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Effective Equilibrium Constant

At a certain ...

Question

At a certain temperature, the equilibrium $K_{c}$ is $16$ for the following reaction.
$S O_{2} (g) + N O_{2} (g) ⇌ S O_{3} (g) + N O (g)$
If $1.0 mol$ of all the four gases is taken in a one litre container the concentration of $N O_{2} (i n {mol L}^{- 1})$ at equilibrium would be:

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Solution

$\begin{matrix} S O_{2} (g) + & N O_{2} (g) ⇌ & S O_{3} (g) + & N O (g) Initial concentration & 1 & 1 & 1 & 1 Equilibrium & 1 - x & 1 - x & 1 + x & 1 + x \end{matrix}$
$K_{c} = \frac{[S O_{3}] [N O]}{[S O_{2}] [N O_{2}]} = \frac{(1 + x)^{2}}{(1 - x)^{2}} = 16 \Rightarrow \frac{1 + x}{1 - x} = 4 \Rightarrow x = 0.6$
$[N O_{2}] = 1 - x = 1 - 0.6 = 0.4 {mol L}^{- 1}$

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