PYQ NEET- Chemical Equilibrium-1 L-5

Question: The equilibrium constants of the following are#

$$ \begin{aligned} & \mathrm{N}_2+3 \mathrm{H}_2 \rightleftharpoons 2 \mathrm{NH}_3 ; \quad \mathrm{K}_1 \ & \mathrm{~N}_2+\mathrm{O}_2 \rightleftharpoons 2 \mathrm{NO} ; \quad \mathrm{K}_2 \ & \mathrm{H}_2+\frac{1}{2} \mathrm{O}_2 \rightleftharpoons \mathrm{H}_2 \mathrm{O} ; \quad \mathrm{K}_3 \end{aligned} $$

The equilibrium constant $(\mathrm{K})$ of the reaction : $2 \mathrm{NH}_3+\frac{5}{2} \mathrm{O}_2 \rightleftharpoons 2 \mathrm{NO}+3 \mathrm{H}_2 \mathrm{O}$ will be

A) $\mathrm{K}_2 \mathrm{~K}_3{ }^3 / \mathrm{K}_1$

B) $\mathrm{K}_2 \mathrm{~K}_3 / \mathrm{K}_1$

C) $\mathrm{K}_2{ }^3 \mathrm{~K}_3 / \mathrm{K}_1$

D) $\mathrm{K}_1 \mathrm{~K}_3{ }^3 / \mathrm{K}_2$

Answer: $\mathrm{K}_2 \mathrm{~K}_3{ }^3 / \mathrm{K}_1$#

Solution:#

$$ \begin{aligned} & 2 \mathrm{NH}_3 \rightleftharpoons \mathrm{N}_2+3 \mathrm{H}_2 ; \quad \frac{1}{K_1} \ & \mathrm{~N}_2+\mathrm{O}_2 \rightleftharpoons 2 \mathrm{NO} ; \quad \mathrm{K}_2 \ & 3 \mathrm{H}_2+\frac{3}{2} \mathrm{O}_2 \rightleftharpoons 3 \mathrm{H}_2 \mathrm{O} ; \quad\left(\mathrm{K}_3\right)^3 \end{aligned} $$

By adding all equations, we get $$ \begin{aligned} & 2 \mathrm{NH}_3+\frac{5}{2} \mathrm{O}_2 \rightleftharpoons 2 \mathrm{NO}+3 \mathrm{H}_2 \mathrm{O} \ & \therefore \mathrm{K}=\frac{K_2 \times\left(K_3\right)^3}{K_1} \end{aligned} $$