Colligative Properties

Colligative properties are solution properties that depend mainly on the number of dissolved particles, not on what those particles are made of. In general chemistry, the usual formulas work best for dilute solutions and often assume the solute is nonvolatile.

If you only remember one idea, use this one: adding solute particles changes how easily solvent molecules can escape, freeze, or move through a membrane. That is why vapor pressure goes down, boiling point goes up, freezing point goes down, and osmotic pressure appears.

The Four Colligative Properties

The four standard colligative properties are vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

Vapor Pressure Lowering

For an ideal solution with a nonvolatile solute, Raoult's law gives

$$P_{\text{solution}} = X_{\text{solvent}} P^0_{\text{solvent}}$$

Here, $X_{\text{solvent}}$ is the mole fraction of the solvent and $P^0_{\text{solvent}}$ is the vapor pressure of the pure solvent. Since adding solute makes $X_{\text{solvent}} < 1$, the solution has a lower vapor pressure than the pure solvent.

Boiling Point Elevation

For a dilute solution,

$$\Delta T_b = i K_b m$$

The boiling point rises because the solution must be heated more before its vapor pressure matches the external pressure.

Freezing Point Depression

For a dilute solution,

$$\Delta T_f = i K_f m$$

The freezing point drops because dissolved particles make it harder for the solvent to form the ordered solid structure.

Osmotic Pressure

For a dilute solution,

$$\pi = i M R T$$

Osmotic pressure is the pressure needed to stop net solvent flow through a semipermeable membrane.

In these formulas, $i$ is the van't Hoff factor, $m$ is molality, $M$ is molarity, and $K_b$ and $K_f$ depend on the solvent.

Why Particle Count Matters

A nonelectrolyte such as glucose usually stays as whole molecules in solution, so 1 mole gives about 1 mole of dissolved particles. An electrolyte such as sodium chloride can produce more particles because it dissociates into ions.

That is why equal amounts of different solutes do not always give equal colligative effects. In introductory problems, the particle count is usually handled with the van't Hoff factor $i$. In real solutions, especially at higher concentrations, the actual effect can differ from the simple ideal estimate.

Worked Example: Freezing Point Depression

Suppose you dissolve glucose in water to make a $0.50\ \mathrm{m}$ solution. For water,

$$K_f = 1.86\ ^\circ\mathrm{C\, m^{-1}}$$

Because glucose is a nonelectrolyte in this context, take

$$i = 1$$

Now calculate the freezing point change:

$$\Delta T_f = i K_f m = (1)(1.86)(0.50) = 0.93\ ^\circ\mathrm{C}$$

Pure water freezes at $0.00\ ^\circ\mathrm{C}$, so the new freezing point is

$$0.00 - 0.93 = -0.93\ ^\circ\mathrm{C}$$

So this solution freezes at

$$-0.93\ ^\circ\mathrm{C}$$

This example shows the key idea: the size of the change comes from particle count. If you kept the same molality but used a solute that produced more particles, the freezing point drop would be larger.

Common Mistakes With Colligative Properties

Using The Formulas Outside Their Best Conditions

The standard colligative formulas are most reliable for dilute solutions. If the solution is concentrated or strongly non-ideal, the simple formulas become less accurate.

Treating Formula Units And Particles As The Same Thing

One mole of dissolved formula units is not always one mole of dissolved particles. Electrolytes can split into ions, so the colligative effect can be larger than for a nonelectrolyte at the same concentration.

Mixing Up Molality And Molarity

For boiling point elevation and freezing point depression, the standard formulas use molality. Osmotic pressure uses molarity in the common dilute-solution form.

Assuming Every Solute Is Nonvolatile

The simple vapor pressure lowering picture is cleanest when the solute does not evaporate significantly. If both components are volatile, you need a more careful model.

Where Colligative Properties Show Up

Colligative properties show up in antifreeze, road salting, food preservation, cell water balance, reverse osmosis, and some molar-mass measurements. The same idea runs through all of them: dissolved particles change how the solvent behaves as a bulk system.

Try A Similar Problem

Try your own version with a $1.00\ \mathrm{m}$ glucose solution in water. Use the same $K_f = 1.86\ ^\circ\mathrm{C\, m^{-1}}$ and find the new freezing point. Then compare it with the $0.50\ \mathrm{m}$ case to see the particle-count relationship directly.