Raoult's law, Henry's Law, relative volatility

[goggles31]

Raoult's law: P = xP* , combined with Dalton's law becomes y = xP*/P
Henry's law: P = kx, combined with Dalton's law becomes y = kx/P
Relative volatility: y = ax/(1 + (a -1)x)

Raoult's law and Henry's law are linear when temperature and pressure are kept constant. But if we vary the temperature while keeping pressure constant, are all three equations equivalent? Is Henry's law a more generalized version of Raoult's law where k = P* ?

 

[Ssnow]

Is Henry's law a more generalized version of Raoult's law

At the first this is true, at least mathematically it is clear ... but chemically speaking when this is true ?

 

[Chestermiller]

In addition to Ssnow's request regarding the limitations of Raoult's and Henry's law, the relative volatility equation you presented only applies if the ratio of the vapor pressures of the two components does not change with temperature (i.e., essentially identical heats of vaporization).