Question

A hypothetical reaction, $A_2+B_2\to AB$ follows the mechanism as given below;
$A_2\rightleftharpoons A+A$ .....(Fast)
$A+B_2\to AB+B$ .....(Slow)
$A+B\to AB$ ....(Fast)
The order of the overall reaction is

• A. 2
• B. 1
• C. $1+\frac{1}{2}$
• D. zero

Answer 1

The correct option is C $1+\frac{1}{2}$

We know that the slowest elementary reaction determines the rate law-
The rate law equation is-
$r=K\left[A\right]\left[B_2\right]$

and from the eqm. reaction $A_2\rightleftharpoons A+A.....\left(Fast\right)$
$K_c=\frac{\left[A\right]\left[A\right]}{\left[A_2\right]}$ or $\left[A\right]=K_c^{1/2}[A_2{]}^{1/2}$

Thus, $r=K\cdot K_c^{1/2}\left[A_2{]}^{1/2}\right[B_2]=K^{\prime }[A_2{]}^{1/2}\left[B_2\right]$

or order is $3/2$.