Chemical Engineering Thermodynamics
A reasonably general expression for vapour-liquid phase equilibrium at low to moderate pressure is Φi yi P = Yi xi fi° where, Φ is a vapor fugacity component, Yi is the liquid activity co-efficient and fi° is the fugacity of the pure component i. the Ki value (Yi = Ki xi) is therefore, in general a function of

Temperature and pressure only
Temperature, pressure, liquid composition xi and vapour composition yi
Temperature, pressure and liquid composition xi only
Temperature only

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Chemical Engineering Thermodynamics
It is desired to bring about a certain change in the state of a system by performing work on the system under adiabatic conditions.

Work alone can not bring out such a change of state
More information is needed to conclude anything about the path dependence or otherwise of the work needed
The amount of work needed is path dependent
The amount of work needed is independent of path

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