When a system undergo a reversible change, the change in free energy with temperature and pressure is given as-
dF = VdP − SdT
at constant temperature-
dF = VdP
or, dF = nRT.(dP/p) (as PV = nRT)
on integrating the above equation we get-
∫dF = nRT∫dP/P
or, ΔF = nRT lnP2/P1
or, ΔF = nRT lnV1/V2 (as P1V1 = P2V2 )