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 #(-)#.