Question

The equilibrium constants for the reactions $N_2+3H_2\rightleftharpoons 2N{H}_3$ and $\frac{1}{2}{N}_2+\frac{3}{2}{H}_2\rightleftharpoons N{H}_3$ are $K_1$ and $K_2$ respectively. Which one of the following is the correct relationship?

• A. $K_1=2K_2$
• B. $K_1=\frac{1}{2}{K}_2$
• C. $K_2=\sqrt{K_1}$
• D. $K_1=K_2$

Answer 1

Answer: (C)

$K_2=\sqrt{K_1}$

$N_2+3H_2\rightleftharpoons 2N{H}_3$
$K_1=\frac{[N{H}_3{]}^2}{\left[N_2\right][H_2{]}^3}....\left(i\right)$

$\frac{1}{2}{N}_2+\frac{3}{2}{H}_2\rightleftharpoons N{H}_3$
$K_2=\frac{\left[N{H}_3\right]}{\left[N_2{]}^{1/2}\right[H_2{]}^{3/2}}....\left(ii\right)$

From Eqs. (i) and (ii), we get:

$\frac{K_1}{K_2^2}=1$

$K_2=\sqrt{K_1}$.

Hence, option C is correct.