If the equilibrium constant for the reaction $2 A B ⇌ A_{2} + B_{2}$ is $49$ , what is the equilibrium constant for $A B ⇌ \frac{1}{2} A_{2} + \frac{1}{2} B_{2}$ ?

7

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\frac{1}{7}

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24.5

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49

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Solution

The correct option is A $7$
$2 A B ⇌ A_{2} + B_{2}$ $K_{c} = 49$

The equilibrium constant for the reaction,

$A B ⇌ \frac{1}{2} A_{2} + \frac{1}{2} B_{2}$

$K = \sqrt{K_{c}}$

$= \sqrt{49} = 7$

Hence, option C is correct.

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