Similarly, for (^) mixS:
(^) mixS8.314
mo
J
lK(0.250 ln 0.250 0.750 ln 0.750)
(^) mixS4.68
mo
J
lK4.00 mol 18.7 J/K
Both state functions show that mixing will be spontaneous.Notice that (^) mixGand (^) mixSsatisfy the general equation
(^) mixG mixHT^ mixS
With (^) mixH0 for an ideal solution, this equation simplifies to
(^) mixGT (^) mixS (7.29)
There is usually one other requirement for the mixing of ideal solutions:
(^) mixV^0 (7.30)
Of all requirements for an ideal solution, it is probably equation 7.30 that is
most easily demonstrated to fail for most real liquid solutions. Most people are
familiar with the example of pure water and pure alcohol. If 1.00 L of pure
water is mixed with 1.00 L of pure alcohol, the resulting solution will be some-
what lessthan 2.00 L in volume.
7.4 Nonideal Two-Component Liquid Solutions
Even simple two-component mixtures are not ideal, as suggested by the com-ment about (^) mixVfor solutions. Molecules in a liquid interact with each other,
and molecules interact differently with liquid molecules of another species.
These interactions cause deviations from Raoult’s law. If the individual vapor
pressures are higher than expected, the solution shows a positive deviationfrom
Raoult’s law. If the individual vapor pressures are lower than expected, then the
solution shows a negative deviationfrom Raoult’s law. The liquid-vapor phase
diagrams for each case show some interesting behavior.
Figure 7.12 shows a liquid-vapor phase diagram for positive deviations from
Raoult’s law. Each component has a higher-than-expected vapor pressure, so
the total pressure in equilibrium with the liquid solution is also higher than
expected. Ethanol/benzene, ethanol/chloroform, and ethanol/water are systems
that show a positive deviation from Raoult’s law. Figure 7.13 shows a similar
diagram, but for a solution that shows a negative deviation from Raoult’s law.
The acetone/chloroform system is one example that exhibits such nonideal
behavior.
For plots ofxiand yiversus composition, it is sometimes easier to use
temperature-composition phase diagrams rather than pressure-composition
phase diagrams. Figure 7.14 shows a positive deviation from Raoult’s law. (Be
sure to keep track of what the “positive” means: that the vapor pressure is
higher than expected from Raoult’s law. With the temperature and pressure
being inversely related, a positive deviation from Raoult’s law leads to a lower
temperature for the boiling point, which is what Figure 7.14 illustrates.)
7.4 Nonideal Two-Component Liquid Solutions 179
p 2
Pressure p 1
0.5
x 1
0.0 1.0
Vapor pressures
from Raoult’s law
True vapor pressures
True total pressure
p 2
Pressure p 1
0.5
x 1
0.0 1.0
Vapor pressures
from Raoult’s law
True vapor pressures
True total pressure
Figure 7.13 A nonideal solution showing a
negative deviation from Raoult’s law. Compare
this, too, to Figure 7.4.
Figure 7.12 A nonideal solution showing a
positive deviation from Raoult’s law. Compare
this to Figure 7.4.