Question

$N_2{O}_2\rightleftharpoons 2NO,K_1;\left(\frac{1}{2}\right)N_2+\left(\frac{1}{2}\right)O_2\rightleftharpoons NO,K_2$;
$2NO\rightleftharpoons N_2+O_2,K_3;NO\rightleftharpoons \left(\frac{1}{2}\right)N_2+\left(\frac{1}{2}\right)O_2,K_4$;
Correct relation (s) between $K_1,K_2,K_3$ and $K_4$ is/are:

• A. $K_1\times K_3=1$
• B. ${\sqrt{K}}_1\times K_4=1$
• C. ${\sqrt{K}}_3\times K_2=1$
• D. $K_1=\frac{1}{{\sqrt{K}}_3}$

Answer 1

Answer: (C), (D)

The correct options are
C ${\sqrt{K}}_3\times K_2=1$
D $K_1=\frac{1}{{\sqrt{K}}_3}$

$K_1\times K_3=\frac{[NO{]}^2}{\left[N_2{O}_2\right]}\times \left(\frac{\left[N_2\right]\left[O_2\right]}{[NO{]}^2}\right)=\left(\frac{\left[N_2\right]\left[O_2\right]}{\left[N_2{O}_2\right]}\right)\ne 1$
${\sqrt{K}}_1\times K_4=\sqrt{\frac{[NO{]}^2}{\left[N_2{O}_2\right]}}\times \frac{\sqrt{\left[N_2\right]\left[O_2\right]}}{\left[NO\right]}\ne 1$
$\sqrt{K_3}\times K_2=\sqrt{\left(\frac{\left[N_2\right]\left[O_2\right]}{[NO{]}^2}\right)}\times \left(\frac{\left[NO\right]}{\left[N_2{]}^{\frac{1}{2}}\right[O_2{]}^{\frac{1}{2}}}\right)=1$
$K_3=\frac{\left[N_2\right]\left[O_2\right]}{[NO{]}^2}$ $K_1=\frac{[NO{]}^2}{\left[N_2{O}_2\right]}=\frac{1}{{\sqrt{K}}_3}$Hence, $K_1=\frac{1}{{\sqrt{K}}_3}$