# How do colligative properties affect freezing point?

Aug 6, 2015

Colligative properties cause freezing point depression.

#### Explanation:

If you examine the following graph:

It shows the change in the chemical potential of a solution versus a change in the temperature, at a constant pressure. (All compounds want to minimize chemical potential, similar to minimizing energy.)

There is an equation which describes colligative properties:

$\setminus m a t h b f \left({\mu}_{j} = {\mu}_{j}^{\text{*}} + R T \ln {a}_{j}\right)$

where ${\mu}_{j}$ is the chemical potential of a solvent $j$ that already contains some amount of solute, ${\mu}_{j}^{\text{*}}$ means pure solution (i.e. just the solvent without added solute), and ${a}_{j}$ means activity of solvent $j$ in the solution.

The activity is defined as:

${a}_{j} = {x}_{j} {\gamma}_{j}$

where ${x}_{j}$ is mole fraction of compound $j$ and ${\gamma}_{j}$ is the activity coefficient of compound $j$. Thus, you can infer that a lower mole fraction of compound $j$ gives a lower activity and vice versa.

Since mole fractions are always <= 100%, the activity can never be higher than 100%, and thus ${a}_{j} \le 1$.

Because of this, and because of the fact that $\ln \left({a}_{j}\right)$ is negative when $0 < {a}_{j} < 1$ ($\ln 1 = 0$), if you add any solute at all to the solution, ${a}_{j}$ will go down, and thus ${\mu}_{j} < {\mu}_{j}^{\text{*}}$.

What this says, then, is that the chemical potential decreases, and so on the graph above, if you are examining a liquid's freezing point, move the straight line that corresponds to the liquid downwards a certain amount.

You would see that the freezing point is shifted left, and the boiling point is shifted right.

Therefore, colligative properties cause freezing point depression (and boiling point elevation).