Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.2 THEADVANCEMENT ANDMOLARREACTIONQUANTITIES 312

bc

bc

0:3

0:2

0:1

0 0:2 0:4 0:6 0:8 1:0

0

xA

(a)

G

(mix)m

=R

T

1 1

2

3

bc bc

0

0:2

0:4

0:6

0:8

1:0

0 0:2 0:4 0:6 0:8 1:0

xA

(b)

aA

3

2

1

Figure 11.5 Binary liquid mixtures at 1 bar. The curves are calculated from the two-

parameter Redlich–Kister series using the following parameter values.

Curve 1:aDbD 0 (ideal liquid mixture).

Curve 2:a=RTD1:8,b=RTD0:36.

Curve 3:a=RTD2:4,b=RTD0:48.

(a) Molar Gibbs energy of mixing as a function of composition.

(b) Activity of component A (using a pure-liquid standard state) as a function of com-

position.

If the properties of the mixture are such thatGEmis positive at each mixture composition
(except at the extremesxAD 0 andxAD 1 where it must be zero), and no portion of the
curve ofÅGm(mix) versusxAis concave downward, there can be no phase separation and
the activityaAincreases monotonically withxA. This case is illustrated by curve 2 in Figs.
11.5(a) and11.5(b).
If a portion of theÅGm(mix)–xAcurve is concave downward, the condition needed
for phase separation, then a maximum appears in the curve ofaAversusxA. This case
is illustrated by curve 3, and the compositions of the coexisting phases are indicated by
open circles. The difference of the compositions at the two circles is amiscibility gap. The
portion of curve 3 between these compositions in Fig.11.5(b) is dashed to indicate it de-
scribes unstable, nonequilibrium states. Although the two coexisting phases have different
compositions, the activityaAis the same in both phases, as indicated in Fig.11.5(b) by the
horizontal dashed line. This is because component A has the same standard state and the
same chemical potential in both phases.
Coexisting liquid phases will be discussed further in Secs.12.6and13.2.3.

11.2 The Advancement and Molar Reaction Quantities

Many of the processes of interest to chemists can be described by balanced reaction equa-
tions, or chemical equations, for the conversion of reactants into products. Thus, for the