Chemistry - Chemical Equilibrium Question with Solution | TestHub

$\begin{array}{cccccc}{\text{PCl}}_5& \rightleftharpoons & {\text{PCl}}_3& +& {\text{Cl}}_2& \left(\text{Total pressure}=\text{P}\right)\\ 1& & 0& & 0& \\ 1-\alpha & & \alpha & & \alpha & \end{array}$

$\therefore {\mathrm{K}}_{\mathrm{P}}=\frac{\left(\frac{\mathrm{\alpha }\mathrm{P}}{1+\mathrm{\alpha }}\right)\left(\frac{\mathrm{\alpha }}{1+\mathrm{\alpha }}\mathrm{P}\right)}{\left(\frac{1-\mathrm{\alpha }}{1+\mathrm{\alpha }}\right)\mathrm{P}}$

$=\frac{{\mathrm{\alpha }}^2}{1-{\mathrm{\alpha }}^2}\mathrm{P}\approx {\mathrm{\alpha }}^2\mathrm{P}\left(\mathrm{\alpha }\ll 1\right)$

Neglecting '${\mathrm{\alpha }}^2$'

${\mathrm{K}}_{\mathrm{P}}={\mathrm{\alpha }}^2\mathrm{P}$

$\therefore \mathrm{\alpha }=\frac{\sqrt{{\mathrm{K}}_{\mathrm{P}}}}{\sqrt{\mathrm{P}}}$