Question

Equilibrium constants $K_1$ and $K_2$ for the following equilibria

• A. $K_2=\frac{1}{K_1}$
• B. $K_2=K_1^2$
• C. $K_2=\frac{K_1}{2}$
• D. $K_2=\frac{1}{K_1^2}$

Answer 1

Answer: (D)

(i) $NO(g)+\frac{1}{2}{O}_2(g)\stackrel{K_1}{\rightleftharpoons }N{O}_2(g)$
So $K_1=\frac{\left[N{O}_2\right]}{[NO]{\left[O_2\right]}^{\frac{1}{2}}}...(i)$
(ii) $2N{O}_2(g)\stackrel{R_2}{\rightleftharpoons }2NO+O_2(g)$
So $K_3=\frac{[NO{]}^2\left[O_2\right]}{{\left[N{O}_2\right]}^2}...(ii)$
From Eq. (i)
$K_1^2=\frac{{\left[N{O}_2\right]}^2}{[NO{]}^2\left[O_2\right]}$
or $\frac{1}{K_1^2}=\frac{[NO{]}^2\left[O_2\right]}{{\left[N{O}_2\right]}^2}...(iii)$
From Eqs. (ii) and (iii)
$K_2=\frac{1}{K_1^2}$