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Effect on Kc

If the equili...

Question

If the equilibrium constant for $N_{2} (g) + O_{2} (g) ⇌ 2 N O (g)$ is $K$ , the equilibrium constant for $\frac{1}{2} N_{2} (g) + \frac{1}{2} O_{2} (g) ⇌ N O (g)$ will be:

K^{1 / 2}

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\frac{1}{2} K

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K

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K^{2}

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Solution

The correct option is A $K^{1 / 2}$
$N_{2} (g) + O_{2} (g) ⇌ 2 N O (g)$
$K = \frac{[N O]^{2}}{[N_{2}] [O_{2}]} . . . . . . (1)$
$\frac{1}{2} N_{2} (g) + \frac{1}{2} O_{2} (g) ⇌ N O (g)$
$K^{'} = \frac{N O}{[N_{2}]^{1 / 2} [O_{2}]^{1 / 2}} . . . . . (2)$
Compairing equation $(1) a n d (2)$ , we get
$∴ K^{'} = \sqrt{K}$

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