# For a very small extent of dissociation of $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$ is a gaseous phase reaction then degree of dissociation, x:

(a) $x \propto P$

(b) $x \propto \frac{1}{P}$

(c) $x \propto \sqrt{P}$

(d) $x \propto \sqrt{\frac{1}{P}}$

Answer: $x \propto \sqrt{\frac{1}{P}}$

$PCl_5 \rightleftharpoons PCl_3 + Cl_2$

Degree of dissociation (or quantity of products formed)

$x \propto (\frac{1}{P}^{\Delta n_g / 2})$

where P is the total pressure.

Here, $\Delta n_g$ = 2 - 1 = 1

$\therefore x \propto (\frac{1}{P})^{\frac{1}{2}}$ or $x \propto \sqrt{\frac{1}{P}}$

edited Nov 23, 2013