Colligative Properties

Colligative properties are properties of solutions that depend on the particular solvent and on the concentration, but they do not depend on the nature of the solute. To a first degree, all colligative properties are related to ideal solutions. These are solutions in which the solute and solvent have identical intermolecular forces. If this is the case, then the enthalpy of solution, \(\Delta H_{solution} = 0\) since making the solution has no effect on the potential energy of the molecules (ions). However, mixing the solution will raise the entropy of the solution, \(\Delta S_{solution} > 0\). Thus, colligative properties are what we would call an entropic effect (they are a result of entropy).

By definition, a colligative property is a property of a solution (an ideal solution) which depends on the solvent and the amount of the solute in the solution, but it is not related to the chemical nature of the solute (its IMF don’t matter).
The nature of the solvent matters as the solution properties are similar to the pure solvent. But the nature of the solute does not since we are assuming the solutes are all similar to the given solvent we are studying (like dissolves like).
What matters most is the entropy of the solution compared to the pure solvent. This is affected by how much of the solute there is. In particular, how many particles there are. Thus 1 mole of sugar = 1 mole of Na⁺ ions = 1 mole of SO₄^2- ions….

There are four properties that we will look at. All are simply related to the concentration of the solution. However, for historical reasons the units for the concentration are different for the different phenomena

They are

The lowering of Vapor Pressure (Raoult’s Law). The vapor pressure of a solution will be lower than the pure substance. This is the basis of understanding distillation. It is also the same idea as boiling point elevation.

Boiling Point Elevation. The boiling point of a solution will be higher than the pure substance. This is the same as the lowering of the vapor pressure. We have a handy formula for the boiling point.

Freezing Point Depression. The freezing point of a solution will be lower than the pure substance. This is why you salt the sidewalk to melt ice. And why you use ice and salt to make ice cream.

Osmosis. Explains the movement of solvent between solutions of different concentrations separated by a membrane. A critical concept for cell biology. An important means to purify water.

Some questions to consider...

Why does the boiling point go up?
Why does the freezing point go down?
Why doesn’t the nature of the solute matter?

Answer: IT IS ALL IN THE ENTROPY!

Remember we have assumed the solutions are ideal. Thus the difference is the entropy, not the enthalpy.

Because what matters is the total amount of solute, it is important to realize that ionic solids break up into multiple ions in solution. Thus 1 M of NaCl solution has an effective concentration of 2M. This is because it has a 1 M concentration of Na⁺ ions and a 1 M concentration of Cl^- ions. It is very important to account for all the dissolved particles in soltion.

the van't Hoff Factor, i

The number of ions that form up dissolving a particular ionic solid is called the van't Hoff factor and is often denoted by a lower case i. For molecular solids i=1 since they don't dissociate in water. For ionic compounds, i is equal to the number of ions in the compound.

So from an ideal solution perspective the freezing point of a 1 M solution of sugar (i=1) will be identical to a 0.333 M solution of RbCl₂ (i=3).

Note: In chemistry we generally assume that ions are dissociated when they are in solution. In fact, at high concentrations positive and negative ions can form pairs that stay in solution. This is different from reaching the solubility limit and having solids precipitated out of solution. Ion pairing reduces the vant' Hoff factor (i) from whole numbers. Measuring a colligative effect is a means to measure "i" to gauge the effect of ion pairing. For example you might predict that a 0.1 m solution of sodium chloride would be effectively 0.2 m in concentration (i=2). However, in practice you might note that the change in properties for the solution is for a concentration of 0.187 m. This difference is the result of ion pairing. We will always be using the "ideal" vant' Hoff factor that assumes total dissociation of ions unless it is explicitly noted.