Relating quantum yields to rate constants

In ground-state chemistry, the measurement of reaction kinetics often provides the rate constant of the process studied directly, because a single reaction dominates. Photoreactions, on the other hand, always compete with photophysical processes, as outlined in Section 2.1.1. In Section 3.7.4, we showed that the efficiency of a specified single-step, first-order process x starting from a reactant or excited state A is equal to the partition ratio rjx, the rate constant kx of the process considered divided by the sum of the rate constants of all processes competing for the depletion the reactant A, r x = kx/Zk, (Equation 3.7). The combined efficiencies of all pathways starting from a given reactant 

The formation of product C, on the other hand, proceeds in two steps with the efficiencies 1 r/isc. (Equation 3.32) and 3rjc 3/cr/(3/cr I 3/qsc I 3/cph + 3kqcq) where 3kr refers to the reaction from the lowest triplet state Ti leading to the photoproduct C, 3/cph is the rate constant of phosphorescence, 3/cisc that of intersystem crossing to the ground state and 3/cq is the second-order rate constant for quenching of I) by a quencher q. The overall quantum yield for the formation of product C is equal to the product of the efficiencies of the two reaction steps, (I visc Vc- Many authors do not distinguish between 

Let us generalize the quantum yield of a multi-step process x is equal to the product of the efficiencies of all steps required to complete that process. This allows us to determine rate constants by measuring quantum yields and lifetimes. Kinetic measurements such as time-resolved fluorescence or kinetic flash photolysis yield observed rate laws for the decay of excited states or of reactive intermediates. When the decay of an intermediate x obeys first-order kinetics, as is frequently the case, then the observed lifetime t = l/kobs is equal to the inverse of the sum of the rate constants of all processes contributing to the decay of the species observed.1 

Equation 3.33 also holds for the efficiency of the reaction forming product C from the triplet state, 3rjc =3k3T. However, the rate constant ikr cannot be determined directly from the quantum yield of that process, c = 1 p[sc3 tjc and the triplet lifetime, 3r, because the efficiency of the first step, 1 t) SC, is involved (Equation 3.34). 

As we shall see in the next section, Stem Volmer analysis of triplet sensitization or quenching experiments can lead to a determination of ISC efficiencies. 

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