${\text{PCl}}_{\text{5}}$ vapour decomposes on heating according to the reaction:
${\text{PCl}}_5\left(\text{g}\right)\rightleftharpoons {\text{PCl}}_3\left(\text{g}\right)+{\text{Cl}}_2\left(\text{g}\right)$
The density of a sample of a partially dissociated ${\text{PCl}}_{\text{5}}$ at $\text{1}\text{.0}$ atm and $\text{500}\text{K}$ was found $\text{4}\text{.8}\text{g/L}\text{.}$ Calculate the degree of dissociation and $\Delta {\text{G}}^{\circ }$  for the reaction at $\text{500}\text{K}\text{.}$
(Given:  $\text{R}=0.082{\text{LatmK}}^{-1}{\text{mol}}^{-1}$ $, \text{R}=8.314{\text{JK}}^{-1}{\text{mol}}^{-1},$ $\ln \text{x}=2.303{\log }_{10}\text{x}$) If your answer is K, mark 2K as answer after rounding off to nearest integer.