Question

Excess solid $N{H}_{4}I$ on rapid heating in a closed vessel develops a constant pressure of $4P_a$ owing to the partial decomposition of solid into $N{H}_3\left(g\right)$ and $HI\left(g\right)$ but the pressure gradually increases further owing to the dissociation of $HI$. The final pressure at equilibrium is $5P_c.K_P$ for $2HI\left(g\right)\rightleftharpoons H_2\left(g\right)+I_2\left(g\right)$ is_________.

• A. $\frac{9}{32}$
• B. $\frac{81}{1024}$
• C. $\frac{1}{16}$
• D. None of these

Answer 1

The correct option is D None of these

$N{H}_4{I}_{\left(s\right)}\rightleftharpoons N{H}_3\left(g\right)+H{I}_{\left(g\right)}$

$P_{Total}=PN{H}_3+PHI$

Let $P_T=x+x$

$2HI\rightleftharpoons H_2\left(g\right)+I_2\left(g\right)$

$\frac{x}{2}$ $\frac{x}{2}$ partial pressure

Total pressure at equilibrium $=5Pa$

$5Pa=x+x+\frac{x}{2}+\frac{x}{2}$

$xPa=\frac{5}{3}Pa$

Now, $k_p=\frac{P{H}_2\times P{I}_2}{(P{H}_I{)}^2}$

$\Rightarrow \frac{\frac{5}{6}\times 5/6}{\frac{5}{3}\times \frac{5}{3}}=\frac{1}{4}$

$k_p=0.25$