Page 122 - Modern physical chemistry

6.5 Aspects of Multicomponent Phase Diagrams 113

and
qp =!lll =Tt.S = -nRT(XA lnXA +XB lnXB).

For dissolving 1 mole BinI mole A, we find

qp = -(2.000 mOIXs.3145 J K- mor X313.15 KXlnO.5000) = 3609 J.
l
l
6.5 Aspects of Multicomponent Phase Diagrams

From the Gibbs phase rule, c + 1 independent intensive variables are needed for each
phase in a c component system. Thus, the diagram representing the conditions under
which phases are stable or metastable is c + 1 dimensional. For convenience, however,
one may employ 2-dimensional slices of the general diagram.
When c is 2, a person may look at a constant pressure slice, with perpendicular axes
for temperature and composition. When c is 3, a person may look at a plane at constant
pressure and temperature, with compositions referred to equilateral triangle axes.
In the laboratory, one would study the behavior of systems of representative com-
positions while being heated or cooled at constant pressure. High temperature phases
generally possess more internal energy than lower temperature ones. Furthermore, tran-
sition of a given amount of material from a low temperature to a high temperature form
requires energy.
The process may occur at a definite temperature. Or it may occur over a range of tem-
peratures. In either case, the transition temperature is identified with the temperature at
which the process may be completed reversibly. The absorption of the extra energy causes
a slowing down or a halting of the temperature rise for a given rate of energy addition.
Generally, the transition temperature for a given phase change in pure B differs from
that in pure A. When the mixtures are nearly ideal, the boundaries of the high tempera-
ture phase H and the low temperature phase L then appear as figure 6.2 shows. The ver-
tical scale may be linear in temperature T; the horizontal scale, linear in mole fraction
X B • Alternatively, the horizontal scale may be linear in the weight per cent of B.
A point between the two curves represents a mixture of ~ moles phase H and n L
moles phase L. The total number n of moles is

n =nH +nL' [6.14]
Suppose at the given temperature the point is distance
[6.15]
from the H boundary and distance
[6.16]

T

FIGURE 6.2 Representative constant pressure equilibrium
diagram for A and B forming nearly ideal solutions in both
A B phase H and phase L.