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Methods for Ester Synthesis

For the follo...

Question

For the following reactions, equilibrium constants are given:
$S (s) + O_{2} (g) ⇌ S O_{2} (g); K_{1} = 10^{52}$

$2 S (s) + 3 O_{2} (g) ⇌ 2 S O_{3} (g); K_{2} = 10^{129}$
Find the equilibrium constant for reaction
$2 S O_{2} + O_{2} (g) ⇌ 2 S O_{3} (g)$

10^{181}

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10^{25}

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10^{77}

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10^{154}

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Solution

The correct option is B $10^{25}$
$S (s) + O_{2} (g) ⇌ S O_{2} (g); K_{1} = 10^{52} . . . . . . . . . . . . (1)$

$2 S (s) + 3 O_{2} (g) ⇌ 2 S O_{3} (g); K_{2} = 10^{129} . . . . . . . . . . . . (2)$

$2 S O_{2} + O_{2} (g) ⇌ 2 S O_{3} (g); K_{3} = x$

Multiplying equation (1) by 2;

$2 S (s) + 2 O_{2} (g) ⇌ 2 S O_{2} (g); {K^{'}}_{1} = K_{1}^{2} == 10^{104} . . . . . . . (3)$

$\Rightarrow$ Substracting (3) from (2); we get

$2 S O_{2} (g) + O_{2} (g) ⇌ 2 S O_{3} (g) K_{e q} = \frac{K_{2}}{{K^{'}}_{1}} = 10^{(129 - 104)} = 10^{25}$

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$S (s) + O_{2} (g) ⇌ S O_{2} (g); K_{1} = 10^{52}$

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