Question

$3moles$ of phosphorus pentachloride are heated in a flask of $4litre$ volume. At equilibrium, it dissociates to give $40$% of phosphorus trichloride and chlorine. Calculate the equilibrium constant.

Answer 1

Degree of dissociation$=0.4$
$P{Cl}_5\left(g\right)\rightleftharpoons P{Cl}_3\left(g\right)+{Cl}_2\left(g\right)$
$a(1-x)$ $ax$ $ax$ (at equilibrium)
Given, $a=3,x=0.4$ and $V=4$
So, at equilibrium,
$\left[P{Cl}_5\right]=\frac{3(1-0.4)}{4}=\frac{3\times 0.6}{4}mol{L}^{-1}$
$\left[P{Cl}_3\right]=\frac{3\times 0.4}{4}mol{L}^{-1}$
$\left[{Cl}_2\right]=\frac{3\times 0.4}{4}mol{L}^{-1}$
applying the law of mass action
$K_c=\frac{\left[P{Cl}_3\right]\left[{Cl}_2\right]}{\left[P{Cl}_5\right]}=0.2$