A mixture of ${SO}_{3}, {SO}_{2} & O_{2}$ gases is maintained at equilibrium in 10 liter flask at a temperature at which Kc for the reaction, $2 {SO}_{2 (g)} + O_{2 (g)} \Leftrightarrow 2 {SO}_{3 (g)}$ is 100 ${mol}^{- 1} litre$ At equilibrium.
a) If number of mole of ${SO}_{3} & {SO}_{2}$ in flask are same, how many moles of $O_{2}$ are present
b) If number of mole of ${SO}_{3}$ in flask are twice the number of mole of ${SO}_{2},$ how many mole of $O_{2}$ are present

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0.1 and 0.4

0.8 and 0.4

0.5 and 0.7

0.1 and 4

answer is A.

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Detailed Solution

a) $K_{C} = \frac{{[{SO}_{3}]}^{2}}{[{SO}_{2}] [O_{2}]} = \frac{{(\frac{x}{10})}^{2}}{{(\frac{x}{10})}^{2} (O_{2})}$

$100 = \frac{1}{[O_{2}]}, [O_{2}] = \frac{1}{100}$

$\frac{n_{O_{2}}}{10} = \frac{1}{100}, n_{O_{2}} = 0.1$

b) $K_{C} = \frac{{[{SO}_{3}]}^{2}}{[{SO}_{2}] [O_{2}]}$

100= ${(\frac{2 x}{10})}^{2} / {(\frac{x}{10})}^{2} [O_{2}], [O_{2}]$

$= \frac{4}{100}, n_{O_{2}} = 0.4$

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