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Effective Equilibrium Constant

For the react...

Question

For the reaction, $N_{2} (g) + O_{2} (g) ⇌ 2 N O (g)$ , the equilibrium constant is $K_{1}$ . The equilibrium constant is $K_{2}$ for $2 N O (g) + O_{2} (g) ⇌ 2 N O_{2} (g)$ . What is K for the reaction $N O_{2} (g) ⇌ \frac{1}{2} N_{2} (g) + O_{2} (g)$ ?

\frac{1}{(K_{1} K_{2})}

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\frac{1}{(2 K_{1} K_{2})}

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\frac{1}{(4 K_{1} K_{2})}

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{(\frac{1}{K_{1} K_{2}})}^{1 / 2}

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Solution

The correct option is D ${(\frac{1}{K_{1} K_{2}})}^{1 / 2}$
$K_{1} = \frac{[N O]^{2}}{[N_{2}] [O_{2}]} K_{2} = \frac{[N O]^{2}}{[N O] [O_{2}]} K = \frac{[N_{2}]^{1 / 2} [O_{2}]}{[N O_{2}]} H e n c e K = {[\frac{1}{K_{1} K_{2}}]}^{1 / 2}$

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