If the equilibrium constant for the reaction $2 A B ⇋ A_{2} + B_{2}$ is $36$ , then what is the equilibrium constant for $A B ⇋ \frac{1}{2} A_{2} + \frac{1}{2} B_{2}$ ?

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Solution

The correct option is B 6
Let $K$ be the equilibrium constant for the reaction $2 A B ⇋ A_{2} + B_{2}$ .
When this reaction is multiplied by $\frac{1}{2}$ , the reaction $A B ⇋ \frac{1}{2} A_{2} + \frac{1}{2} B_{2}$ is obtained.
Let $K^{'}$ be its equilibrium constant.
But, $K^{'} = K^{\frac{1}{2}}$
Substituting values in the above expression, we get
$K^{'} = \sqrt{36} = 6$

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