Physical Chemistry , 1st ed.

expression, this implies that the unit molality can be substituted in the de-

nominator. Therefore, the final answer is

Kf20.83 

m

K

olal



This unit makes more sense if one is using equation 7.48 to determine the

freezing point depression. Cyclohexane has one of the larger Kfvalues for a

common solvent.

There is an analogous derivation for the difference in the boiling point for

a solvent that has a nonvolatile solute dissolved in it. Rather than repeat the

derivation in its entirety, only the final result is presented:

Tb

M

1

s

0

ol

0

ve

0

nt



va

R

p

T

H

(^2) BP
msolute (7.49)
where TBPand (^) vapHnow refer to the boiling point and heat of vaporization
of the solvent. Again, the terms inside the parentheses are constants for any sol-
vent, so equation 7.49 can be rewritten as
TbKbmsolute (7.50)
where Kbis the boiling point elevation constantfor the solvent. It is sometimes
called the ebullioscopic constant.
One thing that the expressions for the change in the freezing point and boil-
ing point do not address: the directionof the change. Although the formal
mathematics indicate the direction of Tfand Tb, they are lost in equations
7.48 and 7.50. That is, they tell us only the magnitude of the change, not the
direction. It is incumbent on us to remember: freezing points go down, but
boiling points go up.
The final colligative property of solutions we will consider is called osmotic
pressure. Although we treat it last, it is probably one of the most important,
because many biological systems like our own cells are influenced by it.
Pressure is defined as force per unit area. Pounds per square inch (psi) is a
common (though non-SI) unit of pressure in the United States. A pressure is
exerted on any object that has liquid above it, as experienced divers know. The
first barometers invented were tubes of water—and later mercury—that were
set up to act against the pressure of the atmosphere. See Figure 7.27.
Consider a system constructed in two parts that are separated by a semi-
permeable membrane, as shown in Figure 7.28. A semipermeable membraneis
a thin film that allows some molecules to pass through it and not others.
Cellophane and other polymers are examples. Cell walls can be considered
semipermeable membranes. Let the system be filled with a solution on the left
side, and the pure solvent on the right side, but to the same height (Figure
7.28a). The tube on either side is open to some external pressure, labeled P.
Curiously, this system is not at equilibrium.In time, solvent (usually water)
molecules, which can easily pass through many semipermeable membranes,
will go from the right side to the left side, further diluting the solution. In doing
so, the heights of the liquids on either side of the membrane change. At some
point, the system achieves equilibrium. That is, the chemical potential of the
solvent on either side of the membrane is equal:
solvent,1solvent,2
At this point, however, the liquid levels on the two sides of the system are dif-
ferent, as shown in Figure 7.28b. The column of liquid on the left side exerts a
196 CHAPTER 7 Equilibria in Multiple-Component Systems
Closed-end tube
containing liquid
Force due to
column of liquid
(Fliq)
Force due to
atmosphere
(Fatm) (water, alcohol,Some liquid
mercury, etc.)
At equilibrium, Fliq  Fatm
Figure 7.27 An illustration of how opposing
pressures act against each other. In this example,
the opposing pressures are the pressure of the at-
mosphere and the pressure of the liquid column
in the long tube. At equilibrium, the two pres-
sures balance each other. (This diagram repre-
sents a simple barometer.)