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Chapter 10 vapor-pressure measurements give the Convention II activities and activity coeffi-
Nonideal Solutions cients. Equations (10.15) and (10.16) give g II, i P /P id-dil and g II,A P /P A id-dil ,
i
i
A
where id-dil stands for ideally dilute.
EXAMPLE 10.2 Convention II activity coefficients

Find the Convention II activity coefficients at 35.2°C for acetone–chloroform
solutions, taking acetone as the solvent. Use Table 10.1.
Ordinarily, one would use Convention I for acetone–chloroform solutions,
but for illustrative purposes we use Convention II. Equation (10.16) for the sol-
vent Convention II activity coefficient g II,A is the same as the Convention I equa-
tion (10.14), so g II,A g . Since acetone has been designated as the solvent,
I,A
we have g II,ac g . The g I,ac values were found in Example 10.1.
I,ac
l
For the solute chloroform, Eq. (10.15) gives g II,chl P /K x . We need
chl
chl chl
the Henry’s law constant K . In Fig. 9.21a, the Henry’s law dotted line for chlo-
chl
roform intersects the right-hand axis at 145 torr, and this is K chl in acetone. (A
l
l
more accurate value of K chl can be found by plotting P /x chl versus x chl and
chl
l
extrapolating to x chl 0. See also Prob. 10.11.) The Table 10.1 data and K chl
145 torr then allow calculation of g II,chl . Time can be saved by noting that g
I,i
l
l
l
P /x P*, so g /g (P /K x ) (P /x P*) P*/K (293 torr)/(145 torr)
i
I,i
i
i
i
i
II,i
i
i
i
i
i
i
2.02. Thus g II,chl 2.02g I,chl . Using the g I,chl values from Example 10.1 and
(10.10), we find:
x ac 0 0.082 0.200 0.336 0.506 0.709 0.815 0.940 1
g II,chl 2.02 1.99 1.93 1.77 1.56 1.31 1.19 1.08 1
g II,ac 0.494 0.544 0.682 0.824 0.943 0.981 0.997 1
The g ’s are plotted in Fig. 10.4. Both g ’s go to 1 as the solvent mole frac-
II
II
tion x → 1, whereas g I,chl → 1 as x chl → 1 and g I,ac → 1 as x → 1 (Fig. 10.3a).
ac
ac
Figure 10.4
Exercise
Convention II activity coefficients
versus composition for acetone– Use Table 10.1 to find g II,ac and g II,chl in a 35.2°C acetone–chloroform solution
l
chloroform solutions at 35°C with with x 0.4188 if acetone is considered to be the solvent. (Answer: 0.751,
ac
acetone taken as the solvent. 1.65 .)
6
Note that g II,chl 1 with acetone as the solvent, whereas g I,chl 1 (Fig. 10.3a).
This corresponds to the fact that P chl in Fig. 9.21a is less than the corresponding
Raoult’s law (ideal-solution) dashed-line partial pressure, and P chl is greater than the
corresponding Henry’s law (ideally dilute solution) partial pressure. g measures
I
deviations from ideal-solution behavior; g measures deviations from ideally dilute
II
solution behavior.
Since g II,chl 7 1 and g II,ac 6 1 for acetone as solvent, m chl in Eq. (10.6) is greater
than m id-dil , the chloroform chemical potential in a hypothetical ideally dilute solution
chl
of the same composition, and m ac 6 m id-dil . In a hypothetical ideally dilute solution,
ac
the chloroform molecules interact only with the solvent acetone, and this is a favor-
able interaction due to the hydrogen bonding discussed earlier. In the real solution,
CHCl molecules also interact with other CHCl molecules, which is a less favorable
3
3
interaction than with acetone molecules; this increases m chl above m id-dil . In an ideally
chl
dilute solution, the interaction of the solvent acetone with the solute chloroform has
an insignificant effect on m id-dil . In the real solution, the acetone–chloroform interac-
ac
tion is significant, and since this interaction is favorable, m is less than m id-dil .
ac
ac