Physical Chemistry , 1st ed.

Say you have a system with a particular liquid-phase composition. It will

have a characteristic vapor-phase composition, determined by the expressions

above. We can use pressure-composition phase diagrams like Figure 7.5 to rep-

resent the connection between the liquid-phase composition and the vapor-

phase composition. A horizontal line in a diagram like Figure 7.5 represents a

constant-pressure or isobaric condition. Figure 7.6 shows a horizontal line,

segment AB, connecting the bubble point line and the dew point line for a liq-

uid that has a certain mole fraction x 1. For a liquid having the composition in-

dicated, the equilibrium vapor pressure for that liquid is found by going up the

diagram until you intersect the bubble point line at point B. However, at that

equilibrium pressure, the composition of the vaporphase is found by moving

horizontally until you intersect the dew point line at point A. Such graphical

representations are very useful in understanding how liquid-phase and vapor-

phase compositions are related.

Example 7.5

At some particular temperature, the vapor pressure of pure benzene, C 6 H 6 ,

is 0.256 bar and the vapor pressure of pure toluene, C 6 H 5 CH 3 , is 0.0925 bar.

If the mole fraction of toluene in the solution is 0.600 and there is some

empty space in the system, what is the total vapor pressure in equilibrium

with the liquid, and what is the composition of the vapor in terms of mole

fraction?

Solution

Using Raoult’s law, we can determine the partial pressures of each component:

pbenzene(0.400)(0.256 bar) 0.102 bar

ptoluene(0.600)(0.0925 bar) 0.0555 bar

The total pressure is the sum of the two partial pressures:

ptot0.102 bar 0.0555 bar 0.158 bar

We could also have used equation 7.17, letting toluene be component 1:

ptot0.256 (0.0925 0.256)0.60

ptot0.158 bar

In order to determine the composition of the vapor (in mole fraction), we

can use Dalton’s law of partial pressures to set up the following:

ytoluene

0

0

.0

.1

5

5

5

8

5

b

b

a

a

r

r

0.351

ybenzene

0

0

.

.

1

1

0

5

2

8

b

b

a

a

r

r

0.646

(The two mole fractions do not add up to exactly 1 because of truncation

errors.) Notice that the vapor phase has been enriched in benzene over the

original solution. This should make sense, given that benzene has a much

higher vapor pressure than toluene.

Referring to Figure 7.6, note that point B is not the boiling pointof the so-

lution having that composition. It is simply the vapor pressure of the solution

7.3 Two Components: Liquid/Liquid Systems 175

p* 2

p* 1

Partial pressure

0.5

B

A

x 1 , y 1

0.0 1.0

Composition

of vapor phase

Composition

of liquid phase

Figure 7.6 A horizontal tie line in a pressure-
composition phase diagram like this connects the
liquid-phase composition with the composition
of the vapor phase that is in equilibrium.