(5) Galus, Z., Lee, H. Y., Adams, R. N., J . Electround. Chem. 5, 17 (1963). (6) Holleck, L., Schindler, R., 2. Elektrochem. 60, 1138 (1960). (7) Kemuh; W., in “ildvances in Polarography, I. S. Longmuir, ed., Vol. I, p. 105, Pergamon Press, New York, 1960. (8) Kemula, W., Kublik, Z., Bull. A c a d . Polon. Sei., Ser. Sci. Chim., Geol., Geograph. 6,661 (1958). (9) Xicholson, R. S., Shain, I., ANAL.
CHEM.36, 706 (1964). (10) Nicholson, R. S., Shain, I., Ibid., 37, 190 (1965). (11) Reinmuth, W. H., Ibid., 34, 1446 (1962). (12) Riha, J., in “Progress in Polarography,” P. Zuman, ed., Vol. 11, Chap. 17, Interscience, New York, 1962. (13) Suzuki, M., Mem. Coll. Agr., Kyoto Unav., 1954,p. 67. (14) Testa, A. C., Reinmuth, W. H., ANAL.CHEJI.33, 1320 (1961).
(15) Testa, A. C., Reinmuth, W. H., J . Am. Chem. SOC.83, 784 (1961).
RECEIVED for review September 21, 1964. Accepted December 7, 1964. Presented in part a t the Division of Analytical Chemistry, 148th Meeting ACS, Chicago, Ill., September 1964. Work was supported in part by the U. s. Atomic Energy Commission under Contract No. AT(11-1)-1083. Other support was received from the National Science Foundation under Grant No. G 15741.
Experimental Verification of an ECE Mechanism for the Reduction of p-Nitrosophenol, Using Stationary Electrode Polarography RICHARD S. NICHOLSON and IRVING SHAIN Chemistry Department, University of Wisconsin, Madison, Wis.
b The reduction of p-nitrosophenol, which involves a chemical reaction interposed between two electron transfer reactions (ECE mechanism), was selected to demonstrate the use of cyclic stationary electrode polarography and to test theoretical calculations for the method. Cyclic polarograms were recorded over a range of scan rates from 20 mv./second to 30 volts/second. From these data the intermediate reactant was detected directly and identified as p-benzoquinoneimine. Both charge transfer reactions were shown to b e reversible and to involve two electrons. Several methods of relating experimental results to theory were used to determine the rate constant of the chemical step. The value obtained was 0.6 second-’, in good agreement with previous work.
R6 )
WORK on the theory of stationary electrode polarography (3, has indicated that the method is extremely useful in the investigation of electrode mechanisms in which chemical reactions are coupled to the charge transfers. Stationary electrode polarography is particularly valuable because the rate of voltage scan appears as an important variable which interacts with the kinetic properties of the electrode reaction. For example, when a chemical reaction follows charge transfer, the system does not exhibit any kinetic effects on the stationary electrode polarograms when the experiment is performed rapidly relative to the reaction kinetics. As the scan rate is decreased, however, the kinetic effects appear. From the effect on the stationary electrode polarograms, the kinetic complication can be characterized and quantitative information aboL1.t the rate constant can be obtained. ECENT
190
ANALYTICAL CHEMISTRY
Since the rate of potential scan can be varied easily over a range of perhaps lo6, a wide range of kinetic effects can be investigated. To demonstrate the use of stationary electrode polarography in the investigation of a kinetic system, the reduction of p-nitrosophenol was selected. This reaction has been studied by several workers, who have used polarographic (2, 7’), chronopotentiometric (1) and potentiostatic experiments (1). The results of these investigations point to a mechanism in which a homogeneous chemical reaction is coupled between two successive electron transfer reactions-referred to as an ECE mechanism (8). Under potentiostatic conditions, the current-time behavior for p-nitrosophenol changes from nearly two electron control a t short times to four electron control a t longer times. This is consistent with a n ECE mechanism in which the intermediate is more reactive than the p-nitrosophenol. However, the intermediate has not been investigated directly, and thus the separation of the formal potentials for the two reactions is not known. In addition, all previous work has involved potentials in the limiting current region of the first charge transfer. Under these conditions, the potential is far cathodic of the formal potential of the second charge transfer and the reversibility of the reaction has no effect on the experimental results. Thus, in addition to demonstrating the use of stationary electrode polarography in the investigation of a fairly complex electrode reaction, the work was designed to provide direct information on the nature of the intermediate and the reversibility of the second charge transfer for the reduction of p-nitrosophenol.
EXPERIMENTAL
Apparatus. All measurements were made with a three-electrode potentiostatic circuit, using a single Philbrick Model SK2-V operational amplifier (G. A. Philbrick Researches, Inc., Boston, Mass.). It was possible to use the SK2-V without stabilization, since after a short warm-up, the d.c. drift was negligible. Although the SK2-V tended to oscillate a t high frequencies, this was suppressed by connecting a 20-pf. capacitor from the output to the summing point. In initial experiments, the output of the SK2-V was boosted with a Krohn-Hite Model DCA-10 power amplifier (Krohn-Hite Corp., Cambridge, Mass.). However, for the frequencies reported here, the currents were within the ratings of the SK2-V, and it was not necessary t o use the booster amplifier. The signal generator consisted of a function generator (which provided the triangular waves) in series with a low voltage power supply (which provided the initial p o t a t i a l and the d.c. offset potential for the amplifier). The low voltage power supply was battery operated so that it could be isolated from ground. The function generator was essentially the same as the one described previously (Reference 9, Figure S), in which the output of a multivibrator square wave generator is integrated to provide the potential variation required for both single scan and cyclic triangular wave experiments. For some experiments involving measurements of anodic currents it was necessary to have a base line constructed from the extension of the cathodic wave. This was obtained by scanning just past the cathodic peak, and then holding the potential constant to record the current-time curve, as discussed previously ( 5 ) . This required a voltage wave form from the signal generator consisting of the first arm of the triangular wave, followed by a
constant potential equal in amplitude t o the triangular wave being used. For this, the function generator was modified by placing a diode (Sylvania 1N98) between the output of the niultivibrator section and ground. Thus, with the diode in position alternate half cycles of the square wave are a t ground potential, and on integrating this signal, the desired wave form is obtained. Tilt in the constant potential portion was less than 1% of the scan rate being used. Two detectors were used, depending on the time scale of the experiment. For scan rates over 50 mv./second, the detector was a Tektronix Model 536 oscilloscope provided with a Polaroid camera attachment (Dumont Type 302). Single cycle and half-cycle experiments were recorded on the oscilloscope using a Tektronix Type D plug-in preamplifier in the vert,ical input, and a Type T time-base plug-in in the horizontal input. The time-base was triggered by the function generator trigger, and was calibrated to +2(r, on all scales used. For the multicycle experiment,s, the time-base plug-in was replaced with a Tektronix Type G plug-in so that t'he horizontal axis could be driven by the cell potential. For scan rates less than 100 mv./ second, the polarograms were recorded on a 10-mv. Leeds and Sorthrup Model G potentiometric recorder, 0.4second full scale response. Selection of the circuit configuration depended on the detector being used, and was guided by a recent classification of potentiost'atic circuits (6). When using the oscilloscope as the detector, the circuit of Figure 4b, Reference 6, was used. The i R drop across the load resist'or was measured by operating t'he oscilloscope in the differential mode. However, this configuration was unsuit'able when t,he recorder was used, because of increased noise when operating the recorder isolated from ground. Thus, for these experiments t,he circuit of Figure 4h in Reference 6 was used, except the load resistor was decoupled from the circuit with a current follower. Cell design was the same as described previously ( I ) , with two major exceptions. First, to minimize uncompensated i R drop, a Luggin capillary probe mas used. Second, t,he counter electrode was a spiral of platinum wire placed directly in the t>est solution. The working electrode was a hanging mercury drop of surface area in the range 0.072 to 0.073 sq. cm. No convection shield was used. The electrode was calibrated for quantitative studies by weighing 50 drops from the dropping mercury electrode capillary. All experiments were carried out a t 25O C. Materials. The purificat,ion and analysis of p-nitrosophenol have been described previously (1). The p-aminophenol was prepared from Eastman white label p-aminophenol hydrochloride by neutralization of a deaerated solution with sodium hydroxide. The resulting p-aminophenol was recrystallized from hot deaerated ethanol and
dried under vacuum. The hydroquinone was Eastman white label and was used without further purification. All test solutions contained 1.0 X 10-3M p-nitrosophenol in the following supporting electrolyte: 0.lM acetic acid, 0.1M potassium acetate, 0.1M potassium nitrate, 20% by volume ethanol, and 0.005% gelatin. The measured pH was 4.9. Fresh solutions were prepared before each set of experiments. RESULTS AND DISCUSSION
Using the single scan method, the stationary electrode polarogram of pnitrosophenol exhibits a well defined peak (EI/? = -0.08 volt us. S.C.E.) corresponding to the electrode reaction
OH
OH
N=O
626 HNOH 2e
2 H+
NH
"*
The intermediate (p-benzoquinoneimine) produced by dehydration of the hydroxylamine is assumed to be more easily reduced than the original pnitrosophenol. The proposed mechanism is supported by potentiostatic, polarographic, coulometric, and spectrophotometric experiments, and the rate constant measured for the dehydration of the p-hydroxylaminophenol by the potentiostatic method is 0.6 second-' for solutions at about pH 5 containing 20y0 ethanol and 0.005% gelatin. Therefore, these experimental conditions were selected for further investigation using stationary electrode polarography, so that the results could be compared directly with the potentiostatic work reported earlier (1). Single Scan Method. Qualitatively, the major effect produced by the chemical step on the stationary electrode polarogram of p-nitrosophenol is that the peak height is not proportional to the square root of the rate of potential scan over the entire range of scan rates. For fast scan rates (1.0 volt per second, or greater) the wave corresponds to a reversible twoelectron reduction. The width of the wave as measured by E , - E,,, is equal t o about 30 mv., compared to the theoretical 28.2 mv. for a reversible two-electron reduction, and the peak height is within 2% of that predicted from theory for the reversible case, However, as the scan rate is decreased, the peak current decreases more slowly than would be predicted on the basis of an uncomplicated reversible electron transfer. This behavior is indicative
of an ECE mechanism and occurs as the time scale of the experiment becomes comparable to the half life of the chemical reaction. Under these conditions, there is a transition in the polarogram from a peak height characteristic of two electrons to one corresponding to four electrons. This behavior can be studied qualitatively by plotting i,/vl'* as a function of scan rate, v. By comparing the results with the diagnostic criteria presented earlier (S, 4) the mechanism can be determined. I n addition, if other experimental parameters (such as electrode area, diffusion coefficient, etc.) are known, the same studies can be used to determine the rate constant, by plotting experimental peak currents obtained a t different scan rates in terms of the current function defined by ( 4 ) :
d i ~ x ( a t+) ( n * / n M a t )I
(1)
Here i, is the peak current, a = nlFv/RT, nl and n2 are the electrons involved in the two charge transfers, CA* is the bulk concentration of the p-nitrosophenol, D is its diffusion coefficient, v is the rate of potential scan, and ut) and +(at) are functions, given in numerical form, which are related to the surface fluxes of p-nitrosophenol and the intermediate, respectively. The other terms have their usual significance. The application of this approach to the reduction of p-nitrosophenol is shown in Figure 1, where the points are experimental and the lines are theoretical. To determine the experimental points according to Equation 1, nl and n2 were taken to be 2; the value used for the diffusion coefficient was sq. cm./second-as deter4.8 X mined previously by the potentiostatic method ( 1 ) . In Figure 1, the horizontal dashed line is the value of the current function for an uncomplicated reversible charge transfer-0.446, independent of the scan rate. K i t h fast scan rates, the experimental current function in Figure 1 approaches this value. Thus, for scan rates greater than about 1 volt/ second, the experiment is over before the interposed chemical reaction and the second charge transfer can make W. significant contribution to the current. Under these conditions, a simple twoelectron reversible reduction is obtained, ilt low scan rates, the experimental current function is significantly higher than 0.446, characteristic of an ECE mechanism with the E" for the second charge transfer anodic of the first. The theoretical limit for the current function a t the low scan rates would be 0.992i.e., twice the value of the current function for a system involving a chemical reaction follom-ing a charge transfer (Reference 3, Case VI). VOL, 37, NO. 2, FEBRUARY 1965
191
O.*t \
A I
* a
3 42
041
0.01
0.I
1.0
0
10
c
v, volt/sec
Figure 1. Variation of current function i,/nFA&L CA* as a function of scan rate for the reduction of 1.0 X 1 O-3M p-nitrosophenol
\ .-
Dashed line, theory for uncomplicated reversible charge transfer; solid lines, theory for ECE mechanism with intermediate more easily reducible than reactant; points, experimental
This limit could not be reached for the p-nitrosophenol system, however, because convection affects the reproducibility when scan rates slower than 10 mv./second are used. The solid lines in Figure 1 were calculated from data obtained by the numerical method described previously (4) for the ECE mechanism in which the first electron transfer is reversible, E o for the intermediate is very anodic of E" for the starting material, and n1 = n2 = 2. Three theoretical curves are shown, for values of the rate constant equal to 0.3, 0.6, and 0.9 second-', and the experimental data agree well with the value 0.6 second-' obtained by the potentiostatic method. The theoretical curves are based on a model for linear diffusion, and any spherical correction would tend to make these curves higher at slower scan rates. However, for the experimental conditions above, the maximum spherical correction (reversible case, without kinetic complication) was calculated to be 5% a t a scan rate of 10 mv./ second, and therefore is relatively unimportant for the case of p-nitrosophenol. The excellent agreement between theory and experiment extends over the entire polarographic wave. Comparison for two scan rates (1.0 volt/second, ki/a = 0.01; and 26 mv./second, ki/a = 0.3) are shown in Figure 2, where the points are experimental and the lines theoretical. I n each case, the theoretical curve was located on the potential axis to provide the best fit with the experimental points. For a value of k j / a equal to 0.01, the kinetic effect is small, and this theoretical curve is identical to a simple reversible charge transfer. The E" for the system would be 28.5/n mv. anodic of the peak potential, or -79 mv. us. S.C.E. For 192
ANALYTICAL CHEMISTRY
0
-30
-60
-120
-90
E vs SCE, mv Figure 2. Stationary electrode polarograms for the reduction of 1 .O X 1 O-3M p-nitrosophenol lines, theory; paints, experimental. Scan rater were 26 mv./sec (k,/o = 0.3) and 1.0 volt/sec. (kf/a = 0.01)
a value of k f / a equal to 0.3, theoretically E " would be 35/n mv. anodic of the peak potential, or -72 mv. us. S.C.E. This difference of 7 mv. is within experimental error. Cyclic Triangular Wave Method. After the primary cathodic peak, three additional peaks can be observed in cyclic triangular wave experiments, depending on the rate of voltage scan. Cyclic polarograms shown in Figure 3 were plotted directly from oscillographic traces, after converting the ordinates to currents, and dividing the currents by the square root of the frequency. When plotted in this way the curves all appear on the same relative scale, and direct comparisons can be made. Thus, if there were no kinetic complications, the three polarograms in Figure 3 would be identical (except for the charging current, for which no correction was made). For discussion, the waves have been numbered as indicated on the polarogram obtained a t 0.1 C.P.S. Wave I is the primary cathodic wave for the reduction of p-nitrosophenol to p hydroxylaminophenol; Wave I1 is the reverse reaction-the oxidation of the p-hydroxylaminophenol. Since the potentials for Waves I and I1 are cathodic of the E ofor the intermediate, some of the intermediate is reduced to the final product during the first portion of the scan. Thus, Wave I11 is the oxidation of the final product-i.e., reduced form of the intermediate.
Then, when the scan direction is reversed again, Wave IV appears for the reduction of the intermediate. Unfortunately, the E o for the intermediate is close to the dissolution wave
0.1 cps
, 02
0
-0.2
V vs S C E Figure 3. Multicycle stationary electrode polarograms for 1 .O X 1 O-3M p-nitrosophenol Scan rates were 30 volt/sec. (30 c.P.s.), 1 volt/sec. (1.0 c.p.s.1, and 100 mv./sec. (0.1 c.p.s)
of the mercury electrode, and for rapid rates of potential scan, the combined effects of charging current and mercury oxidation-reduction current preclude making quantitative measurements on Waves I11 and IV. Thus, for convenience in recording, the curves in Figure 3 actually were taken from multicycle experiments for 30 C.P.S. and 1.0 c.p.s. Except for minor changes in peak heights and peak potentials which take place during the first few cycles, these results are comparable to the first cycle theoretical data (4). For fast scan rates, Waves I and I1 correspond to a reversible two-electron system. As the rate of voltage scan is decreased, the chemical step becomes relatively more important, more intermediate is produced, and \F7ave I becomes larger. (The apparent anomalously large peak height for Wave I a t 30 c.p.s. is caused by charging current). At the same time, Wave I1 decreases as relatively more of the p-hydroxylaminophenol is used up in the chemical step, and for a rate of voltage scan in the range of 20 to 50 niv.;second (0.02 to 0.05 c.P.s.), Wave 11 disappears entirely. This emphasizes the importance of using a wide range of scan rates for qualitative investigations using stationary electrode polarography, since a t low scan rates, the reduction of p-nitrosophenol appears to be totally irreversible. From the shape of Wave I1 and the fact that it disappears entirely, it can be concluded that relative to the time scale used in these experiments, the chemical step is irreversible. Wave I1 remains peak-shaped a t all rates of voltage scan, whereas if the chemical reaction were reversible, S-shaped waves would be expected a t low scan rates. Waves I11 and IV also change markedly with changes in rate of voltage scan, as expected for an ECE mechanism of this type. At high rates of potential scan (30 c.p.s.) the currents corresponding to the intermediate are quite small, since the p-hydroxylaminophenol is reoxidized before significant chemical reaction can take place. As the rate of voltage scan is decreased, however, increasing amounts of intermediate become available, and at 1.0 volt/second, Waves I11 and IV assume the characteristics of a reversible 2-electron system with E" a t about f220 mv, us. S.C.E. The anodic and cathodic waves are separated by about 30 mv., compared to the theoretical 28 mv. for a two-electron reaction, and the width of the cathodic wave as measured by n(E, - Egi2)is about 25 mv. These results also provide direct evidence that the theoretical approach used previously in the chronopotentiometric study (1) was valid. There it was assumed that the reduction potential for the intermediate was
significantly anodic of Wave I in order to apply a boundary condition that the concentration of intermediate at the electrode surface was zero. The E" separation measured here of about 300 mv. is sufficient to meet this condition. From the macroscale electrolyses and spectrophotometric studies reported previously, it had been concluded that the intermediate was p-benzoquinoneimine, and that the final product was p-aminophenol, as in Equation I. Although the time scales of the experiments are quite different, the coulometric results indicated that the intermediate probably was not hydroquinone, which had been suggested as an alternate possibility. Using cyclic stationary electrode polarography, this could be checked directly by obtaining polarograms of 1.0 X lO+M p-aminophenol in the same indifferent electrolyte as used in the electrolysis of the p-nitrosophenol. A polarogram a t a frequency of 1.0 C.P.S. (Figure 4A) shows that p-aminophenol forms a reversible two-electron system with a cathodic peak potential of +0.2 volt us. S.C.E., confirming that the intermediate couple is the p-benzoquinoneimine-p-aminophenol system. This was further verified by adding p-aminophenol to a solution of p-nitrosophenol on which a cyclic polarogram was being observed. The only effect was an increase in the peak height for the intermediate, and no other differences in the polarogram were observed. A polarogram for an equimolar mixture of paminophenol and p-nitrosophenol (both 1.0 X 10-3X) is included in Figure 4B. Cyclic polarograms of a 1.0 x 10-3M solution of hydroquinone in the same supporting electrolyte as used for the p-nitrosophenol electrolyses also were recorded (Figure 4C). These showed a reversible two-electron system, but with a cathodic peak potential of +0.15 volt us. S.C.E. or about 50 mv. cathodic of the wave corresponding to the intermediate in the p-nitrosophenol reduction. Therefore, the results of these experiments confirm that Equation l is the mechanism for the reduction of p-nitrosophenol under the conditions used here. Rate Constant Measurements. For a complicated system such as this E C E mechanism, there are several ways of obtaining kinetic data. All four waves are functions of the kinetic parameter k f / a , but in general, it is not convenient to work with Waves I11 and I V because the exact relations depend on wave separation and switching potential, in addition to the previously listed parameters. If kinetic calculations are restricted to Waves I and 11, there are several ways of determining the rate constant for the chemical reaction. First, it is possible to make direct
+ 0.05
-0.05 & O
0.2
0
-0.2
V vs S C E Figure 4. Multicycle stationary electrode polarograrns for A, 1 .O X 1 0-3 M p-arninophenol; 6, 1.0 X p-arninophenol plus 1.0 X 1 O - W p-nitrosophenol; C, 1.0 X 10-3Mhydroquinone Scan rate 1.0 volt/sec. (1.0 c.P.s.)
comparison of theoretical and experimental results such as in Figure 2. This usually is inconvenient, however, because it is necessary to construct many theoretical curves. Probably the most convenient way to use the cathodic wave alone, is to use the data of Figure 1 to compare the peak currents for kinetic and diffusion controlled currents. For this ECE case, a working curve can be constructed in which the ratio of the kinetic peak current (k,/a finit)e) to the diffusion controlled peak current ( k f / a zero) is plotted for different values of k f / a . Data for construction of such a curve can be obtained from Reference 4, Tables I11 and VII. For the present case, when 721 = n2, the empirical equation
can be used. In this equation, ik is the peak current measured a t a scan rate vl~such that kinetic effects are observed, and i d is the diffusion controlled peak current which would have been measured at the same scan rate if the kinetic effects had not been present. The latter can be calculated (3) if the electrode area, diffusion coefficient, and VOL 37, NO. 2, FEBRUARY 1965
193
I
0.0I
I
I .o
0.I
IO
V, volt,/sec. Figure 6. Determination of the rate constant for the chemical step in the reduction of p-nitrosophenol, using the ratio ia/ic of anodic to cathodic peak currents Points, experimental; line, theoretical for
I /a
Figure 5. Determination of the rate constant for the chemical step in the reduction of p-nitrosophenol, using data from the primary cathodic wave with Equations 2 m d 3
other parameters are known, or can be obtained from experimental data at high rates of voltage scan where the kinetic effects are small. If ik and id are obtained a t different scan rates, the data can be normalized by ,-
where v d is the rate of potential scan at which id' is measured. For either method of determining the current ratio, the term a in Equation 2 is defined as ?aFvk/RT. Equation 2 was found to describe the working curve to about 1% except for very large values of k j / a . (For very large values of k,la ilie values of the current ratio predicted by Equation 2 are low by not more than 4'33.) This method of measuring the rate constant was applied to the p-nitrosophenol system. I n this case, V d could be any value larger than about 1.0 volt/second. The data are summarized in Figure 5 where values of kf/a obtained from Equation 2 are plotted against l / a . The rate constant determined by the slope is 0.60 second-'. Kinetic data also ran be obtained from Wave 11, but here, the switching potential becomes an important additional parameter. On the other hand, it is possible to measure the ratio of the anodic to cathodic peak current so that knowledge of the electrode area, diffusion coefficient, and precise concentration are not required. This approach can be used, however, only if theoretical data are available for the exact system being investigated, with calculations made for the experimental switching potential, E"-Ex. Unfortunately, the working curve for the ratio of anodic to cathodic peak cur194 *
ANALYTICAL CHEMISTRY
rents as a function of k j / a is very dependent on the exact value of E" Ex, a t least for switching potentials reasonably near the cathodic peak. Thus, the experimental results for anodic waves do not agree with theory quite as well as did the cathodic wave. The use of this approach to obtaining kinetic data is shown in Figure 6, where experimental ratios iJiCof the anodic to cathodic peak currents are plotted as a function of the rate of potential scan. The anodic currents were measured to the extension of the cathodic wave as a base line. The switching potential E" -Ex was 45 =k 3 mv., with the uncertainty resulting from using the oscilloscope for potential measurements. The theoretical curve was calculated for k , = 0.6 second-', and for E" Ex = 45 niv. The agreement between theory and experiment is reasonable, considering the uncertainty in the experimental values of E" - Ex. The high results a t the slowest scan rate are caused by difficulty in measuring the veiy hmall anodic peaks obtained when k,/a becomes large. The deviations a t fast scan rates, where the current3 are fairly high, are probably related to uncompensated iB drop, which causes low cathodic peak currents. The above method for obtaining kinetic data from the anodic wave requires extrnsive numerical calculations for each ~7alueof the switching potential and therefore an alternate method was sought where this limitation coiild be avoided. Because of the similarities between this ECE mechanism and the behavior of a system in which a reversible charge transfer is followed by a single irreversible chemical reaction, an attempt was made to use the method developed earlier in Reference 3, Case VI. There, it was found that for a constant value of the parameter k,r (where T is the time in seconds from E o to the switching potential), the ratio iJiC of peak currents was a constant. Thus, a large number of theoretical cyclic polarogranis for the ECE
kj
= 0.6 sec.-I
h 0.2 0.6 1.0
O.O
T , sec. Figure 7. Determination of the rate constant for the chemical step in the reduction of p-nitrosophenol, using the ratio of anodic to cathodic peak currents for different switching potentials and different scan rates
mechanism were calculated, varying both k,/a and the switching potential. It was fourld that if n1 = n2,the ratio ia/icis a constant for a constant value of k , ~ ,and furthermore, it was found that the working curve relating iJiC and k / ~ was , the same (aithin 2Yo) as the working curve previously presented (Reference S, Figure 12, Table XI). IJsing this working curve, values of kjT were obtained from experimental ratios of iJiC for different scan rates. These data were plotted as a function of 7 (Figure 7 ) and the rate constant obtained from the slope was 0.6 second-'. The main disadvantage to this method is that the switching potential must be known very accurately. The experimental uncertainty of =t3 mv. in the term E" - Ex for these data results in an uncertainly of about 1 0 . 1 second-' in the rate constant. However, for a quick estimate of the rate constant, the method is very convenient, sincc the working curve is independent of switch-
(3) Nicholson, R. S., Shain, I., ANAL.
ing potential, and as mentioned above, the ratio ia/icis independent of electrode area, diffusion coefficient, and concentration of reactant. LITERATURE CITED
(1) Alberts, G. S., Shain, I., ANAL.
CHEM.35,1859 (1963).
( 2 ) Holleck, L., Schindler, R., 2. Elektrochem. 60, 1138 (1960).
CHEM.36, 706 (1964). (4) . , Nicholson. R. S.. S h a h, I.,. Ibid., 37. 178 (1965).' (5) Reinmuth, W. H., Columbia Univ., New York, unpublished results, 1964. (6) Schwarz, W. M., Shain, I., ANAL. CHEM.35, 1770 (1963). (7) Suzuki, M., Mem. Coll. Agr., Kyoto Univ. 67, (1954). (8) Testa, A. C., Reinmuth, W. H., ANAL. CHEM.33, 1320 (1961).
(9) Underkofler, W. L., Shain, I., Ibid., 35, 1778 (1963). RECEIVEDfor review September 21, 1964. Accepted December 7 . 1964. Presented in part at the Division of Analytical Chemistry, 148th Meeting ACS, Chicago, Ill., September 1964. Work %-as supported. @ part by the Atomic Energy No. Commission under Contract AT(ll-1)-1083. Other support was received from the National Science Foundation under Grant No. Gl5741.
Effect of a Coupled Chemical Reaction on the Faradaic Admittance GORDON H. AYLWARD and JOHN
W. HAYES
School o f Chemistry, University o f New South Wales, Kensington, Australia
b The application of a x . polarography to the measurement of the rate constant of a coupled chemical reaction by comparing faradaic admittances is demonstrated. The equation tested is restricted to fast electron transfer systems where the d.c. process is controlled by the kinetics of the chemical reaction but the periodic mass transfer remains diffusion controlled. The values of the rate constant for the reaction of cadmium ions with (ethylenedinitri1o)tetraacetic acid determined by d.c. polarography compare favorably with the values obtained by the a.c. method. The dependence of the admittance on frequency in the presence of the following reaction verifies diffusion controlled periodic mass transfer but apparently anomalous phase angle measurements are recorded.
E
to the theory of ax. polarography are opening up new possibilities for more exact studies of electrode reactions (3, 10, 11, 17). Smith has related the frequency and potential dependence of phase angles to the kinetics of electron transfer and (17 ) . coupled chemical reactions Recent publications and discuq-ions (1, 2,11, I 2 , 1 6 ) on the time dependence of a x . polarographic currents highlight some of the possible applications of the extended theories. I n a previous paper (3) an equation was derived for the amplitude of the peak height of an alternating current (ax.) polarogram for an electrode process involving a monomolecular chemical reaction following the electron transfer reaction. The expression was derived under the following assumptions: the electron XTEKSIONS
Present address, Department of ChemUniversity of North Carolina, Chapel Hill, N. C. 1
istry,
transfer reaction is reversible in d.c. polarography; the rate constant of the chemical reaction is greater than 10 second-1 ( I S ) but less than the angular frequency of the alternating voltage. I n this paper the equation is tested by comparing the values of the rate constants calculated from changes in the faradaic admittance with values obtained from the shift in the half-step potentials (E,/z) of the d.c. polarograms (14). For this study the oxidation of cadmium amalgam in acetate buffer solution containing (ethylenedinitri1o)tetraacetic acid (EDTA) was chosen as an example of an electron transfer process coupled to a following chemical reaction. Koryta and ZBbranski (14) have measured by the d.c. polarographic method the rate constant of this following reaction and have demonstrated that the predominant reaction in acetate buffer is Cd+2 HY-S --t CdHY(I)
+
where Y-4 is the tetravalent anion of EDTA. These authors assumed that only the aquo-cadmium ions react with HY-3; the concentration of cadmium ions was corrected for the formation of acetato-cadmium(I1) complexes. This simplifying assumption is accepted. EXPERIMENTAL
Cadmium amalgam was prepared and used in an all glass apparatus similar to that reported by Furman and Cooper (8). Preliminary a.c. polarograms were recorded on a modified Leeds & Northrup Electrochemograph Type E (9). The manual a.c./d.c. polarograph was of conventional design (6). A Philips GM6012/GM4574 combination voltmeter/preamplifier was used to measure the alternating current. A Hewlett Packard 200CD oscillator provided the source of alternating voltage which was kept a t 15 mv. root mean square. A Tektronix 502 dual beam
oscilloscope was used to measure the phase angles by observing the distance between corresponding maxima in the waveform of the applied alternating voltage and the polarographic alternating current. The series resistance was determined by measuring the current at a frequency of 50 kilocycles second-1 ( 5 ) . The faradaic admittance vas calculated in the conventional manner (5). The temperature of the polarographic cell was controlled a t 25' =t 0.2" C. The capillary used had an m value of 1.04 m?. second-1 and a drop time of 6.25 seconds a t a head of 50 em. (uncorrected) in 0.2X acetate buffer 0.4M KC1 a t a potential of -0.62 volt us. S.C.E. To test our equation the rate of the chemical reaction I must be reduced. This is achieved by adding excess calcium chloride to the system. The calcium-EDTA complex is known to be labile (20) and, from its stability constant and the ionization constants of the EDTA (7, 15, do), the concentration of free HY-3 is calculated. The solution also acts as a buffer with respect to EDTA and so the concentration of HY-3 a t the electrode surface is held constant. I n the measurement of the rate constant of the following reaction by the a s . polarographic method, the faradaic admittance a t the summit potential for a fast electron transfer process in the presence of the following reaction, Yj, is compared to the admittance, a t the summit potential, in the absence of the following reaction, Yd. Since, for a diffusion controlled process (4),
+
Yd
=
- n2F2AC;
(WDO)'/*
4RT
(1)
and, from the equation under test ( 3 ) , Yf
=
VOL. 37, NO. 2, FEBRUARY 1965
195
