4.5 g of PCl₅ on vaporization, occupied a volume of 1700 mL at 1 atmosphere pressure and 227°C temperature. Its degree of dissociation is

Let the degree of dissociation be $\mathrm{\alpha }$, then
$\underset{(1-\mathrm{\alpha })}{{\mathrm{PCl}}_5}⟶\underset{\mathrm{\alpha }}{{\mathrm{PCl}}_3}+\underset{\mathrm{\alpha }}{{\mathrm{Cl}}_2}$
(M) Molecular weight of PCI₅ = 31 + 5 x 35.5 = 208.5
Total number of molecules before dissociation = 1
Total number of molecules after dissociation
= $1-\mathrm{\alpha }+\mathrm{\alpha }+\mathrm{\alpha }=1+\mathrm{\alpha }$
Thus, each gram mole changes to (1 + $\mathrm{\alpha }$) gram-mole.
Thus $\mathrm{PV}=\frac{\mathrm{W}}{\mathrm{M}}(1+\mathrm{\alpha })\mathrm{RT}$
(V = volume after dissociation)
$\text{ or }1\times \frac{1700}{1000}=\frac{4.5}{208.5}(1+\mathrm{\alpha })\mathrm{RT}\left[1700\mathrm{ml}=\frac{1700}{1000}\mathrm{L}\right]$
$\text{ or }\mathrm{\alpha }=0.921$
$\therefore \mathrm{\%}\text{ age dissociation }=92.1\mathrm{\%}$