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Q. The decomposition of $N_{2}O_{4}$ to $NO_{2}$ is carried out at $280$ K in chloroform. When equilibrium has been established, $0.2\, mol$ of $N_{2}O_{4}$ and $2 \times 10^{-3}\, mol$ of $NO_{2}$ are present in $2\, litre$ solution. The equilibrium constant for reaction $N_{2}O_{4} \rightleftharpoons 2NO_{2}$ is

Equilibrium

Solution:

$K=\frac{\left[NO_{2}\right]^{2}}{\left[N_{2}O_{4}\right]}=\frac{\left[2\times\frac{10^{-3}}{2}\right]^{^2}}{\left[\frac{2}{2}\right]}=\frac{10^{-6}}{10^{-1}}=10^{-5}$