SATHEE: Equilibrium Question 568

Equilibrium Question 568

Question: The equilibrium constant for the reaction $N_{2} + 3 H_{2}$ ⇌ $2 N H_{3}$ is $K,$ then the equilibrium constant for the equilibrium $N H_{3}$ ⇌ $\frac{1}{2} N_{2} + \frac{3}{2} H_{2}$ is [CBSE PMT 1996; UPSEAT 2001]

Options:

A) $1 / K$

B) $1 / K^{2}$

C) $\sqrt{K}$

D) $\frac{1}{\sqrt{K}}$

Show Answer

Answer:

Correct Answer: D

Solution:

$K_{1}$ for $N_{2} + 3 H_{2}$ ⇌ $2 N H_{3}$

$K_{2}$ for $N H_{3}$ ⇌ $\frac{1}{2} N_{2} + \frac{3}{2} H_{2}$

$K_{1} \times K_{2} = \frac{{[N H_{3}]}^{2}}{[N_{2}] {[H_{2}]}^{3}} \times \frac{{[N_{2}]}^{1 / 2;} {[H_{2}]}^{3 / 2;}}{[N H_{3}]}$

$K_{1} \times K_{2} = \frac{1}{K_{2}}$ ; $K_{2} = \frac{1}{\sqrt{K_{1}}}$

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