Cliffs AP Chemistry, 3rd Edition

Experiment 4: Determination of Molecular Mass by Freezing-Point Depression

Background: If a nonvolatile solid is dissolved in a liquid, the vapor pressure of the liquid sol-
vent is lowered and can be determined through the use of Raoult’s Law, P 1 = X 1 P 1 °. Raoult’s
Law is valid for ideal solutions wherein ∆H = 0 and in which there is no chemical interaction
among the components of the dilute solution (see Figure 1).

Figure 1

This phenomenon results in higher boiling points and lower freezing points for the solution as
compared to the pure solvent. Vapor pressure, freezing-point depressions and boiling-point ele-
vations are known as colligative properties. Colligative properties depend only on the number
of particles present, not on what type of particles they are. Each solvent has its own unique
freezing-point depression and boiling-point elevation constants — values that must be factored

into an equation to solve for molecular mass. For water, the constant kb= 0.52 °C ⋅m–1and kf=

1.86 °C ⋅m–1. To determine the molecular mass of a solute from a freezing-point depression

you use the equation

Tikmikmoles of solutekg of solvent ikkg solventMM

g solute

∆ ff==::::::f =f solute

which can be rearranged to produce

MM kg of solvent T

i k g solute

solute ∆ f

f

:

::

=

where i, known as the van’t Hoff or dissociation factor, represents the degree to which the
solute ionizes. For non-ionic compounds, i = 1; for NaCl, i = 2 since for every one mole of
NaCl there results two moles of ions, Na+and Cl–; i = 3 for NiBr 2 , and so on. The van’t Hoff
factor is only approximate except in infinitely dilute solutions. Otherwise, one must use activity
coefficients for the ions at their concentrations.

Figure 2 shows the cooling curve for a pure solvent and for a solution. Supercooling may re-
sult. Should this occur, as the crystals begin to form, the temperature will increase slightly and
then remain relatively constant as the pure solvent freezes.

Vapor

Pressure

Temperature

ab

a = freezing point

of solution

b = freezing point

of solvent

1 atm

Solid

Liquid

Pure

Solvent

Solution

Gas

Laboratory Experiments