What is the overall effect of adding a solute to a solution?

Several colligative properties conspire to give the following three most common effects:

• Lower vapor pressure above the solution of the solvent in solution relative to that of the solvent by itself
• Higher boiling point of the solution relative to that of the pure solvent
• Lower freezing point of the solution relative to that of the pure solvent

Osmotic pressure `Pi = cRT` is affected as well, but is not all that interesting.

Vapor pressure for the solvent above the solution is given by Raoult's law for ideal solutions:

`bb(P_i = chi_i P_i^"*")`

where `chi_i = n_i/n_"tot"` is the mol fraction, `P_i` is the partial pressure of the solvent above the solution, and `P_i^"*"` is the pure vapor pressure of the solvent above itself.

When we consider component `j ne i` in a two-component solution, we have that `chi_i = 1 - chi_j`. Therefore:

`P_i = (1 - chi_j)P_i^"*"`

Since `chi_i <= 1`, it follows that `1 - chi_j < 1`. Therefore, `P_i < P_i^"*"`, and the vapor pressure of the solvent decreases due to adding any solute to the solution.

Boiling point elevation occurs as follows:

`bb(DeltaT_b = iK_bm)`,

where:

• `DeltaT_b = T_b - T_b^"*" > 0` is the change in boiling point due to adding solute. Of course, `T_b` is the boiling point of the solution, and `T_b^"*"` is the boiling point of the solvent by itself.
• `i` is the van't Hoff factor that is approximately how many particles go into solution for every solute formula unit.
• `K_b = "0.512"^@ "C"cdot"kg/mol"` is the boiling point elevation constant.
• `m` is the `"mol solute"/"kg solvent"` (the molality).

From the equation we can see that as concentration of solute increases, `T_b` increases.

Freezing point depression is analogous. The only difference is the numbers used:

`bb(DeltaT_f = iK_fm = T_f - T_f^"*")`

Whatever `DeltaT_f` you get, it should always be negative. If it numerically does not turn out that way, check your work or set your sign to `(-)`.