the concentrations are those in the body of the solution and el and ka are assumed to be constants independent of solution composition. Farrington and associates evaluated kl and k4 from the slopes of titration lines (like those in Figure 2) when the solution contained excess cuprous copper and excess bromine, respectively, and they assumed that the same values applied when the indicator current was minimal. They were led to this treatment by the supposition that the indicator current corresponds to the limiting current for the particular extant concentrations of cuprous copper and bromine a t all stages of the titration. From the current-electrode potential curves in Figure 3, and the attendant discussion above, it is clear that these assumptions are not valid, I n other words, Equation 3 is invalid with constant applied e.m.f. because the potentials adopted by the indicator electrodes correspond neither to the limiting sections of the current-potential curves, nor to any other fixed, relative point on the curves. as the concentrations of bromine and cuprous copper are varied. Because it rests on an invalid premise, the final equation given by Farrington and associates relating the minimum current, k l , k4, and the equilibrium constant of Reaction 2 (their Equation 6) cannot be correct, and it is understandable that the apparent value of K which they computed differs from the true value. To obtain a correct relation between the indicator current a t constant applied e.m.f. and concentrations of cuprous copper and bromine in the solution, one must take into account the fact that the concentrations of these reacting species a t the surfaces
of the indicator electrodes are not negligibly small (or zero) compared to their bulk concentrations. As the current is the same a t both indicator electrodes, it is necessary to conEider only the situation a t one of the electrodes, say, the anode. At any stage of the titration the reactions a t the indicator anode are expressed by Equations 5 and 6, the total current being the sum of a contribution from the oxidation of cuprous copper and a contribution from the oxidation of bromide ion. Each of these contiibutions is proportional to a difference in concentration between the electrode surface and the body of the solutionviz.
icU = kcU[(CuBr2-) - (CuBrZ-),J
(4)
- (BI--)~,J
(5)
ig, =
k&[(Br-)
where (2) and ( L ) . ~represent concentrations in the solution and a t the anode surface, respectively. Since a steady state is attained in which the rate of transfer of bromine (tribromide ion) away from the electrode balances the rate of transfer of bromide ion to the electrode, one tan also nrite ig, =
kB,[(Brg-)on- Eh--)]
(6)
Hence the total indicator current is
i
= kcu[(CuBr,-) - (CuBr?-j,,]
+ h - ~ ~ [ ( B r -~ -(Bra)] )~~
(7)
If both reactions proceed reversibly, then
E,, - E = RT -In 2F
(B1-3-1~~ (Br3-)
where Ea, is the actual working potential of the indicator anode and E is the potential of an unpolarized platinum indicator electrode in the solution, both measured against the same external reference electrode. The difference E,, - E, is the “polarization of the anode.” From these relations it follon s that (CuBrl-)2(Br3-) = ( CuBrz-):n(Br3-)afi
(10)
which is simply one way of stating that the relative proportions of Reactions 5 and 6 are such as to maintain equilibrium of Reaction 1, provided both reactions proceed reversibly. From Equations 7 , 8, and 9 the total indicator current is
i
=
+
kcu(CuBr2-)[1 - exp[(E - E,,)F/RT] ) k ~ , ( B r ~ - ) { e s p [ ( E ,-, E ) 2F/RT] - I] (11)
Comparison with Equation 3, assumed by Farrington and associates, shows t h a t h-1
= k c u { 1 - exp[(E -
Ea-) F / R T ] j
(12)
It is clear that 121 and k4 could be constants (for a constant voltage impressed across the indicator electrodes) only if the polarization of the anode, E,, - E, remained constant. Actually E,, E varies during the course of a titration as the concentrations of cuprous copper and bromine change. The exponential terms, and hence kl and k4, do approach constant values with either a large excess of cuprous copper or a large excess of bromine. The data in Table I provide an idea of the magnitudes of these variations in a typical case. The exponential term, and hence k l , varies almost twofold. Because the values of kl and kd are different with excess cuprous copper, excess bromine, and a t the indicator current minimum, the limiting values of kl and k4 evaluated from the slopes of the two branches of the titration curve are not applicable to the minimum current when the titration is performed with constant voltage across the indicator electrodes.
1874
ANALYTICAL CHEMISTRY
Table I.
-
Polarization of Indicator Anode in Typical Titration
60 mv., CuSO4 = 0.067F NaBr = l.OF,HnSOd = 0.33F, solution volume = 150 ml., gen'eration current, io = 12.9 ma.) Indicator Eon u s . E us. Current, s.c.E., s.c.E., on E , (1 pa. Mv. Mv. Mv. RTIF 3.5 0 81 1.4 0.81 0.87 0.83 0.54 0.75 0.67 0.57 0.79 0.5l 0.96 0.50 2.2 0.44 6.2 0.41
(Ea
P
I
I
-
-
I
I
I
I
5
IO
15
20 0
(Bra-) = K(Cu++)Z(Br-)7 (CuBrz-)2
i
1
IO
15
20
G E N E R A T I O N TIME, sec
-
If the titration is performed with E., E held constant, by appropriate adjustment of the voltage applied across the indicator electrodes a t each measurement point, kl and kp do become constants and Equation 3 becomes valid. I n view of Equation 2,
I 5
Figure 4.
Amperometric titration curves
-
Polarization E,, E of indicator anode constant a t 10 mv. 2. Total voltage applied across two indicator electrodes constant at 60 mv. Solution composition same as in Figure 2
1.
(14)
which can be substituted into Equation 3 to express i as a function of (CuBrz-) 2,
i
= kl(CuBr2-)
f+)l(Br + k4K((Cu CuBr2-)2
-)7
As the concentrations of cupric and bromide ions are so very large that they are virtually constant, Equation 15 can be differentiated in respect to generation time, the differential dildt equated to zero to correspond to the minimum current, i,, and the following relation is obtained
::I
I
4i:
K = 27 k? k4(Cu++)2(Br-)7 Figure 4 shows two typical titration curves obtained with the same solution. Curve 1 was obtained with E,, - E held constant a t 0.010 volt by appropriate adjustment of the applied voltage across the indicator electrodes a t each point. Curve 2 was obtained with the applied voltage constant at 0.060 volt. The minimum current is only half as large with constant polarization as with constant applied voltage. The value of K derived from curve 2 by the method of Farrington and associates is 3.8 X 10-16, which agrees with the values reported by them. From curve 1,the value of K is 0.76 X 10-l6. From six experiments like curve 1 with 0.0678' cupric sulfate, 1F sodium bromide, and 0.338' sulfuric acid, values of K from 0.29 to 0.76 X 10-'6 resulted, the average being 0.46 (A0.16) X 10-l6. From potential measurements in solutions of the same composition as the solution used to obtain these data, and containing known concentrations of CuBr2- and Br3-, the formal potential of the cupric-cuprous couple was found to be $0.301 volt us. S.C.E., and that of the bromine-bromide couple to be $0.800 volt. From these formal potentials the values of K was computed to be 0.13 X l O b 1 8 under the conditions of these experiments. Although the value of K obtained by the present treatment (0.46 x 10-18) agrees better with the value based on the formal potentials (0.13 X 10-l6) than the value (3.8 X l O - I 6 ) by the technique of Farrington and associates, the discrepancy is larger than can be attributed t o accidental error. The authors have found that the residual discrepancy results chiefly from the circumstance that the several electrode reactions do not proceed with the thermodynamic reversibility assumed by the foregoing treatment. Significant overpotentials are included in the observed potentials of the indicator electrodes, and consequently Equations 8 and 9 are not strictly obeyed. That reduction of tribromide ion does not proceed reversibly at a platinum cathode is demonstrated by the current-cathode potential curves in Figure 5. For reversible reduction of tri-
E v s S C E , mv
Figure 5.
Current-cathode potential curves for bromine reduction at a platinum cathode
From solution containing ca. 2 X lO-SF bromine 1 F sodium bromide, and 0.33F sulfuric acid. Cathode area 3 sq. cni., solufion stirred 1. With previously used cathode 2. After freshly cleaning cathode with aqua regia
bromide ion according to Equation 3, in a solution containing such a large concentration of bromide ion that its concentration a t the cathode surface is practically the same as in the body of the solution, the equation of the current-cathode potential curve is
+
E, = E o - 0.0296 log k ~ , ( B r - ) ~ 0.0296 log ( i d - i) (17) I n this equation is defined by Equation 6, E" is the standard potential of Reaction 3, and i d is the limiting diffusion current. Because the concentration of bromide ion is so large that it is virtually eonstant, the second term in this equation is a constant. The dashed curves in Figure 5 correspond to Equation 17, using the observed value of i d and the observed value of the cathode potential a t zero current. The overpotential is decreased by cleaning the cathode with aqua regia just prior to use (curve 2). but is not entirely eliminated. The curves in Figure 5, like all the data in this study, were ohtained with stirred solutions. The curves in Figure 5 are not a sufficient proof that the electrode reaction involves an overpotential-i.e., proceeds irrever-
1875
V O L U M E 2 8 , NO. 12, D E C E M B E R 1 9 5 6 sibly. The discrepancy could also result in whole or in part if transfer of tribromide ion to the cathode surface followed some relation different than that assumed by Equation 6. T o test this possibility the authors studied current-cathode potential curves for the reduction of triiodide ion in solutions containing a large concentration of iodide ion. The iodine-iodide system is
,-
I I
O
h
150
’
100
I
50
I
0
-50
E vs. S.C.E., mv.
Figure 6. Current-cathode potential curves for reduction of ca 8 X 10-sF iodine From solution containing 1F potassiuni iodide and 0 . 3 3 F sulfuric acid, other conditions same as Figure 5 Predicted by Equation 17 for reversible reduction 0 Experimental points
____
the exact analog of the bromine-bromide system, and the equation of the current-potential curve is identical in form with Equation 17. The dashed curve in Figure 6 is the theoretical curve for reversible reduction (Equation 17) and the points are the experimental observation for the iodine-iodide system. It is evident not only that the iodine-iodide couple behaves reversibly but also that the assumption involved in Equation 6 is valid under the conditions of these experiments-i.e., the current a t any point is indeed proportional to the simple difference in concentration of the electroactive species between the solution and electrode surface. Kolthoff and Jordan (8) also concluded that the iodine-iodide couple is reversible. Consequently, the discrepant current-potential curves for the bromine-bromide system (Figure 5) do result from irreversible behavior. The authors have also found that the oxidation of bromide ion a t a platinum anode involves a significant overpotential of about the same magnitude as that observed for the reduction of bromine. On the other hand, anodic current-potential curves for the oxidation of the cuprous bromide complex correspond very closely
wit’h the curves expected for reversible oxidation, provided the platinurn anode is freshly cleaned with aqua regia. The effect of this irreversibility of the bromine-bromide couple is in the right direction to account for the discrepancy between the apparent value of K from the amperometric measurements and the value predicted from the formal potentials. There is no question that amperometry with two polarized platinum electrodes is a very useful technique for the empirical detection of titration end points. Hoxever, the technique bristles with too many interpretative complexities to be attractive as a means of exactly measuring concentrations or evaluating thermodynamic constants. The drawbacks revealed by this study are inherent in the tn-o-electrode amperometric system, and fundamentally stem from the simultaneous and unequal polarization of the two electrodes. The foregoing treatment demonstrates that correct concentration measurements with the t\yoelectrode system can be obtained only when the electrode reactions proceed reversibly and if the degree of polarization of the electrodes is either measured or kept constant by appropriate readjustment of the total applied voltage a t each measurement point.. These limitations do not pertain to amperometric measurements with a single polarized electrode in combhation with an unpolarized auxiliary electrode. With the single electrode the electrode reaction need not be reversible, because the working potential is adjusted to correspond to the limiting current region of the current-potential curve, a c,ondition which permits unambiguous and exact concentration determination. Furthermore, under this condition a constant condition of polarization is maintained by a constant applied voltage. However, single-electrode amperometry is unsuited to the cupric bromide system, because with the equivalence point solution the cathodic current nearly exactly compensates the anodic current, so that the net current is too close to zero for practical measurement (see curve 3 in Figure 3). ACKNOWLEDGMENT
The authors are grateful to the Mallinckrodt Chemical Works for partial financial support of this study. .4ppreciation is also expressed to t’he National Heart Institute for a fellowship held by one of them (F.C.A.). LITERATURE CITED
(1) Bradbury, J. H., Trans. Faraday SOC.49, 304 (1953). (2) Buck, R. P., Swift, E. H., AXAL.CHEM.24, 499 (1952). (3) Delahay, P., “Sew Instrumental Methods in Electrochemistry,” Interscience, New York, 1954. (4) Duyckaerts, G., Anal. Ckim. Acta 8 , 57 (1953). (5) Farrington, P. S., Aleier, D. J., Swift, E. H., ANAL.CHEV.25, 5.91 (1953). (6) Foulk, C. W., Bawden, -4.T., J . -477~. Chem. SOC.48, 2045 (1926). ( 7 ) Kolthoff, I. A l . , A s . 4 ~ CHEM. . 26, 1685 (1954). ( 8 ) Kolthoff, I. AI., Jordan, J., J . A4m.Chem. SOC.75, 1571 (1953). (9) Lingane, J. J., “Electroanalytical Chemistry,” Kew York, Interscience, 1953. RECEIVED for review January 30, 1956. .Accepted August 22, 1956.
