# Effect of an inert gas on steam vapor pressure at equilibrium

Suppose we have a closed container with mobile walls, so it will change its volume in order to equal the external pressure(constant) to the internal pressure. This container has inside it a liquid phase only of component 1 and a vapor phase of 1 and the inert gas(2) that is insoluble in the liquid phase. If the external pressure is constant how will change the vapor pressure of the component 1 changing the temperature? (suppose we know the molar partial enthalpy of the the components in gas phase and of 1 in liquid phase at the required temperature) $$\left( \frac{\partial P_{vap}}{\partial T} \right)$$

I have tried to find this relation by equaling the chemical potentials, and proceeding in the same manner of the demonstration of the Clausius-Clapeyron equation. However I am not sure of the result. Can anybody help me in the search of this partial derivative?