Raoult's Law

Established by François-Marie Raoult in 1882, Raoult's law states:

The vapour pressure of an ideal solution is directly dependent on the vapour pressure of each chemical component and the mole fraction of the component present in the solution.

Once the components in the solution have reached equilibrium, the total vapour pressure p of the solution is:

and the individual vapour pressure for each component is

where

p_i is the partial pressure of the component i in the mixture (in the solution)

p*_i is the vapor pressure of the pure component i

x_i is the mole fraction of the component i in the mixture (in the solution)

If a pure solute which has zero vapor pressure (it will not evaporate) is dissolved in a solvent, the vapor pressure of the final solution will be lower than that of the pure solvent.

This law is strictly valid only under the assumption that intermolecular forces between unlike molecules are equal to those between similar molecules: the conditions of an ideal solution. Comparing measured vapor pressures to predicted values from Raoult's law provides information about the true relative strength of intermolecular forces. If the vapor pressure is less than predicted (a negative deviation), fewer molecules of each component than expected have left the solution in the presence of the other component, indicating that the forces between unlike molecules are stronger. The converse is true for positive deviations.

Raoult’s law assumes ideal behavior based on a simple picture 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 approach zero, so the behavior of gases approach ideality. Raoult’s law similarly assumes that the physical properties of the components are identical. The more similar the components are, the more their behavior approaches that described by Raoult’s law. For example, if the two components differ only in isotopic content, then the vapor pressure of each component (i) will be equal to the vapor pressure of the pure substance times the mole fraction in the solution. This is Raoult’s law.

Using the example of a solution of two liquids, A and B, if no other gases are present, then the total vapor pressure p above the solution is equal to the weighted sum of the "pure" vapor pressures of the two components, p_A and p_B. Thus the total pressure above solution of A and B would be

Since the sum of the mole fractions is equal to one,

which is a linear function of the mole fraction x_B as shown in the graph.