Facile Analysis of EC Cyclic Voltammograms Conor F. Hogan,* ,†,§ Alan M. Bond, † Jan C. Myland, ‡ and Keith B. Oldham ‡ School of Chemistry, Monash University, Clayton, Melbourne, Victoria 3800, Australia, and Department of Chemistry, Trent University, Peterborough, Ontario, Canada K9J 7B8 It has been found empirically that, for an E rev C irrev process, the forward/ backward ratio of the peak height magnitudes in cyclic voltammetry equals 1 + kτ, where k is the rate constant of the chemical reaction and τ is the time required for the scan to travel between the half-wave and reversal potentials. The relationship is largely indepen- dent of the scan rate and the reversal potential, except insofar as these influence τ. Though not exact, the relationship is obeyed closely enough to provide accurate rate constants under favorable conditions. The utility of this simple formula in extracting homogeneous kinetic information is demonstrated using experimental data for the electron-transfer-induced isomerization of an octahe- dral manganese complex. An explanation of the relation- ship is presented, as is a more exact formula that reduces to 1 + kτ when k is small. A semiquantitative explanation of the relationship is provided. Not infrequently, the product P of an electron-transfer reaction undergoes a subsequent first-order homogeneous reaction. If the lifetime of P is long enough, the process can be described successfully within the framework of the EC model. This consti- tutes an important class of mechanisms, with implications in many areas of interest in chemistry. For example, the chemical step may involve intermediates of consequence in electrosynthetic reactions. 1,2 Moreover, conformational changes or other molecular motions may be involved which are of significance in the field of nanotechnology, 3 or the reactions may be important in the area of organometallic catalysis. 4 Our interest here is in the frequently encountered case in which the electrode reaction is reversible, whereas the homoge- neous chemical reaction is irreversible One of the most popular tools for investigating such reaction mechanisms is cyclic voltammetry. There are many published instances of homogeneous rate constants being measured by such a procedure. 5,6 Typically, the scan rate is varied, and the depen- dence on the experimental timescale of the peak potential, 7 the peak current, 8 or the ratio of forward to back peak currents 9,10 is probed to gain an estimate of the homogeneous rate constant. These methods usually require comparison of the data with a working curve, as described, for example, by Nicholson and Shain 10 for the relationship between peak current ratio and experimental time scale. Another common approach for obtaining the desired kinetic information from voltammetric data has been the comparison of experimental results with simulations of the diffusion/ electrochemical/ chemical problem, 11,12 but although these methods are of great value in terms of the accuracy of the results they yield, they are often laborious and sometimes mathematically demanding. We have found an intriguingly simple relationship which reveals that for an E rev C irrev process, the forward/ backward ratio of the peak height magnitudes in cyclic voltammetry equals 1 + kτ, where k is the rate constant of the chemical reaction and τ is the time required for the scan to travel between the half-wave and reversal potentials. Ideally, and if available, the use of an exact mathematical equation would most likely be recommended in preference to all the approaches presently employed. In this context, the empirical, approximate equation presented in this paper may be advocated as an interim measure that may be considered until such time as an exact analytical solution to the EC mechanism becomes available under conditions of cyclic voltammetry. A recent interest in this laboratory has been the investigation of the electrochemical properties of the 18-electron octahedral- type complex cis-[bis(diphenylphosphino)methane]cyanodicar- bonyl(triphenyl phosphite)manganese(II). 13 The oxidation of this species, at a potential of 1.17 V vs Ag/ AgCl in acetonitrile, is followed by a chemical step corresponding to the isomerization of the thermodynamically unstable 17-electron cis + complex, as shown in Scheme 1. * Corresponding author. E-mail: c.hogan@ latrobe.edu.au. † Monash University. ‡ Trent University. § Present address: Department of Chemistry, La Trobe University, Bundoora, Victoria 3086, Australia. (1) Webster, R. D. J. Chem. Soc., Perkin. Trans. 1999 , 2, 263-270. (2) Doherty, A. P.; Scott, K. J. Electroanal. Chem. 1998 , 442, 35-40. (3) Armaroli, N.; Balzani, V.; Collin, J.; Gavini, P.; Sauvage, J.; Ventura, B. J. Am. Chem. Soc. 1999 , 121, 4397-4408. (4) Olivero, S.; Clinet, J. C.; Dunach, E. Tetrahedron Lett. 1995 , 36, 4429- 4432. (5) Howell, J. O.; Wightman, R. M. J. Phys. Chem. 1984 , 88, 3915-3918. (6) Vallat, A.; Person, M.; Roullier, L.; Laviron, E. Inorg. Chem. 1987 , 26, 332- 335. (7) Nadjo, L.; Saveant, J. M. J. Electroanal. Chem. 1973 , 48, 113-145. (8) Kontturi, A.-K.; Other, A. N. J. Electroanal. Chem. 1996 , 418, 131-137. (9) Nicholson, R. S.; Shain, I. Anal. Chem. 1965 , 37, 190-195. (10) Nicholson, R. S.; Shain, I. Anal. Chem. 1964 , 36, 706-723. (11) Feldberg, S. W. J. Electroanal. Chem. 1990 , 290, 49-65. (12) Alden, J. A.; Compton, R. G. J. Phys. Chem. B 1997 , 101, 9606-9616. (13) Hogan, C. F.; Bond, A. M.; Neufeld, A. K.; Connelly, N. G.; Llamas-Rey, E. J. Phys. Chem. A 2003 , 107, 1274-1283. S(soln) - ne - { \ } reversible E 1/ 2 P(soln) 9 8 irreversible k X(soln) (1) Anal. Chem. 2004, 76, 2256-2260 2256 Analytical Chemistry, Vol. 76, No. 8, April 15, 2004 10.1021/ac035108m CCC: $27.50 © 2004 American Chemical Society Published on Web 03/11/2004