Effect of an inert gas on steam vapor pressure at equilibrium
If the gas phase can be treated as an ideal gas mixture and the Poynting correction for the liquid can be neglected, then the partial pressure of component 1 in the gas phase will be the equilibrium vapor pressure of component 1 at the temperature of the system.  The partial pressure of the non-condensible component 2 will be determined by the ideal gas law, based on the number of moles of this component, the temperature of the system, and the volume of head space.

If the gas phase cannot be treated as an ideal gas mixture but can still be regarded as an ideal solution, then the Lewis Randall law can be used to determine the fugacity of component 1 in the vapor, and this can be matched to that of component 1 for the liquid, with the Poynting correction included.

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