Marcus theory calculated outer-sphere rate constant

How do we obtain kis and kos from such a complicated rate expression As indicated in equations (5.13) and (5.14), we can determine kso experimentally by carrying out the reaction between [Co(ox)2(en)] and [Co(en)3]2+ under pseudo-first-order conditions with varying excess [Co(en)3]2+. A plot of kobs vs [Co(en)3]2+ will give the second-order rate constant (kso) f°r the reaction. Using equation (5.15), and given the value for the inner-sphere rate constant, kis, which has been measured independently, the outer-sphere rate constant, kos, will be determined. In Experiment 5.6, Marcus theory will be used to model this reaction and the calculated vs the observed outer-sphere rate constants will be compared. 

EXPERIMENT 5.6 MARCUS THEORY THEORETICAL CALCULATION OF THE OUTER-SPHERE RATE CONSTANT, kos, FOR THE REACTION BETWEEN [Co(ox)2(EN)] AND [Co(en)3]2+11... 

Marcus attempted to calculate the minimum energy reaction coordinate or reaction trajectory needed for electron transfer to occur. The reaction coordinate includes contributions from all of the trapping vibrations of the system including the solvent and is not simply the normal coordinate illustrated in Figure 1. In general, the reaction coordinate is a complex function of the coordinates of the series of normal modes that are involved in electron trapping. In this approach to the theory of electron transfer the rate constant for outer-sphere electron transfer is given by equation (18). 

The Marcus theory provides an appropriate formalism for calculating the rate constant of an outer-sphere redox reaction from a set of non-kinetic parameters[347 350]. The simplest possible process is a self-exchange reaction, where AG = 0. In an outer-sphere electron self-exchange reaction the electron is transferred within the precursor complex (Eq. 11.5). 

Marcus theory showed a good correlation between experimental and calculated rate constants using Eq. (5). The 22 value was set at 10 M sec for this purpose and is considered as an upper limit for selfexchange of the diethyldithiocarbamate radical/anion pair. From the oxidation rates it was also estimated that E (edtc /edtc ) = 0.43(3)V vs SCE. A free-energy analysis for the oxidation of diethyldithiocarbamate (edtc ) by [FeiCNlgT also showed that the initial outer-sphere oxidation of the thiolate anion to its thio radical (Eq. 36) is the main energy barrier to be crossed along the reaction coordinate. 

Aj may be evaluated from x-ray and infrared (IR) data or from theoretical calculations. However, for organic outer sphere electron transfers, this contribution is usually much smaller than Ao. In our opinion one of the greatest merits of the Marcus [43] and Levich-Dogonadze [44] theories is that they allow rather correct predictions of Aq through simple equations. Thus for most outer sphere electron transfers, reasonably accurate values of the rate constants can be predicted. 

In this experiment, the outer-sphere electron transfer rate constant for the reaction between [Co(en)3]2+ and [Co(ox)2(en)] will be calculated using Marcus theory. The calculated value will then be compared with the rate constant determined in Experiment 5.5. 

Marcus theory has been so successful in predicting cross reaction rates in outer-sphere electron transfer reactions that it is often used to give evidence that an outer-sphere reaction is taking place. If the observed rate constant is within an order of magnitude of the calculated rate constant, then it is likely that an outer-sphere mechanism is occurring. In this way, you will use Marcus theory to give evidence for the reaction mechanism assigned to your rate constant, kos, determined in Experiment 5.5. 

It was possible to deduce the second-order rate constants from the decay of Yb " " and Sm monitored spectrophotometrically. Variations of these rate constants with Cl concentration was also studied. Sm + is always more reactive than Yb " (as expected from the related ). It was established that the reactions take place mainly by an inner-sphere mechanism in the case of cobalt complexes and by an outer-sphere mechanism with the ruthenium complexes. The reaction with [Ru(NH3)J enabled Christensen et al. (1970) to apply the Marcus outer-sphere mechanism theory for calculating the rates of electron exchange Ln + Ln + -F e (Ln = Sm or Yb). Rates... 

---