Mechanism of Electrode Reactions and the Stoichiometric Number P. Radhakrishnamurty Central Electrochemical Research Institute, Karaikudi 623 006 lndia
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R. Arun Mozhi Selvan RES Photovoltaics, D-13A, Phase V, Jeedimetla, Hyderabad - 500 855, lndia In teaching the kinetics and mechanism of electrode reactions of multielectron transfer reactions of the type A+ne=Z we assume that the probability of the simultaneous transfer of several electrons is much smaller than that of the transfer of one electron. With this premise we split the multielectron transfer reaction into a series of elementary step reactions (1-7). Because stoichiometric number is one of the important diagnostic criteria of reaction mechanisms, each step is assigned a stoichiometric number, vi 2 1. To simplify the understanding of the principles involved in the determination of mechanisms, we assume that one of the steps is the rate-determining step (RDS). We then write the rate expression for the assumed RDS alone and relate the rate of the RDS to the rate of the overall reaction, whose properties are obtained experimentally and compared with those predicted by the proposed mechanism. Relation between the Rates of the RDS and the Overall Reaction Steps in Series That Behave as if in Parallel We consider a n electrode reaction, v1vAA+ ne = v,vZZ taking place through a series of steps as follows. vl(v& + nle = vbB)
We assume steps other than RDS to he single-electrontransfer reactions, that is, nk, = 1and n, > 1,and all v?s are unity except that of the RDS, that is, v, = 1and v, > 1. Because the steps are in series, they all occur a t the same rate, so we write, However, when we come to relating the rate of the RDS to that of the overall reaction, we write . i zr=-
(3) explaining that, though the steps are in series, they behave as if in parallel as far as the electrun-transferreaction is concerned ( I ) ,or the measured current is proportional to the total number of electronsper mole of the reactant converted (2). Many times eq 2 is implicitly assumed, and eq 3 is explicitly used (3-7). Students immediately see a contradiction between eqs 2 and 3; the explanation that they behave as if in parallel is by itself not sufficiently convincing. No explanation is easily available in the books (1-7) on electrochemistry to resolve this apparent paradox. n
Use of Equation 3 We are concerned with the use of eq 3 as the relation between i, and i ( I , 2) for all cases whether nrv, is equal to or greater than 1. Below we show the following. The fact that the steps are in series does not mean the step currents are equal. Equation 3 is true only when n,v, = 1 and leads to wrong results when n,v, > 1. The theory of stoichiometry of reactions requires that
.L
.x
.r
where E, stands for the extent of reaction and is defined (8) for a reaction, z v i v J + ne = z v i v &
VAA+ VBB+ ...... = vLL+ vMM+ ...
(5)
which becomes
where species A is the reactant; and Z is the product. All other species are intermediates that get canceled in the addition, and cv;n; = n 'Present address; Consultants India, I I D , south Leith Castle Road, Santhome. Madras-0600028,India.
where (IXA, ~ X B...... , represent the change in the number of moles of the species represented by the subscripts. Several reaction steps Ri, involved in an overall reaction, each with a stoichiometric number vi, are represented using vlRl + v& + ......= R (7) which leads to the result given by eq 4. Volume 72 Number 10 October 1995
895
Equation 4 can be written as
where n,. -.n.,. -. ..... re~resentthe number of electrons involved in the step reactions represented by the subscripts and pive the eauivalents Der mole of the res~ectivereactions: n represent; the same 'for the overall reaction.
This result, that the sum of the s t e currents ~ is eaual to the overall reaction current, gives the impression &at the steps are in parallel as far as the electron-transferreaction is concerned. From eq 9, we get for the rate of RDS,
&
'7 ---i v, n
This shows that it is not the step currents that are equal when the steps are in series, but only the ratios shown, so we get
Literature Cited 1. Boduls, J. WM.;Reddy, A. K N. Modpm E k t m c b m i s t r y ; Flenum: New York, 1911: Val. 2 , p 1004. 2. Bard, A. J.; FauUuler, R. I.E l . c t m b m i d Methods, ~ ~ m , , t t l and l s Applimtiona; Wdey New York. 1960: p 111. 3. Rieger, E H. Elecfmck~mistry;Prenti-Hall: New Jersey, 1987; Chapter 5. 4. Albery. W.J. EleefmdoKinoflcs;Clarendon: Oxford. 1915; Chapter 5. 5. Brenet, J.P;h o n , K ?)omfir Cmfi~iientsin Elecfmck.miml Kinetics; Academic:
Because Znjvi = n, we get Cii=i
896
(13)
Thus, it can be seen from eqs 12 and 13 that eq 3 will not lead to correct results in all cases where n,v, > 1.
Journal of Chemical Education
(11)
landon, 1971: p 43. 6 . Think, H.R.;Hamso", J. A. A Guide to the Study of Eledmdo Kinotlw: Academic: Iandon, 1912: p 15. I. Vetter K J.ElectmhpmimlKimfic8;Acadd~rm:London. 1965; p 151. 8. Pligogine, I. lnfmduction to ThPrmodymmi
