The following equilibrium given byN2+3H2⇌2NH3;K1N2+O2⇌2NO;K2H2+12O2⇌H2O;K3the equilibrium constant of the reaction 2NH3+52O2⇌2NO+3H2O in terms of K1,K2 and K3 is

2NH3⇌N2+3H2 K=1K1N2+O2⇌2NO K′=K23H2+32O2⇌3H2O K′′=K332NH3+52O2⇌2NO+3H2O∴ for the given reaction K=K′×K′×K′′′K=1K1×K2×K33=K2K33K1.

The following equilibrium given byN2+3H2⇌2NH3;K1N2+O2⇌2NO;K2H2+12O2⇌H2O;K3the equilibrium constant of the reaction 2NH3+52O2⇌2NO+3H2O in terms of K1,K2 and K3 is

2NH3⇌N2+3H2 K=1K1N2+O2⇌2NO K′=K23H2+32O2⇌3H2O K′′=K332NH3+52O2⇌2NO+3H2O∴ for the given reaction K=K′×K′×K′′′K=1K1×K2×K33=K2K33K1.

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The following equilibrium given by
$\begin{array}{l} N_{2} + 3 H_{2} ⇌ 2 {NH}_{3}; K_{1} \\ N_{2} + O_{2} ⇌ 2 NO; K_{2} \\ H_{2} + \frac{1}{2} O_{2} ⇌ H_{2} O; K_{3} \end{array}$
the equilibrium constant of the reaction
$2 {NH}_{3} + \frac{5}{2} O_{2} ⇌ 2 NO + 3 H_{2} O$ in terms of $K_{1}, K_{2}$ and $K_{3}$ is

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$\frac{K_{1} K_{3}^{2}}{K_{2}}$

$K_{1} K_{2} K_{3}$

$\frac{K_{1} K_{2}}{K_{3}}$

$\frac{K_{2} K_{3}^{3}}{K_{1}}$

answer is A.

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Detailed Solution

$\begin{array}{l} 2 {NH}_{3} ⇌ N_{2} + 3 H_{2} K = \frac{1}{K_{1}} \\ N_{2} + O_{2} ⇌ 2 NO K^{'} = K_{2} \\ \frac{3 H_{2} + \frac{3}{2} O_{2} ⇌ 3 H_{2} O K^{''} = {(K_{3})}^{3}}{2 {NH}_{3} + \frac{5}{2} O_{2} ⇌ 2 NO + 3 H_{2} O} \end{array}$

$∴$ for the given reaction

$\begin{array}{l} K = K^{'} \times K^{'} \times K^{'''} \\ K = \frac{1}{K_{1}} \times K_{2} \times {(K_{3})}^{3} = \frac{K_{2} {(K_{3})}^{3}}{K_{1}} . \end{array}$