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Characteristics of Chemical Equilibrium

Homogeneous e...

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Homogeneous equilibrium : $K_{c}$ is gaseous system
A mixture of $S O_{3}, S O_{2}$ and $O_{2}$ gases is maintained at equilibrium in $10$ litre flask at a temperature at which $K_{c}$ for the reaction, $2 S O_{2} (g) + O_{2} (g) ⇌ 2 S O_{2} (g)$ is $100 m o l^{- 1}$ litre. At equilibrium.
(a) If no. of mole of $S O_{3}$ and $S O_{2}$ in flask are same, how many mole of $O_{2}$ are present?
(b) If no. of mole of $S O_{3}$ in flask are twice the no. of mole of $S O_{2}$ , how many mole of $O_{2}$ are present?

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Solution

$2 S O_{2} + O_{2} ⇌ 2 S O_{3}$
(1) $k_{c} = \frac{[S O_{3}]^{2}}{[S O_{2}]^{2} [O_{2}]}$
$[S O_{3}] = n / 10$
$[S O_{2}] = n / 10$
$[O_{2}] = m / 10$
$100 = \frac{[n / 10]^{2}}{{[\frac{n}{10}]}^{2} [\frac{m}{10}]}$
$100 = \frac{10}{m}$
$m = 0.1$
(2) $k_{c} = 100$
$[S O_{3}] = 2 m / 10$
$[S O_{2}] = n / 10$
$[O_{2}] = m / 10$
$100 = \frac{40}{m}$
$m = 0.4$

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