For the complex reaction A + B -> P, the following reaction mechanism is proposed (assume each elementary reaction is first order with respect to each reactants): 2A ↔ A2 (fast to equilibrium, equilibrium constant K1)
A + B ↔ C (fast to equilibrium, equilibrium constant K2)
A2 + C -> P + 2A (slow, rate constant k3)
a. Based on the mechanism, derive an expression for the rate of the reaction as a function of the concentrations of only reactants and stable product, and provided equilibrium and rate constants.
b. In a particular experiment, equal concentrations of A and B were mixed, and both the initial rate v0 and the half-life, t1/2 were determined. Based on your answer to part a., predict for a subsequent experiment:
(i) The effect on v0 if the initial concentrations of both A and B are doubled.
(ii) The effect on t1/2 if the initial concentrations of both A and B are doubled.
(iii) The effect on v0 if the initial concentration of A is unchanged and the initial concentration of B is increased tenfold.