The equilibrium constant for the reaction $2 A + 2 B ⇌ 2 C + 2 D$ is 200. The equilibrium constant for the reaction $A + B ⇌ C + D$ , at the same temperature is :

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100

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200

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None of these

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Solution

The correct option is C None of these
As we know,
$2 A + 2 B ⇌ 2 C + 2 D$
$K_{C} = C^{2} D^{2} / A^{2} B^{2}$
and for reaction
$A + B ⇌ C + D$
$K_{C}^{'} = C D / A B$
so,
$K_{C}^{'} = \sqrt{K_{C}} = \sqrt{200}$

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