The vapor pressure and composition in equilibrium with a solution can yield valuable information regarding the thermodynamic properties of the liquids involved. Raoult’s law relates the vapor pressure of components to the composition of the solution. The law assumes ideal behavior. It gives a simple picture of the situation just as the ideal gas law does. The ideal gas law is very useful as a limiting law. As the interactive forces between molecules and the volume of the molecules approache zero, so the behavior of gases approach the behavior of the ideal gas. Raoult’s law is similar in that it assumes that the physical properties of the components are identical. The more similar the components the more their behavior approaches that described by Raoult’s law.
Using the example of a solution of two liquids, A and B, if no other gases are present the total vapor pressure Ptot above the solution is equal to the sum of the vapor pressures of the two components, PA and PB.
f the two components are very similar, or in the limiting case, differ only in isotopic content, then the vapor pressure of each component will be equal to the vapor pressure of the pure substance Po times the mole fraction in the solution. This is Raoult’s law.
Thus the total pressure above solution of A and B would be
Graphically this can be represented by a diagram in which the horizontal axis gives the composition from one pure component to the other as shown below.
With actual mixtures the plots of vapor pressure vs. composition usually depart from the straight lines shown above, some curve above, some below due to intermolecular forces. Below is an example of a positive deviation from ideality. The thin lines represent the ideal behavior.
As the curves approach the extremes of the pure components, molecules of the minor component are surronded by molecules of the major component. Thus the departures from the ideal give information about the interaction of the components. The partial vapor pressure above the solution is obviously related to the escaping tendency and thus the chemical potential. At equilibrium the chemical potential of a component i (mi) is the same in the solution and in the vapor phase.