Question

The following equilibria are given :
$N _{2}+3 H _{2} \rightleftharpoons 2 NH _{3}\, K _{1}$
$N2 + O2 \rightleftharpoons 2NO\, K_2$
$H_2 + \frac{1}{2} O_2 \rightleftharpoons H_2 O \, K_3$
The equilibrium constant of the reaction
$2NH_3 + \frac{5}{2} O_2 \rightleftharpoons 2NO + 3H_2 O$ in terms of $K_1,\, K_2$ and $K_3$ is

• A. $K_1 K_1 K_3$
• B. $\frac{K_1 K_2}{K_3}$
• C. $\frac{K_1 K_3^2}{K_2}$
• D. $\frac{K_2 K_3^3}{K_1}$

Answer 1

Answer: (D)

For equilibrium ${{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)$,${{K}_{1}}=\frac{{{[N{{H}_{3}}]}^{2}}}{[{{N}_{2}}]{{[{{H}_{2}}]}^{3}}}$ ..... (i)

${{N}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2NO(g),$${{K}_{2}}=\frac{{{[NO]}^{2}}}{[{{N}_{2}}]\,[{{O}_{2}}]}$ $.....(ii)

$

${{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\rightleftharpoons {{H}_{2}}O(g),$${{K}_{3}}=\frac{[{{H}_{2}}O]}{[{{H}_{2}}]\,{{[{{O}_{2}}]}^{1/2}}}.....(iii)

$ For reaction,

$2N{{H}_{3}}(g)+\frac{5}{2}{{O}_{2}}(g)\rightleftharpoons 2NO(g)+3{{H}_{2}}O(g)$

$K=\frac{{{[NO]}^{2}}\times {{[{{H}_{2}}O]}^{3}}}{{{[N{{H}_{3}}]}^{2}}\,{{[{{O}_{2}}]}^{5/2}}}....(iv)

$

From equations number (i), (ii) and (iii)

$K=\frac{{{K}_{2}}\times {{K}_{3}}^{3}}{{{K}_{1}}}$