small potential excursions, the theory for diffusion limited charge-transft,r can be obtained through a linearization procedure analogous to that of Berzins and Delahay for the galvanostatic method ( I ) . The potential-time expression for the impulse case is the derivatile of the result given by thcse authors. This result corresponds well with intuition because the systemdisturbing function in the impulse case is the derivative of the disturbing function in the galvanostatic step case. More dctailed discussion of the theory for various relaxation schemes will be given in works in preparation. Delahay and Mohilner ( 2 ) h a r e independently suggested a “coulostatic” method for the study of adsorption
kinetics. The principlp of their method is essentially the same as that of the method herein described, and the term is an a p t one because the system rrlaxes from the effect of rapid transfer of a small amount of charge from one electrode to the other. Qualitative examination of the experimental data of Figurw 2 and 3 shows clearly that relaxation times are much shorter in the mercurous nitrate than in the mercuric-EDTh system. I n the latter case the dccay is resolvable into two components suggesting a two-step relaxation process presumably involving a slow chemical step. Further discussion of these c a m will be given in future works. As anticipated, essentially no relaxation occurs
in solutions containing only supporting electrolytes. A typical example is shown in Figure 4. LITERATURE CITED
(1) Berzins, T., Delahay, P., J . A m . Chem. SOC.,77,6448 (1955). (2) Delahay, P., Mohilner, D. M., Ibid., in
press
W.H. REINMUTH~ C. E. WILSON
Department of Chemistry Columbia University New York 27, N. Y. RECEIVEDfor review June 4, 1962. Accepted June 19, 1962. Fellow of the Alfred P. Sloan Foundation, 1962-64.
Note on “An Impulse (Coulostatic) Relaxation Method for the Study of Rapid Electrode Processes by W. H. Reinmuth and C. E. Wilson” SIR: I n connection with the above communication by Reinmuth and Wilson, I wish to point out that work on the coulostatic method and its application to the study of fast electrode processes (9, 51, adsorption kinetics (4, 7 , 8), and the determination of traces ( I , 2, 6) has been carried out for some time in this laboratory. The principle of the coulostatic method was described in the paper (7) cited by Reinmuth and Wilson, and the expression “coulostatic method” was coined in that paper. Work in progress on application to electrode kinetics and analytical determinations of traces was announced in that paper, and application to sdsorption kinetics was discussed a t some length. .4 detailed investigation of the application to fast electrodc reactions has already been accepted for publication (3, 5 ) . This 1Toi-k is summarized as follows: Part I ( 3 ) . A new method (chargestep or coulostatic) for t h e kinetic study of fast electrode processes is discussed. T h e method involves charging of t h e electrode with a known quantity of electricity b y means of a coulostat t o cause a departure from t h e equilibrium potential, a n d recording of t h e overvoltage-time curve during t h e subsequent discharge of the double layer capacity c d by the electrode reaction. Overvoltage-time
curves are derived for the following cases: constant c d and linearized current-overvoltage ( I - 7 ) characteristic without mass transfer control or with mass transfer controlled by semi-infinite linear diffusion; constant c d and quadratic and cubic approximations of the I-? characteristic in the absence of mass transfer control; and variable double layer capacity. Conditions for pure control by either diffusion or the charge transfer reaction are derived, and it is shown that conditions can be selected for which diffusion need not be considered when the apparent standard rate constant does not exceed 0.2 to 0.3 cm. set.-' The method has about the same potentialities a8 the potentiostatic and single-pulse galvanostatic methods but has the advantage of somewhat greater simplicity of technique and interpretation of results. The coulostatic method also allows the determination of the differential capacity of the double layer even when a fast charge transfer reaction occurs on the electrode. Part I1 (5). Methodology for t h e coulostatic study of electrode kinetics is discussed, and application is made t o the discharge of Zn(I1) on a Znamalgam hanging drop in 1M KC1. Known quantities of electricity were supplied to the Zn-amalgam electrode by discharge of a small capacitor
(-300 ppf.), initially charged a t a known voltage (-10 volts), across the electrochemical cell. Overvoltage-time curves were recorded by means of a cathode-ray oscilloscope in the interval 0 to 40 psec. after charging. The theory of Part I was verified experimentally, and essentially pure control by the charge transfer reaction was achieved. The influence of the cell resistance is treated quantitatively. Kinetic parameters a t 25’ 1’ C.: apparent standard rate constant, 0.0041 cm. sec.-l; transfer coefficient. cy = 0.30.
*
LITERATURE CITED
(1) Delahay, P., ANAL.CHEM.,in press. (2) Delahay, P., Anal. Chim. Acta, in
press.
(3) Delahay, P., J . Phys. Chem., in press. (4) Delahay, P., Technical Report to the
Office of Naval Research, Project NR 051-258, May 1962. (5) Delahay, P., Aramatata,A., J . Phys. Chem., in press. (6) Delahay, P., Ide, Y., unpublished data. ( 7 ) Delahay, P., Mohilner, D. M., J . Am. Chem. SOC.,in press. (8) De!ahay, P., Takemori, Y., unpublished data.
PAULDELAHAY
Coates Chemical Laboratories Louisiana Sta.te University Baton Rouge 3, La. VOL. 34, NO. 9, AUGUST 1962
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