Consider the following equations for a cell reaction, then:
$A + B ⇌ C + D$ , $E^{o} = x$ volt, $K_{e q} = K_{1}$
$2 A + 2 B ⇌ 2 C + 2 D, E^{o} = y$ volt, $K_{e q} = K_{2}$

x = y, K_{1} = K_{2}

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x = 2 y, K_{1} = 2 K_{2}

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x = y, K_{1}^{2} = K_{2}

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x^{2} = y, K_{1}^{2} = K_{2}

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Solution

The correct option is B $x = y, K_{1}^{2} = K_{2}$
The given reaction are :-
$A + B ⇌ C + D; E^{0} = x v$
$K_{e q} = K_{1} = \frac{[C] [D]}{[A] [B]} \to (I)$
$2 A + 2 B ⇌ 2 C + 2 D; E^{0} = y v$
$\Rightarrow K_{e q} = K_{2} = \frac{{[C]}^{2} {[D]}^{2}}{{[A]}^{2} {[B]}^{2}}$
$K_{2} = {K_{1}}^{2}$
Now, EMF of the cell having a particular reaction does not change on multiplying or dividing the balanced chemical reaction with a constant.
So, $x = y$ , ${K_{1}}^{2} = K_{2}$ .

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