with from equation 5.7 we have: where has the usual meaning in expressions for rate constants. Equation [5.10], as presented above, explains how the activation energy associated with the first electron transfer step ( ) affects the overall reaction rate. A decrease in the activation energy required for the initial step leads to an increase in the reaction rate. As we showed in Chapter 3 , the presence of imidazolium cations acts as a promoter for the first electron transfer step. Interestingly, even for catalysts where CO desorption is rate-determining, the addition of imidazolium cations improves the overall reaction rate by increasing the equilibrium surface concentration of [*CO2 .- ]. A critical observation is that for catalysts where the first electron transfer is the rate-determining step, the overall reaction rate is determined exclusively by equation [5.1]. This underscores the pivotal role played by the imidazolium cation in determining the activity of these catalysts through the modification of the rate constant () for the electron-induced CO2 adsorption step.
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