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Le Chatelier's Principle for Del N Equals to 0

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

1 / (2 K_{1} K_{2})

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1 / (4 K_{1} K_{2})

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[1 / K_{1} K_{2}]^{1 / 2}

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1 / (K_{1} K_{2})

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Solution

The correct option is C $[1 / K_{1} K_{2}]^{1 / 2}$
The reactions $N_{2} + O_{2} ⇌ 2 N O K_{1} . . . . . . . . (i)$ and $2 N O + O_{2} ⇌ 2 N O_{2} K_{2} . . . . . . . . (i i)$ are added and reversed. The net reaction is then divided by 2 to obtain the reaction $N O_{2} ⇌ \frac{1}{2} N_{2} + O_{2}$ .
Hence, the expression for the net reaction becomes $K = \sqrt{\frac{1}{k_{1} . k_{2}}}$ .

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