The uncatalyzed decomposition of compound S to product P occurs via a first-order…

CHEMISTRY · Single correct · A Level · Chemistry · Introduction to organic chemistry · Introduction to organic chemistry

Problem

The uncatalyzed decomposition of compound S to product P occurs via a first-order elementary step with rate constant

k_{\text{u}}

. In the presence of catalyst Q, the reaction also follows the mechanism below. (1) Q + S

\rightleftharpoons

QS (fast equilibrium, equilibrium constant

K

) (2) QS

\rightarrow

Q + P (slow, rate constant

k_{\text{cat}}

) Both the uncatalyzed and catalyzed pathways operate simultaneously, and

[\text{Q}]

remains constant during the reaction. Which expression best represents the overall rate of formation of P? (a)

k_{\text{cat}}K[\text{Q}][\text{S}]

(b)

k_{\text{u}}[\text{S}] + k_{\text{cat}}K[\text{Q}][\text{S}]

(c)

k_{\text{u}}[\text{S}] + k_{\text{cat}}[\text{Q}]

(d)

k_{\text{u}}[\text{S}] + k_{\text{cat}}K[\text{S}]^{2}