Consider the thermal decomposition of peroxide P in solution, for which two competing product pathways have been proposed. The mechanism is outlined below (rate constants shown beside each elementary step).
Step 1 (slow) P → I k1
Step 2a (fast) I + Q → R k2a
Step 2b (fast) I + S → T k2b
P is the only reactant initially present. Species Q and S are added to the reaction mixture in known initial concentrations and remain in large excess. R and T are distinct final products.
Answer the following.
(a) Write an expression for the rate of formation of R and an expression for the rate of formation of T, each in terms of the appropriate rate constants and the measurable concentrations of P, Q, and S.
(b) Derive an expression for the instantaneous ratio rate of formation of Trate of formation of R. Simplify your result as much as possible.
(c) Explain how varying the initial concentration of Q while holding the concentration of S constant would influence the product distribution. Support your answer with reference to the expression derived in part (b).