Phosphorus pentachloride dissociates according to the reaction: [ mathrm{PCl}_{5}(mathrm{~g}) ightarrow mathrm{PCl}_{3}(mathrm{~g})+mathrm{Cl}_{2}(mathrm{~g}) ] Show that (K_{P}=frac{alpha^{2}left(frac{P}{P^{0}} ight)}{1-alpha^{2}}),

Phosphorus pentachloride dissociates according to the reaction:

\[ \mathrm{PCl}_{5}(\mathrm{~g}) \rightarrow \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \]

Show that \(K_{P}=\frac{\alpha^{2}\left(\frac{P}{P^{0}}\right)}{1-\alpha^{2}}\), where \(P\) is the total pressure and \(\alpha\) is the degree of dissociation.