Question

$K_1, K_2$ and $K_3$ are the equilibrium constants of the following reactions (I), (II) and (III) respectively:
(I) $N_2 + 2O_2 \rightleftharpoons 2NO_2$
(II) $2NO_2 \rightleftharpoons N_2 +2O_2$
(III) $NO_2 \rightleftharpoons \frac{1}{2}N_2 +O_2$
The correct relation from the following is

• A. $K_{1}=\frac{1}{K_{2}}=\frac{1}{K_{3}}$
• B. $K_{1}=\frac{1}{K_{2}}=\frac{1}{\left(K_{3}\right)^{2}}$
• C. $K_{1}=\sqrt{K_{2}}=K_{3}$
• D. $K_{1}=\frac{1}{K_{2}}=K_{3}$

Answer 1

Answer: (B)

(I) $N _2+2 O _2 \xrightleftharpoons{K_1} 2 NO _2$
$K_1=\frac{\left[N O_2\right]^2}{\left[N_2\right]\left[O_2\right]^2} \ldots(i)$
(II) $2 NO _2 \xrightleftharpoons{ K _2} N _2+2 O _2$
$K_2=\frac{\left[N_2\right]\left[O_2\right]^2}{\left[N O_2\right]^2} \ldots(ii)$
(III) $NO _2 \xrightleftharpoons{A_3} \frac{1}{2} N _2+ O _2$
$K_{3}=\frac{\left[N_{2}\right]^{1/2}O_{2}}{\left[NO_{2}\right]}$
$\therefore \left(K_{3}\right)^{2}=\frac{\left[N_{2}\right]\left[O_{2}\right]^{2}}{\left[NO_{2}\right]^{2}}\, ...\left(iii\right)$
$\therefore $ from equation (i), (ii) and (iii)
$K_{1}=\frac{1}{K_{2}}=\frac{1}{\left(K_{3}\right)^{2}}$