Consider the two gaseous equilibrium involving ${SO}_{2}$ and the corresponding equilibrium constant at 299 K
$S O_{2} (g) + \frac{1}{2} O_{2} (g) ⇌ S O_{3} (g); K_{1}$
$4 {SO}_{3} (g) ⇌ 4 {SO}_{2} (g) + 2 O_{2} (g) K_{2}$
The value of the equilibrium constant are related by

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$K_{2} = K_{1}^{4}$

$K_{2} = \frac{1}{{(K_{1})}^{4}}$

$K_{2} = {(\frac{1}{K_{1}})}^{\frac{1}{4}}$

$K_{2} = \frac{1}{K_{1}}$

answer is A.

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Detailed Solution

$S O_{2} (g) + \frac{1}{2} O_{2} (g) ⇌ S O_{3} (g); K_{1}$

$4 {SO}_{3} (g) ⇌ 4 {SO}_{2} (g) + 2 O_{2} (g) K_{2}$

$K_{1} = \frac{[{SO}_{3}]}{[{SO}_{2}] {[O_{2}]}^{1 / 2}} \dots . (1)$

$K_{2} = \frac{{[{SO}_{2}]}^{4} {[O_{2}]}^{2}}{{[{SO}_{2}]}^{4}} . . . . . (2)$

$from 1 & 2 K_{2} = \frac{1}{{(K_{1})}^{4}}$

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