Question

A reaction: $A_2+B\to$ Products, involves the following mechanism:

$A_2\rightleftharpoons 2A$ (fast)
($A$ being the intermediate)

$A+B\underset{k_2}{\overset{}{\to }}$ Products (slow).

The rate law consistent to this mechanism is:

• A. Rate $=k\left[A_2\right]\left[B\right]$
• B. Rate $=k{\left[A_2\right]}^2\left[B\right]$
• C. Rate $=k{\left[A_2\right]}^{1/2}\left[B\right]$
• D. Rate $=k\left[A_2\right]{\left[B\right]}^2$

Answer 1

The correct option is C Rate $=k{\left[A_2\right]}^{1/2}\left[B\right]$

From the slow step:
Rate = $k_2\left[A\right]\left[B\right]....\left(i\right)$

From the fast step:
$K_e=\frac{{\left[A\right]}^2}{\left[A_2\right]}$

$\left[K_e\right]=K_e^{1/2}{\left[A_2\right]}^{1/2}......\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$, we get:

Rate$=k_2{k}_e^{1/2}{\left[A_2\right]}^{1/2}\left[B\right]$

$=k{\left[A_2\right]}^{1/2}\left[B\right]$