Question

In hypothetical reaction, $A_2+B_2⟶2AB$, follows the mechanism as given below:
$A_2\rightleftharpoons A+A$ (fast reaction)
$A+B_2⟶AB+B$ (slow reaction)
$A+B⟶AB$ (fast reaction)
Give the rate law and order of reaction.

Answer 1

Slowest step is rate determining.
Rate $=k\left[A\right]\left[B_2\right]$ ...(i)
Here, $\left[A\right]$ should be eleminated.
$K_c=\frac{\left[A\right]\left[A\right]}{\left[A_2\right]}=\frac{{\left[A\right]}^2}{\left[A_2\right]}$
$\left[A\right]=K_c^{1/2}{\left[A_2\right]}^{1/2}$
From equation (i), Rate $=k{K}_c^{1/2}{\left[A_2\right]}^{1/2}\left[B_2\right]$
$=K{\left[A_2\right]}^{1/2}\left[B_2\right]$; $[K=k\cdot K_c^{1/2}]$
Order $=1+1/2=3/2$