The decarboxylation of 3-keto-dicarboxylic acids

Here the situation becomes one stage more complex. The acid can form both the anion and dianion and all three species can decarboxylate, e.g., for 2-oxobutanedioic acid (oxaloacetic acid) 

Each of the fractions will be pH dependent. At very low pH values, the fraction [A2 ]actual/[H2A]total will be small and, unless k3 is sufficiently large, this term can be ignored. kobs then reduces to a two-term expression from which k and k2 can be found as given for the /3-keto-monocarboxylic acids. The value of k3 can then be found from experiments at higher pH values where the fraction [A2 ]actual/[H2A]total makes a significant contribution. 

This illustrates the complexities introduced into the kinetic analysis when reactant species are involved in equilibria, as well as in reaction. Most of the difficulties lie in the handling of the equilibria calculations, rather than in the kinetics. 

All reactions of this type must be studied at constant ionic strength because of the considerable non-ideality of the solutions, and the equilibrium calculations should be given in terms of activities rather than concentrations. 

Question. The decarboxylation of 2-oxobutanedioic acid, p. 341 (oxaloacetic acid), H2A, at constant pH has three contributing steps  

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