Question
Equilibrium constant, $K_c$ for the reaction
$\text{N}_2\text{ (g) + 3H}_2\text{ (g)}\rightleftharpoons2\text{NH}_3\text{ (g) at 500k is 0.061}$
At a particular time, the analysis shows that composition of the reaction mixture is $3.0 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~N}_2, 2.0 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{H}_2$ and $0.5 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{NH}_3$. Is the reaction at equilibrium? If not in which direction does the reaction tend to proceed to reach equilibrium?

Answer

The given reaction is:$\text{N}_2\text{ (g) + 3H}_2\text{ (g)}\rightleftharpoons2\text{NH}_3\text{ (g)}$
According to available data.
$\text{N}_2=[3.0];\text{H}_2=[2.0];\text{NH}_3=[0.50]$
$\text{Q}_{\text{c}}=\frac{[\text{NH}_3\text{(g)]}^2}{[\text{N}_2\text{(g)][H}_2\text{(g)}]^3}=\frac{[0.50]^2}{[3.0][2.0]^3}=\frac{0.25}{24}=0.0104.$
Since the value of $Q_c$ is less than that of $k_c(0.061)$, the reaction is not is a state of equilibrium. It will proceed in the forward direction till $Q_c$ becomes the same as $k_c$.

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