Genera I ized Chro no po te ntio metric PotentiaI Time Equations and Their Application to Quasi- Reversib le Processes LARRY B. ANDERSON1 and DANIEL J. MACER0 Department o f Chemistry, Syracuse University, Syracuse, N . Y.
b A general potential-time relationship for quasi-reversible first-order electrode reactions without kinetic complications, which allows the use of concentrations other than zero for both the oxidized and reduced forms, is derived. A similar equation is derived for the potential-time relation for the reverse process upon reversal of the current at or before the transition time. The significance of the equations is discussed and suggestions are made for their application to the and E”’. determination of ka,h#CY,
IN
years, there have been many excellent treatments of chronopotentiometric potential-time equations for various electrode reaction schemes (2, 4, 6, 7 , 9 , 2 1 ) . I n almost all of these, however, attention has been focused on completely reversible and/or completely irreversible processes. Very little consideration has been given to intermediate or quasi-reversible electron transfer processes. In a n important paper dealing with the interpretation of chronopotentiometric potential-time curves, Reinmuth (9) has touched upon the type of relation to be expected for such intermediate processes in the absence of any kinetic and catalytic effects. He uses this relationship to define the practical limits of application of the simple totally reversible and totally irreversible chronopotentiometric equations. In the present work, we have considered a more general potential-time relationship for quasi-reversible, firstorder electrode reactions without kinetic complications. This equation allows the use of concentrations other than zero for both the oxidized and reduced forms. X similar equation is derived for the potential-time relation for the anodic process upon reversal of the current. The equations given here are written for the case where a reduction process is followed by reoxidation. They apply equally well, of course, to RECENT
Present address, Department of Chemistry, University of North Carolina, Chapel Hill, X . C. 1
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ANALYTICAL CHEMISTRY
an oxidation process followed by a reduction. A discussion is given of the significance of these equations and suggestions are made for their application to the determination of the quantities ks.h,a,and E”.
form in two limiting cases-reversible or diffusion control of the rate and irreversible or electron transfer control. Reinmuth has shown (9) that, if Condition 5 holds, the electrode reaction may be considered to be electrochemically reversible.
THEORY
I n the case of a first-order electrode reaction
O+ne-eR (1) the rate of the reaction may be described in terms of the current as i,/nF = ka,hea[Cos- c R s / e ] ;0 -i,’/nF
