The oxidation of compound S by molecular oxygen in the gas phase proceeds by the following sequence at high temperature:
Step 1 S + O_2 ⇌ U (fast)
Step 2 U + O_2 ⇌ V (fast)
Step 3 U ⇌ W (fast)
Step 4 W → Products (slow)
Both V and W can, in principle, lead to products via additional rapid pathways that are negligible under the experimental conditions described here. The overall stoichiometry determined experimentally is S + 2 O_2 → oxidized products.
(a) Express [U], [V], and [W] individually in terms of [S] and [O_2] using stepwise equilibrium constants.
(b) Derive a rate law for product formation that involves only [S], [O_2], and kinetic/equilibrium constants. Clearly indicate any assumptions you must introduce to simplify the expression.
(c) Show algebraically how the presence of the competing fast pathway through V modifies—or does not modify—the overall reaction order with respect to O_2 under conditions where [O_2] is large compared with [S].
(d) Design an experiment, specifying the measurable quantities and the range of conditions, that could discriminate between the mechanistic roles of intermediates V and W in controlling the observed kinetics.