12
Experiment 1: Colligative Properties
Determination of the Molar Mass of a Compound by Freezing Point Depression.
Objective:
The objective of this experiment is to determine the molar mass of an unknown solute by
measuring the freezing point depression of a solution of this solute in a solvent as compared to the
freezing point of the pure solvent.
Background:
Colligative properties
are properties of a solvent, such as freezing point depression and
boiling point elevation, which depend on the concentration of solute particles dissolved in the solvent.
The decrease in freezing point,
Δ
T
f
(freezing point depression) for a near ideal solution can be
described by the equation:
Δ
T
f
= k
f
·
m
Eq 1
where k
f
is the
molal freezing point depression constant
of the solvent with units
°
C · kg
solvent/mole solute.
m
is the molal concentration of the solute dissolved in the solvent expressed as
moles of solute/kg solvent.
Since the molar mass
M
(traditionally and often, but erroneously called the molecular weight) of a
compound has units g/mole, we can solve for moles and substitute the result into the molal
concentration relationship, and then into Eq 1 as is shown below.
M
= g/ mole
Eq 2
Rearranging Eq 2 gives
moles = g/
M
Eq 3
Now substituting Eq 3 into the unit definition of molality yields
m
= g/(
M
· kg solvent)
Eq 4
And substituting Eq 4 into Eq 1 gives
Δ
T
f
= (k
f
· g)/(
M
· kg solvent)
Eq 5
We can rearrange Eq 5 and solve for the molar mass, mol wt, as is shown in Eq 6, below.
M
= (k
f
· g)/(
Δ
T
f
· kg solvent)
Eq 6
Therefore, if we know the mass of unknown compound added to a known mass of solvent and
determine the change in freezing point of the solution, relative to pure solvent, we can use Eq 6 to
determine the molar mass of the unknown compound.
At the freezing point of any substance, an equilibrium exists in which both liquid and solid are present.
liquid
⇄
solid
Eq 7

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