Page 121 - Modern physical chemistry

112 Relationships between Phases

With the Gibbs free energy defined as
G=H-TS [6.4]
and
MI=O, llT =0, [6.5]
condition (6.3) yields
[6.6]

Since X A and X B are fractions, this quantity is negative and the process is spontaneous.
For a general process at constant temperature, the definition of G yields
llG = MI - TllS. [6.7]
At constant pressure, we also have
[6.8]

Now, llG for dissolving B in A may turn positive in a certain concentration range if in
that range (a) the solution process is sufficiently endothermic and/or (b) the molecules
fonn sufficiently organized combinations. Condition (a) makes MI sufficiently positive;
condition (b) contributes negatively to llS. In such a concentration range, complete solu-
tion does not occur spontaneously; rather, immiscibility appears.
One may measure the nonideality of a solution by the deviations of the llS and llG
from their ideal values. The excess entropy change on mixing substances A and B is

[6.9]
where llSrrux is the actual entropy of mixing, while the excess Gibbs function change is

[6.10]

where ll.Grrux is the Gibbs function change in the solution process.
Generally, the average interaction among the A and B molecules in the solution is not
the same as the average of the A - A and B - B interactions in the pure materials. Then
the enthalpy of mixing is not zero,
[6.11]
and we expect
[6.12]

But the effect on the arrangement of molecules is less. So as an approximation, one may
consider the excess entropy of mixing to be small:

SE ::0. [6.13]
When approximation (6.13) holds, the solution is said to be regular.

Example 6.2

What endothermicity causes a regular solution of B in A to begin to separate into two
phases at temperature 40° C and concentration X B = 0.5000?
This critical point separates the temperatures over which B dissolves spontaneously
in A to fonn the solution in which X B = 0.5000 from a range in which the process is not
spontaneous at a fixed T and P. So at this point, we have