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Section 10.3
since m° m* [Eq. (10.7)]. Then Determination of Activities
I,i
i
and Activity Coefficients
¢ mix G 38.314 J>1mol K241308.4 K2

510.200 mol2 ln 310.544210.20024 10.800 mol2 ln 310.957210.800246
1685 J
Exercise
l
For an acetone–chloroform solution at 35.2°C with x 0.4188, use Table 10.1
ac
to find g I,ac and g I,chl . Find mix G when 0.4188 mol of acetone and 0.5812 mol
of chloroform are mixed at 35.2°C and 1 bar. (Answers: 0.751, 0.820, 2347 J.)

From the activity coefficients calculated in this example, we can find relative par-
tial molar Gibbs energies (Fig. 9.11) in the solutions using m m* RT ln g x .
i
i
I,i i
Use of P g x P* in the mix G equation in this example gives mix G
i
I,i i
i
n RT ln (P /P*). This equation (previously given in Prob. 9.64) allows mix G to be
i
i
i
i
calculated directly from vapor-pressure data (Sec. 9.3).
The large negative deviations of g from 1 in this example (and the corresponding
I
large negative deviations in Fig. 9.21a from Raoult’s law) indicate large deviations
from ideal-solution behavior. Nuclear magnetic resonance spectra indicate that these
deviations are due to hydrogen bonding between acetone and chloroform according to
Cl COH OPC(CH ) [A. Apelblat et al., Fluid Phase Equilibria, 4, 229 (1980).]
3
3 2
The hydrogen bonding makes the acetone–chloroform intermolecular attraction
stronger than the average of the acetone–acetone and chloroform–chloroform attrac-
tions. Therefore, mix H is negative, compared with zero for formation of an ideal
solution. The hydrogen bonding gives a significant degree of order in the mixture,
making mix S less than for formation of an ideal solution. The enthalpy effect turns
out to outweigh the entropy effect, and mix G mix H T mix S is less than mix G
E
E
E
for formation of an ideal solution. Figure 10.3b shows H /n, TS /n, and G /n for
acetone–chloroform solutions at 35°C, where the excess quantities are (Sec. 10.2) H
E
mix H, S mix S mix S , and G mix G mix G .
id
E
E
id
Both energy effects ( mix H) and entropy effects ( mix S) contribute to deviations
from ideal-solution behavior. Sometimes the entropy effect is more important than the
energy effect. For example, for a solution of 0.5 mol of ethanol plus 0.5 mol of water
E
E
at 25°C, H mix H is negative ( mix H 400 J/mol), but TS is much more nega-
E
E
E
E
E
tive than H (TS 1200 J/mol), so G H TS is highly positive. The solu-
tion is less stable than the corresponding ideal solution. This solution shows positive
deviations from ideality, even though the mixing is exothermic.
Convention II
Now suppose we want the Convention II activity coefficients. The standard states
in Convention II are the same as for an ideally dilute solution. Whereas m m°
i
i
RT ln x for an ideally dilute solution, we have m m° RT ln a II,i in a nonideal so-
II,i
i
i
l
lution. Hence, exactly the same steps that led to Henry’s law P K x [Eq. (9.63)]
i
i
i
l
for the solutes and Raoult’s law P x P* [Eq. (9.64)] for the solvent lead to modi-
A
A A
fied forms of these laws with mole fractions replaced by Convention II activities.
Therefore, the partial vapor pressures of any solution are
x for i A, ideal vapor
P K a K g II,i i l (10.15)
i
i
i II,i
P a II,A A II,A A l A (10.16)
P* g
x P* ideal vapor, P not very high
A
where A is the solvent. To apply (10.15), we need the Henry’s law constant K .
i
This can be found by measurements on very dilute solutions where g II, i 1. Thus,