Analytical form of the chemical potential in ideal liquid solutions

3 ANALYTICAL FORM OF THE CHEMICAL POTENTIAL IN IDEAL LIQUID SOLUTIONS 

As a generalization of the behavior of real solutions the ideal solution follows Raoult s law over the entire range of concentration. Taking this definition of an ideal liquid solution and combining it with the general equilibrium condition leads to the analytical expression of the chemical potential of the solvent in an ideal solution. If the solution is in equilibrium with vapor, the requirement of the second law is that the chemical potential of the solvent have the same value in the solution as in the vapor, or 

Using Raoult s law, p = xp°, in this equation and expanding the logarithm, we obtain 

If pure solvent were in equilibrium with vapor, the pressure would be p° the equilibrium condition is 

In this equation, nothing pertaining to the vapor phase appears omitting the subscript liq, the equation becomes 

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