# The equilibrium constants of the following are N2 + 3H2 ⇌ 2NH3; K1, N2 + O2 ⇌ 2NO; K2, H2 + 12O2 ⇌ H2O; K3

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The equilibrium constants of the following are

$N_2 + 3H_2 \rightleftharpoons 2NH_3\ ;\quad K_1$

$N_2 + O_2 \rightleftharpoons 2NO\ ;\quad\quad K_2$

$H_2 +{1\over2}O_2 \rightleftharpoons H_2O\ ;\quad\ \ K_3$

The equilibrium constant (K) of the reaction :

$2NH_3+{5\over2}O_2\rightleftharpoons 2NO+3H_2O$ will be

(a) $K_2K_3^3/K_1$

(b) $K_2K_3/K_1$

(c) $K_2^3K_3/K_1$

(d) $K_1K_3^3/K_2$
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Direct solve and answer type question

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Ans. (a) $K_2K_3^3/K_1$

Sol: From the given equations,

$2NH_3\rightleftharpoons N_2 + 3H_2;\quad {1\over K_1}$

$N_2 + O_2 \rightleftharpoons2NO;\quad\quad K_2$

$3H_2 +{3\over2}O_2 \rightleftharpoons3H_2O;\ \ K_3^3$

By adding equations (i), (ii) and (iii), we get

$2NH_3+{5\over2}O_2\rightleftharpoons 2NO+3H_2O;\ K={K_2K_3^3\over K_1}$

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