Question

Two moles of $N{H}_3$ gas are introduced into a previously evacuated one litre vessel in which it partially dissociates at high temperature as $2N{H}_3\left(g\right)\leftrightharpoons N_2\left(g\right)+3H_2\left(g\right)$. At equilibrium, one mole of $N{H}_3\left(g\right)$ remain. The value of $K_c$ is:

• A. $3$
• B. $\frac{27}{16}$
• C. $\frac{3}{2}$
• D. $\frac{27}{64}$

Answer 1

Answer: (B)

$\frac{27}{16}$

$\underset{2-2x}{{2N{H}_3}_{\left(g\right)}}\leftrightharpoons \underset{x}{{N_2}_{\left(g\right)}}+\underset{3x}{{3H_2}_{\left(g\right)}}$

Conc. of $N{H}_3$ at equillibrium $=2-2x$

Given that Conc. of $N{H}_3$ at equillibrium = 1

$\therefore 2-2x=1\Rightarrow x=0.5$

$\therefore$ Conc. of $H_2$ at equillibrium $=3x=3\times 0.5=1.5$

Conc. of $H_2$ at equillibrium $=x=0.5$

$\therefore$ Equillibrium constant $\left(K_c\right)=\frac{\left[N_2\right]{\left[H_2\right]}^3}{{\left[N{H}_3\right]}^2}$

$\Rightarrow K_c=\frac{0.5\times {\left(1.5\right)}^3}{{\left(1\right)}^2}=\frac{27}{16}$

Hence, option $B$ is correct.