The Foundations of Chemistry

The vapor pressure of a solvent in an ideal solution is directly proportional to the

mole fraction of the solvent in the solution.

The relationship can be expressed mathematically as

PsolventXsolventP^0 solvent

where Xsolventrepresents the mole fraction of the solvent in a solution, P^0 solventis the

vapor pressure of the puresolvent, and Psolventis the vapor pressure of the solvent in the

solution(see Figure 14-9). If the solute is nonvolatile, the vapor pressure of the solution

is entirely due to the vapor pressure of the solvent, PsolutionPsolvent.

The loweringof the vapor pressure, Psolvent, is defined as

PsolventP^0 solventPsolvent

Thus,

PsolventP^0 solvent(XsolventP^0 solvent)(1Xsolvent)P^0 solvent

Now Xsolvent
Xsolute1, so 1XsolventXsolute. We can express the loweringof the

vapor pressure in terms of the mole fraction of solute.

PsolventXsoluteP^0 solvent

Solutions that obey this relationship exactly are called ideal solutions.The vapor pres-

sures of many solutions, however, do not behave ideally.

EXAMPLE 14-4 Vapor Pressure of a Solution of Nonvolatile Solute

Sucrose is a nonvolatile, nonionizing solute in water. Determine the vapor pressure lowering,

at 25°C, of the 1.25 msucrose solution in Example 14-2. Assume that the solution behaves

ideally. The vapor pressure of pure water at 25°C is 23.8 torr (Appendix E).

Plan

The solution in Example 14-2 was made by dissolving 50.0 grams of sucrose (0.146 mol) in

117 grams of water (6.50 mol). We calculate the mole fraction of solute in the solution. Then

we apply Raoult’s Law to find the vapor pressure lowering, Psolvent.

Solution

Xsucrose0.0220

Applying Raoult’s Law in terms of the vapor pressure lowering,

Psolvent(Xsolute)(P^0 solvent)(0.0220)(23.8 torr) 0.524 torr

You should now work Exercise 38.

When a solution consists of two components that are very similar, each component

behaves essentially as it would if it were pure. For example, the two liquids heptane, C 7 H 16 ,

and octane, C 8 H 18 , are so similar that each heptane molecule experiences nearly the same

intermolecular forces whether it is near another heptane molecule or near an octane mole-

0.146 mol



0.146 mol
6.50 mol

Figure 14-9 Raoult’s Law for an
ideal solution of a solute in a volatile
liquid. The vapor pressure exerted
by the liquid is proportional to its
mole fraction in the solution.

558 CHAPTER 14: Solutions

The vapor pressure of water in the
solution is (23.80.524) torr
23.3 torr. We could calculate this
vapor pressure directly from the mole
fraction of the solvent (water) in the
solution, using the relationship

PsolventXsolventP^0 solvent.

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 14.7, Colligative Properties (1):
Vapor Pressure and Raoult’s Law.

Vapor pressure of solvent

Xsolvent

P^0 solvent

Xsolute

0 0

0

0

1

1