Question

For the reaction $2\mathrm{NO}+{\mathrm{Br}}_2\to 2\mathrm{NOBr}$the following mechanism has been given:
$\mathrm{NO}+{\mathrm{Br}}_2\rightleftharpoons {\mathrm{NOBr}}_2$
${\mathrm{NOBr}}_2+\mathrm{NO}\to 2\mathrm{NOBr}\left(\mathrm{slow}\right)$
Hence, the rate law is :

• A. $k\left[NO{]}^2\right[B{r}_2]$
• B. $k\left[NO\right]\left[B{r}_2\right]$
• C. $k\left[NOB{r}_2\right]\left[NO\right]$
• D. $k\left[NO\right][B{r}_2{]}^2$

Answer 1

The correct option is A $k\left[NO{]}^2\right[B{r}_2]$

$\mathrm{The}\mathrm{mechanism}\mathrm{is}\mathrm{given}\mathrm{as}\mathrm{NO}+{\mathrm{Br}}_2\stackrel{K_C}{\rightleftharpoons }{\mathrm{NOBr}}_2{\mathrm{NOBr}}_2+\mathrm{NO}\stackrel{\mathrm{slow}}{\to }2\mathrm{NOBr}\mathrm{So},\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{the}\mathrm{reaction}\mathrm{is},\frac{\mathrm{dx}}{\mathrm{dt}}=k\left[{\mathrm{NOBr}}_2\right]\left[\mathrm{NO}\right].......\left(1\right)K_c=\frac{\left[{\mathrm{NOBr}}_2\right]}{\left[\mathrm{NO}\right]\left[{\mathrm{Br}}_2\right]}......\left(2\right)\Rightarrow \left[{\mathrm{NOBr}}_2\right]=K_c\left[\mathrm{NO}\right]\left[{\mathrm{Br}}_2\right]\mathrm{putting}\mathrm{this}\mathrm{value}\mathrm{of}\left[{\mathrm{NOBr}}_2\right]\mathrm{in}\mathrm{equation}\left(1\right),\mathrm{we}\mathrm{get}\frac{\mathrm{dx}}{\mathrm{dt}}={\mathrm{kK}}_c\left[{\mathrm{NO}]}^2\right[{\mathrm{Br}}_2]=k^{\prime }[{\mathrm{NO}]}^2\left[{\mathrm{Br}}_2\right]$