ond, the rise to the diffusion plateau with eathodically increasing potential would not be as steep as in the present case. Third, the decay of current with time would be much slower at the foot of the diffusion plateau. CONCLUSIONS
The
potential-current-time
surface
with its associated equation gives excellent qualitative and in most cases quantitative agreement with more rigorous treatments for various voltammetric techniques. It may prove useful in the evaluation of. proposed new techniques for which exact theoretical
treatments are difficult. Moreover, experience indicates that it is a valuable teaching aid. The fundamental similarities among various voltammetric processes as well as their differences become apparent with the aid of the surface. These similarities seem to escape many students when they deal only with the more abstract algebraic equations describing the methods. ,
LITERATURE CITED
(1) Delahay, P., “New Instrumental Methods in Electrochemistry,’’ p. 55, Interscience, New York., 1954. (2) Delahay, P., Mamantov, G., Anal. Chem. 27, 478 (1955).
(3) Heyrovsky, J., Ilkovió, D., Collection Czechoslov.
Chem.
Commune.
7,
198
(1933). (4) Kambara, T., Tachi, I., J. Phys. Chem. 61, 1405 (1957). (5) MacGillavry, D., Rideal, E. K., Rec. trav. chim. 56, 1013 (1937). (6) Mamantov, G., Delahay, P., J. Am. Chem. Soc. 76, 5323 (1954). (7) Oldham, K. B., Kivalo, P., Laitinen, H. A., Ibid., 75, 5712 (1953). (8) Reilley, C. N., Cooke, W. D., Furman, N. H., Anal. Chem. 23, 1226(1951). (9) Reinmuth, W. H., J. Am. Chem. Soc.
79,6358(1957). M., Rev. (10) Senda, (Japan) 4, 89 (1956).
Polarography
Received for review April 28, 1960. Accepted August 15, 1960.
Chronopotentiometry with Current Reversal Application to p-Benzoquinone Imine Hydrolysis A. C. TESTA and W. H. REINMUTH
Department of Chemistry, Columbia University, New York 27, N. The hydrolysis of p-benzoquinone imine was studied by generating the species electrochemically at constant current, then following its hydrolysis chronopotentiometrically by reversing the current. The data were consistent with theory on the assumption of an irreversible reaction first order in pPseudo-first benzoquinone imine. order rate constants for the hydrolysis are: 0.140, 0.103, 0.032 second-1 in 0.05, 0.1, and 0.5M sulfuric acid,
respectively. of
the
inviting possibilities of methods is that
electrochemical One
of preparing and studying under controlled conditions species which are accessible only with difficulty by more conventional chemical techniques. Often the initial product of an electrochemical reaction is unstable with respect to subsequent chemical decomposition. It should be possible then to generate the species in question and follow the course of its decomposition entirely by electrochemical means with good accuracy and over short time periods.
Chronopotentiometry with current reversal appears to be an advantageous technique to apply to such an investigation because the theory of the method is relatively simple, and the accuracy of the results depends only on the determination of times at which potential breaks occur, rather than on accurate current and potential measurements. After completion of the present study
1512
·
ANALYTICAL CHEMISTRY
Y.
the theory of the method was published independently by Dracka (£). To demonstrate the feasibility of this method, a specific chemical system, p-aminophenol (PAP)-p-benzoquinone imine (PQI), was investigated. The reactions involved are as follows: HO—C6H4—NH,
-
2e wi
0=C6H4=NH + 2H;0
—
0=C6H4=NH + 2H + 0=C6H4=0 + nh3
The chemical oxidation of PAP has previously (1, 4). In 1949, Knobloch (6) made polarographic studies, and more recently Snead and Remick (10) estimated the hydrolysis rate of PQI by analysis of potential-time curves for the chronopotentiometric oxidation of PAP. been investigated
EXPERIMENTAL
The PQI used in this experiment was generated at a platinum electrode by the anodic oxidation of PAP. The electrolytic cell used in this work was a jacketed H-cell resembling that described by Reilley et al. (9). The apparent area of the indicating platinum electrode was 12.6 sq. cm., and the auxiliary platinum electrode was A saturated placed in the side arm. calomel electrode was used as reference.
Nitrogen was purified by passage through a vanadous sulfate train (?'). A modification of a constant current supply described in the literature (8) was used for all measurements. For most of the data, a current of 1.30 ma. was
applied to the cell.
The potential difference between the reference and indicating electrodes was fed through a Leeds & Northrup pH meter, Model No. 7664 to a Sargent recorder, Model No. S72150. The chart speed was 12 inches per minute. For the recording of transition times
shorter than 10 seconds, potentials were fed through a G. A. Philbrick Researches’ K2-X amplifier as follower into a Hewlett-Packard oscilloscope, Model No. 130B, with a Du Mont polaroid camera attachment. All measurements ° were made at 30.0° ± 0.1 C. Eimer-Amend c.p. PAP was purified by the method of Dunn (3). The melting point (under nitrogen) was 189° to 190°, uncorrected. J. T. Baker reagent grade sulfuric acid was the supporting electrolyte, and the three concentrations of acid studied were determined by titration with NaOH solution. Weighed amounts of PAP were added to deaerated H2SO4 solutions of appropriate concentration, and the resulting solutions manipulated under nitrogen to prevent air oxidation of PAP. The solutions were 1.00 X 10-3M in PAP, with the exception of the strongest acid solution studied, which was 0.75 X -3 PAP. RESULTS
Figure curves
1 shows typical potential-time observed on electrolysis at
constant current followed by current reversal. On application of anodic current, the potential shifts rapidly from its initial value, e¡, to a region where it is controlled by the ratio of PAP to PQI. There is then a potential holdup during which the concentration
cently the solution to this boundary value problem. When the ratio of current densities for oxidation and reduction is unity, the transition time is related to the rate constant and the time of current reversal by the following equation: 2
08
0.6
0.4
VOLTS
VS.
0.2
0.0
-0.2
S.C.E.
obFigure 1. Potential-time curves tained with 1.00 X 0 ~SM p-amino1
phenol in 0.1 M H2SO4
Cell current, 1.29 ma.; sq.
electrode area,
12.6
cm.
of the PAP at the electrode surface decreases. At ta the current is reversed, and two reduction waves arc observed. The first corresponds to reduction of PQI, and the second to reduction of benzoquinone. By definition, the transition time is the time at which the concentration of depolarizer becomes zero at the electrode surface. In Figure 1, n is the transition time for the PQI, and r2 is the transition time for benzoquinone. Point b on curve 3 corresponds to the time at which the PQI concentration becomes zero at the electrode surface; point c corresponds to the disappearance of the benzoquinone concentration. The relative amounts of PQI and benzoquinone found on current reversal vary with the time (ta) of the forward (anodic) electrolysis. At longer times the fraction of PQI which hydrolyzes becomes greater (curve 3), whereas at sufficiently short times the benzoquinone wave diminishes to negligible values. The over-all reverse transition time is in all cases one third the forward transition time. This is the theoretically expected value, assuming the current efficiencies of the forward and reverse processes to be the same (11). The potential-time curves thus qualitatively confirm the postulated mechanism of the electrode process. Theoretical Working Curve. The electrode process under study can be represented as follows: R Ox
—
2e
+ H20
Ox
Z
—
with the condition that at i 0, CR (x,0) Cr°, Co(x,0) 0. The cur=
=
=
rent is assumed to be anodic between ta, and cathodic for times greater Dracka (2) has published re-
0< t< than ta.
erf (fcn)1'2
=
erf k(U +
)1'2
(1)
where erf is the error function, k is the hydrolysis rate constant (second-1), and ta, n, were defined previously, Dracka’s treatment of this equation assumes that the argument of the right hand side is large enough that the error function becomes unity. In the present case that assumption is not justified. By choosing arguments for the left hand side of Equation 1, the corresponding argument on the right hand side can be computed. This procedure leads to simultaneous equations relating the arguments of the two error functions to numerical values. Appropriate rearrangement of these equations allows
Figure 2. Variation of transition time with time of current reversal
calculated by least squares analysis of the slopes; however, the actual uncertainties, due to possible systematic errors in the measurement of transition times, are somewhat larger. The uncertainty becomes larger for smaller rate constants. In principle this uncertainty could be reduced by investigating the behavior at larger ta; however, practically, this procedure is of limited value because of the difficulty of avoiding convective mass transfer at times over 60 seconds. In short-time investigations, another practical difficulty arises—namely, that an appreciable fraction of the current is used for capacitive charging of the double layer. This factor, although not of prime importance in the present investigation, limits at the upper end rate constants which can be determined by this method. The problem can be alleviated by increasing the concentration of the reactive species and the current density, because the fraction of the current used in charging the double layer is diminished whereas the kinetic process is unaffected (see below). Therefore, Dracka’s estimate of 1.1 X 102 seconds-1 as the upper limit of the rate constants determinable by this method may be too conservative. This procedure of operating with abnormally high concentration and current densities might also allow circumvention of the complication, which would arise if one or more of the species involved in the process were surfaceactive, because of the general tendency to leveling of adsorption isotherms at high concentrations. Again, the difficulty was not encountered in the present study. DISCUSSION
The treatment of the data
the construction of a working curve shown in Figure 2. The working curve confirms the qualitative observation that the ratio n/ta approaches one third as ta becomes smaller—i.e., the effect of the kinetic complication becomes negligible under these conditions. For any experimentally observed ratio n/ta, the theoretical value of kta can be obtained directly Data were obtained from this curve. over a wide range of ta and treated by this procedure. Results are plotted in Figure 3. The linearity of the curves in Figure 3 and the fact that they extrapolate to the origin confirm the validity of the theoretical model. The slopes of these lines yield the rate constants directly. The rate constants corresponding to the curves in Figure 3 are: 0.140 ± 0.002 second-1, 0.103 ± 0.003 second-1, 0.032 ± 0.005 second-1 in 0.049, 0.102, and 0.5KL1Í H2S04, respectively. The errors given are standard deviations as
assumes
Kinetic data from chronopotentiometry of p-aminophenol Figure 3. Curve 1. Curve 2. Curve 3.
1.00 X 0 -3M PAR in 0.049M H2S04 1.00 X 10 -3M PAP in 0.1 02M H2S04 0.75 X 10-3M PAP in 0.51 0M H2S04 1
VOL. 32, NO. 11, OCTOBER 1960
·
1513
first order kinetics, whereas chemically the possibility exists of second or higher order. To eliminate these alternatives,
the experiments should be repeated at various current densities. If the chemical reaction is first order, / should depend only on kta and be independent of the current density (Equation 1). However, for other reaction orders this is not the case (11). In the present study, /ta remained constant over a sixfold change in current (1.312 to 0.233 ma.). An alternative method of demonstrating first order kinetics would have been to vary the initial concentration of PAP and observe the constancy Of Tl/ta. Because our concern
was
mainly with
the development of the technique rather than the specific chemical sy'stem, more detailed studies were not made and the mechanism was investigated only to the extent of confirming that it was first order in p-benzoquinone imine. The value of the rate constant in 0.05.1/ H2S04 determined in the present work (k 0.140 second-1) differs appreciably from that reported previously by Snead and Remick (10) 0.020 second-1). Recalculation (k of their data gives a value of 0.031 seccond-1. Evidently, a superfluous factor 2.303 was also included in their calcula=
=
tion.
There are a number of practical difficulties involved in the analysis of data by the method of Snead and Remick, based as it is on the change of the difference between two quantities as both of them tend to infinity'. This difficulty is pronounced especially when one of the quantities is the potential of an electrode near time zero in a chronopotentiometric process. In this region the potential curve is distorted highly because of the capacitive charging of the double la3-er occasioned by' the rapidly changing potential. The extrapolation to time zero, proposed by them, has the further disadvantage in that the theoretical curve has its greatest curvature in the most difficult region experimentally near time zero. Further discussion of these points will be undertaken in a subsequent communication. CONCLUSION
Study of the kinetics of chemical reactions following electron transfer makes accessible a number of hitherto unexplored systems. Previous methods of investigations suffer from various disadvantages. The method of Snead and Remick (10) demands that the system obey the Nernst equation, while in the present case the only necessity is that the electrochemical reaction be reversible in the gross sense—
i.e., that reversal of current result in reversal of direction of the electrode process. Hanging drop polarograpby with forward and reverse potential scans, as practiced by Kemula and coworkers (5), is excellent for qualitative studies; however, the theory is sufficiently' complex that, as yet, it is impossible to obtain quantitative measures of rate constants from their experiments. The present work indicates the applicability of chronopotentiometry' with current reversal to such cases. LITERATURE CITED
(1) Conant, J. B., Pratt, M. F., J. Am. Chem. Soc. 48, 3178 (1926). (2) Dracka, O., Collection Czechoslov. Chem. Communs. 25, 338 (1960). (3) Dunn, S. A., J. Am. Chem. Soc. 76, 6191 (1954).
(4) Feiser, L. F., Ibid., 52, 4915 (1930). (5) Kemula, W., Kublik, Z., Roczniki Chem. 32, 941 (1958). (6) Knobloch, I. E., Collection Czechoslov. Chem. Communs. 14, 508 (1949). (7) Meites, L., Meites, T., Anal. Chem.
20,984(1948). (8) Reilley, C. X., Cooke, W. D., Furman, X. H., Ibid., 23,1030 (1951). (9) Reilley, C. X., Everett, G. W., Johns, R. H., Ibid., 27, 483 (1955). (10) Snead, W. K., Remick, A. E., J. Am.
Chem. Soc. 79, 6121 (1957). (11) Testa, A. C., Reinmuth, W. H., unpublished data. Received for review April 29, 1960. Accepted August 15,1960.
Chronopotentiometric Potential-Time Curves and Their Interpretation W.
H. REINMUTH
Department of Chemistry, Columbia University, New York 27, N. Y.
Potential-time relations are derived a number of common chronopotentiometric reduction mechanisms in which no complication other than diffusion precedes electron transfer. Theoretical limits on the validity of the approximations involved are presented. Diagnostic criteria are proposed by which these schemes can be distinguished from one another.
for
RECENT RESURGENCE of chrOnO-
THE potentiometry
after 40 years has demonstrated amply' its usefulness both for analysis and for the study of electrode reactions. Most of the recent work has been concerned with measurements of transition times and relatively little attention has been devoted to the interpretation of potential-time curves. Such studies might yield valuable information, both qualitative and quanti-
1514
·
ANALYTICAL CHEMISTRY
tative, about the kinetics of reaction. The present work was undertaken to derive the potential-time relations for a number of common kinetic schemes together with their limits of applicability and to suggest diagnostic criteria by which these schemes can be distinguished from one another. Schemes in which some complication other than pure diffusion precedes electron transfer can be distinguished by the inconstancy' of ' with varying current density'. These cases are not considered in the present discussion. Before the relations presented herein can be applied validly to any specific case, the constancy of 0 /! must be established. To reduce complication to a minimum, only' reductions are discussed and the reduced form of the electrochemically reactive species is assumed to be
absent from solution prior to electrolysis. All symbols are defined in the nomenclature section. For ease in comparison, the predictions of the diagnostic criteria and equa-
tions for the potential-time curves are summarized in tabular form. As Table I shows, four criteria are proposed. The first is the linearity of a plot of some logarithmic function of time vs. potential and the slope of that log plot. The second is the variation of the quartertime potential with applied current density. The third is the variation of quarter-time potential with concentration of the reactive species in solution. The fourth is the ratio of the transition time observed when the current is reversed at the forward transition time to the original forward transition time. In connection with the last criterion, the current can be reversed at any time
