Show that if a liquid is in equilibrium with its own vapour and an inert gas in a closed vessel, then

\[\frac{\mathrm{d} p_{v}}{\mathrm{~d} p}=\frac{ho_{v}}{ho_{l}}\]

where \(p_{v}\) is the partial pressure of the vapour, \(p\) is the total pressure, \(ho_{\mathrm{v}}\) is the density of the vapour, \(ho_{1}\) is the density of the liquid.