Question

For the reaction : $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
equilibrium constant, $K_{c}=\frac{\left[\mathrm{NH}_{3}\right]^{2}}{\left[\mathrm{~N}_{2}\right]\left[\mathrm{H}_{2}\right]^{3}}$
Some reactions are written below in Column I and their equilibrium constants in terms of $K_{c}$ are written in Column II. Match the following reactions with the corresponding equilibrium constant.

Column I (Reaction)		Column II (Equilibrium constant)
i	$2 \mathrm{~N}_{2(g)}+6 \mathrm{H}_{2(g)} \rightleftharpoons 4 \mathrm{NH}_{3(g)}$	(a)	$2 K_{c}$
ii	$2 \mathrm{NH}_{3(g)} \rightleftharpoons \mathrm{N}_{2(g)}+3 \mathrm{H}_{2(g)}$	(b)	$K_{c}^{1 / 2}$
iii	$\frac{1}{2} \mathrm{~N}_{2(g)}+\frac{3}{2} \mathrm{H}_{2(g)} \rightleftharpoons \mathrm{NH}_{3(g)}$	(c)	$\frac{1}{K_{c}}$
		(d)	$K_{c}^{2}$

• A. $(i) \to (b), (ii) \to (a), (iii) \to (c)$
• B. $(i) \to (c), (ii) \to (d), (iii) \to (a)$
• C. $(i) \to (d), (ii) \to (c), (iii) \to (b)$
• D. $(i) \to (c), (ii)\to (a), (iii) \to(d)$

Answer 1

Answer: (B)

$(\mathrm{i}) \rightarrow(\mathrm{d}),(\mathrm{ii}) \rightarrow(\mathrm{c}),(\mathrm{iii}) \rightarrow(\mathrm{b})$
For $\mathrm{N}_{2(g)}+3 \mathrm{H}_{2(g)} \rightleftharpoons 2 \mathrm{NH}_{3(g)}$
$K_{c}=\frac{\left[\mathrm{NH}_{3}\right]^{2}}{\left[\mathrm{~N}_{2}\right]\left[\mathrm{H}_{2}\right]^{3}}$
(i) $2 \mathrm{~N}_{2(g)}+6 \mathrm{H}_{2(\mathrm{~g}} \rightleftharpoons 4 \mathrm{NH}_{3(g)} ; \mathrm{K}_{c}^{\prime}=K_{c}^{2}$
(ii) $2 \mathrm{NH}_{3(g)} \rightleftharpoons \mathrm{N}_{2(g)}+3 \mathrm{H}_{2(g)} ; K_{c}^{\prime}=\frac{1}{K_{c}}$
(iii) $\frac{1}{2} \mathrm{~N}_{2(g)}+\frac{3}{2} \mathrm{H}_{2(g)} \rightleftharpoons \mathrm{NH}_{3(g)} ; K_{c}^{\prime}=K_{c}^{1 / 2}$