Question

How do colligative properties affect freezing point?

Answer 1

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:

`\mathbf(mu_j = mu_j^"*" + RTlna_j)`

where `mu_j` is the chemical potential of a solvent `j` that already contains some amount of solute, `mu_j^"*"` 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_jgamma_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 <= 1`.

Because of this, and because of the fact that `ln(a_j)` is negative when `0 < a_j < 1` (`ln1 = 0`), if you add any solute at all to the solution, `a_j` will go down, and thus `mu_j < mu_j^"*"`.

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).