# Colligative Properties of Solutions

## Colligative Properties

Figure %: The Vapor Pressure of a Solution is Lower than that of the Pure Solvent

The French chemist Francois Raoult discovered the law that mathematically describes the vapor pressure lowering phenomenon. Raoult's law is given in :

Figure %: Raoult's Law Describes the Mathematics of Vapor Pressure Lowering

Raoult's law states that the vapor pressure of a solution, P, equals the mole fraction of the solvent, csolvent, multiplied by the vapor pressure of the pure solvent, Po. While that "law" is approximately obeyed by most solutions, some show deviations from the expected behavior. Deviations from Raoult's law can either be positive or negative. A positive deviation means that there is a higher than expected vapor pressure above the solution. A negative deviation, conversely, means that we find a lower than expected vapor pressure for the solution. The reason for the deviation stems from a flaw in our consideration of the vapor pressure lowering event--we assumed that the solute did not interact with the solvent at all. That, of course, is not true most of the time. If the solute is strongly held by the solvent, then the solution will show a negative deviation from Raoult's law because the solvent will find it more difficult to escape from solution. If the solute and solvent are not as tightly bound to each other as they are to themselves, then the solution will show a positive deviation from Raoult's law because the solvent molecules will find it easier to escape from solution into the gas phase.

Solutions that obey Raoult's law are called ideal solutions because they behave exactly as we would predict. Solutions that show a deviation from Raoult's law are called non-ideal solutions because they deviate from the expected behavior. Very few solutions actually approach ideality, but Raoult's law for the ideal solution is a good enough approximation for the non- ideal solutions that we will continue to use Raoult's law. Raoult's law is the starting point for most of our discussions about the rest of the colligative properties, as we shall see in the following section.

### Boiling Point Elevation

One consequence of Raoult's law is that the boiling point of a solution made of a liquid solvent with a nonvolatile solute is greater than the boiling point of the pure solvent. The boiling point of a liquid or is defined as the temperature at which the vapor pressure of that liquid equals the atmospheric pressure. For a solution, the vapor pressure of the solvent is lower at any given temperature. Therefore, a higher temperature is required to boil the solution than the pure solvent. is a phase diagram for both a pure solvent and a solution of that solvent and a nonvolatile solute that explains that point graphically.

Figure %: Phase Diagram for a Solvent and its Solution with a Nonvolatile Solute

As you can see in the the vapor pressure of the solution is lower than that of the pure solvent. Because both pure solvent and solution need to reach the same pressure to boil, the solution requires a higher temperature to boil. If we represent the difference in boiling point between the pure solvent and a solution as ΔTb, we can calculate that change in boiling point from the :

In the we use the units molality, m, for the concentration, m, because molality is temperature independent. The term Kb is a boiling point elevation constant that depends on the particular solvent being used. The term i in the above equation is called the van't Hoff factor and represents the number of dissociated moles of particles per mole of solute. The van't Hoff factor is 1 for all non-electrolyte solutes and equals the total number of ions released for electrolytes. Therefore, the value of i for Na2SO4 is 3 because that salt releases three moles of ions per mole of the salt.