Oxidation of phenols by Cr VI

The rate of product formation according to this mechanistic proposal is 

Assuming that equilibrium formation of the chromate ester is fast, this rate expression maybe rewritten as Equation 4.22  

AtpH 5, deprotonation ofphenolic groups can be neglected, so [ArOH] ss [ArOHJx, and the following mass balance holds for Cr( VI)  

Because Ke is very small and the formation of chromate dianion is minimal in the working pH range, this may be approximated to give 

Accordingly, an overall second-order rate law is expected at constant pH (first order in phenol and in Cr(VT)), and there will be a complex dependence on acidity varying between kinetic order 0 and 2. In addition, the k2 (two-electron transfer) pathway should be the main route at higher acidities, with predominance of the products derived from the phenoxy cation, X2. 

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Scheme 4.10 Proposed one-electron and two-electron transfer pathways for the oxidation of phenols by Cr(VI) [20],...

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