12.9: Ideal Solutions

According to Raoult’s law, the partial vapor pressure of a solvent in a solution is equal or identical to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution. However, Raoult's Law is only valid for ideal solutions. For a solution to be ideal, the solvent-solute interaction must be just as strong as a solvent-solvent or solute-solute interaction. This suggests that both the solute and the solvent would use the same amount of energy to escape to the vapor phase as when they are in their pure states. This is only possible when the different components of the solution are chemically similar, as in the case of benzene and toluene or hexane and heptane.

Since many solutions do not have uniform attractive forces, the vapor pressure of these solutions deviates away from the pressure predicted by Raoult’s law. For instance, when ethanol is dissolved in water, there are strong attractions between the water molecules and the ethanol molecules. These attractive forces tend to slow down the loss of water molecules from the surface of the solution. However, if the solution is sufficiently dilute, the surface will have more water molecules. Some of these surface water molecules may not be surrounded by any ethanol molecules and can still escape to the vapor phase at the same rate as they would in pure water. Such dilute solutions are said to approach ideal behavior.

For non-ideal solutions, deviation from Raoult’s law can either be negative or positive. The negative deviation takes place when the vapor pressure is lower than that expected due to Raoult’s law. A solution of water and hydrochloric acid exhibits negative deviation because the hydrogen bonds between water and hydrochloric acid prevent the surface water molecules from vaporizing as readily.

Alternatively, positive deviation occurs when the attraction between the molecules of each component, either solute-solute or solvent-solvent, is greater than the attraction between the solvent and the solute. In such solutions, both components can easily escape into the vapor phase. An example of a positive deviation is a solution of benzene and methanol as the intermolecular forces between the benzene and methanol are weaker than found in pure methanol.

In a solution, there are three major attractive intermolecular forces: attractions between the solvent molecules, attractions between the solute molecules, and attractions between the solute and the solvent molecules.

If the strength of each of the three types of interactions are similar in magnitude, the solution is called an ideal solution.

An ideal solution obeys Raoult’s law at all concentrations. 

For an ideal solution with two volatile components, such as toluene and benzene, the partial vapor pressure of each component will be given by Raoult’s law as a product of the vapor pressure of the pure component and its mole fraction.

In a given solution, the mole fraction for toluene is 0.4 and the mole fraction for benzene is 0.6. As the vapor pressures of the pure toluene and pure benzene are 22 and 75 torr, respectively, the partial pressures of toluene and benzene in this solution will be 8.8 and 45 torr, respectively.

The total vapor pressure is the sum of the partial pressure of each component and is equal to 54 torr.

For such an ideal solution, a plot of vapor pressure against mole fraction yields a straight line.

When the intermolecular forces within a solution are not uniform, the solution deviates from Raoult’s law and is called non-ideal.

If the solvent-solute interactions in a solution are weaker than the solvent–solvent interactions, as in the case of a benzene and methanol solution, the solute will allow more solvent particles to escape into the gaseous state than in the pure solvent.

Thus, vapor pressure would tend to be greater than that predicted by Raoult’s law. Such solutions show a positive deviation from Raoult’s law.

Conversely, in a solution with strong solute-solvent interactions, the solute will prevent the solvent from vaporizing and the vapor pressure of the solution will be less than that predicted by Raoult’s law. 

This is observed in an aqueous solution of acetone and chloroform, where strong hydrogen bonding between the two leads to a negative deviation from Raoult’s law.