Question

Derive an expression for the Rate (k) of reaction :
$2N_2{O}_5\left(g\right)\to 4N{O}_2\left(g\right)+O_2\left(g\right)$

With the help of following mechanism:

$N_2{O}_5\stackrel{K_a}{\to }N{O}_2+N{O}_3$
$N{O}_3+N{O}_2\stackrel{K_{-a}}{\to }{N}_2{O}_5$
$N{O}_2+N{O}_3\stackrel{K_b}{\to }N{O}_2+O_2+NO$
$NO+N{O}_3\stackrel{K_c}{\to }2N{O}_2$

• A. $Rate=\frac{k_a\times k_b}{k_{-a}+2k_b}\left[N_2{O}_5\right]$
• B. $Rate=\frac{k_a\times k_b}{k_{-a}-2k_b}\left[N_2{O}_5\right]$
• C. $Rate=\frac{k_a\times k_b}{k_{-a}+k_b}\left[N_2{O}_5\right]$
• D. $Rate=\frac{k_a\times k_b}{2k_{-a}-2k_b}\left[N_2{O}_5\right]$

Answer 1

Answer: (A)

$Rate=\frac{k_a\times k_b}{k_{-a}+2k_b}\left[N_2{O}_5\right]$

Rate $=k_b\left[N{O}_2\right]\left[N{O}_3\right]$ .....(1)

But $\frac{\left[N{O}_2\right]\left[N{O}_3\right]}{\left[N_2{O}_5\right]}=\frac{K_a}{K_{-a}+2k_b}$

Hence $\left[N{O}_2\right]\left[N{O}_3\right]=\frac{K_a}{K_{-a}+2k_b}\left[N_2{O}_5\right]$......(2)

Substitute equation (2) in equation (1):

$Rate=\frac{k_a\times k_b}{k_{-a}+2k_b}\left[N_2{O}_5\right]$