Question

The reaction mechanism for the reaction $P\to R$ is as follows: $P\stackrel{k_1}{\rightleftharpoons }Q$ (fast) and $Q+P\stackrel{k_2}{\to }R$ (slow).
The rate law for the main reaction $(P\to R)$ is:

• A. $k_1\left[P\right]\left[Q\right]$
• B. $k_1{k}_2\left[P\right]$
• C. $k_1{k}_2[P{]}^2$
• D. $k_1{k}_2\left[Q\right]$

Answer 1

Answer: (C)

$k_1{k}_2[P{]}^2$

The second step is the slow step. It is the rate-determining step.

$r=k_2\left[P\right]\left[Q\right]$......(1)

The first step is the equilibrium reaction. It is a fast step.

$k_1=\frac{\left[Q\right]}{\left[P\right]}$

$\left[Q\right]=k_1\left[P\right]$.....(2)

Substitute equation (2) in equation (1).

$r=k_1{k}_2[P{]}^2$

Option C is correct.