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Characteristics of Equilibrium Constant

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

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K^{2}

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K^{\frac{1}{2}}

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\frac{1}{2} K

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Solution

The correct option is C $K^{\frac{1}{2}}$
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 $K^{\frac{1}{2}}$

$K = \frac{[N O]^{2}}{[N_{2}] [O_{2}]}$

$K^{'} = \frac{[N O]}{\sqrt{[N_{2}] [O_{2}]}} = \sqrt{\frac{[N O]^{2}}{[N_{2}] [O_{2}]}} = K^{\frac{1}{2}}$

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