E1 Colligative Properties of Solutions:
Freezing Point Depression
PURPOSE
The experiment to be performed is divided into three sections:
(a) In part 1, the FP of the pure solvent, cyclohexane, is determined by constructing and/or observing a
cooling curve.
(b) In part 2 we determine the value of the molal freezing point depression constant, kf , of cyclohexane
by measuring the freezing point depression (relative to the FP of pure cyclohexane determined in
part 1 of a solution with a known molality of solute.
(c) In part 3 the molality of cyclohexane solution with an unknown solute is found. This makes possible
the calculation of the molar mass of the unknown.
Complete advanced study assignment (pre-lab) before coming to lab and hand it in before lab starts!
INTRODUCTION
Consider a hypothetical cooling curve which describes
the changes in phase of a pure substance in which heat
is lost at a steady rate at constant pressure (see figure 1).
The Freezing Point of Pure Liquid:
This experiment will focus on the region in which the
cooling liquid approaches and achieves the
freezing point (The boxed area on cooling curve in
Figure 1 is seen close up in Figure 2 below).
At the freezing point both liquid and solid are present. If the
system becomes thermally insulated from its surroundings,
that is, heat can neither enter or leave the system, a state of
equilibrium will be established. Here the number of molecules
moving from solid to liquid is the same as the number of
molecules moving from liquid to solid. This means that
the relative quantities of solid and liquid present will remain
constant and the temperature will remain constant until all of
the pure substance has solidified. Liquid õ Solid + Heat (1)
The phenomenon of supercooling occurs when liquids do not
solidify even below their normal freezing point. In the non aqueous system used in this experiment
supercooling by the solvent is not expected.
, The Freezing Point of a Solution:
Now consider the effect of a nonvolatile solute upon a freezing solution. Any added solute would
dissolve in the liquid phase but will be excluded from the solid crystal lattice. This means that, in effect,
the concentration of liquid solvent molecules has been diminished and the rate of liquid solvent
molecules moving to solid will decrease. On the other hand, the molecules of solid solvent (which
remains pure), continue to move from solid to liquid at the same rate. If the temperature is held at the
normal freezing point of the pure solvent, the system is thrown out of equilibrium and liquid phase is
formed at the expense of solid phase, to a point where only liquid solution is present. In order to
reestablish freezing, the temperature of the system needs to be lowered. This causes heat to be removed
from the system and restores an equilibrium in which solid is present. The solution, therefore, has a
lower freezing temperature than the pure solvent and the freezing point is said to be depressed.
Now as a solution freezes, solvent molecules are removed
from the liquid solution as they form the solid. This increases
the concentration of solute in the liquid solution and the
freezing point declines further. A solution therefore does not
have a sharply defined freezing point (FP). Usually the
freezing point of a solution is taken as the temperature at
which solid solvent crystals first begin to appear (Figure 3).
The FP depression is one of a set of physical properties of solutions (vapor pressure lowering, boiling
point elevation, and osmotic pressure) known collectively as colligative properties. These properties are
affected by the quantity of solute particles dissolved in the solution, regardless of their identity. The FP
depression (or the change in temperature of freezing) is described quantitatively by the following
equation:
&Tf = -kf ¥ m. (2)
&Tf = Tf,solution Ð Tûf,solvent . &Tf is negative because the temperature of the solution is lower than that of
the pure solvent.
Molality is moles of solute per kilogram of solvent. The concentration unit mol/kg is temperature
independent, unlike the mol/L concentration unit, because volume changes with temperature but mass
does not.
molality = m = = (3)
The magnitude of the freezing point change is proportional to the molality of the dissolved solute:
&Tf ? [solute] = m. The proportionality constant, kf , is called the molal freezing point depression
constant. It is the property of the given solvent. The kf expresses the sensitivity of the solvent to having
its FP depressed by an added solute. The units are ûC/m, which may be viewed as the number of degrees
the FP is depressed per one molal of solute concentration. As stated above each solvent has its own
unique value for kf.
So expanding equation 2:
Tf,solution Ð Tûf,solvent = &Tf = - kf (4)
-2-
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