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If the equilibrium constant for $N_{2 (g)} + O_{2 (g)} ⇌ 2 {NO}_{(g)}$ is K, then equilibrium const for $\frac{1}{2} N_{2 (g)} + \frac{1}{2} O_{2 (g)} ⇌ {NO}_{(g)}$ will be

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$\sqrt{K}$

$\frac{1}{2} K$

K²

answer is A.

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Detailed Solution

$N_{2 (g)} + O_{2 (g)} ⇌ 2 {NO}_{(g)}; K = \frac{[NO]^{2}}{[N_{2}] [O_{2}]}$
$\frac{1}{2} N_{2 (g)} + \frac{1}{2} O_{2 (g)} ⇌ {NO}_{(g)}; K^{1} = \frac{[NO]}{{[N_{2}]}^{1 / 2} {[O_{2}]}^{1 / 2}}$
$∴ K = {(K^{1})}^{1 / 2}$ or $\sqrt{K}$

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