Concise Physical Chemistry

c09 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

TWO-COMPONENT PHASE DIAGRAMS 135

The mole fraction of a two-component system runs from 0 to 1.0 (Fig. 9.4) wherenB

is the number of moles of component B andnA+nBis the total number of moles of

both components.

9.6.1 Type 1

In a two-component one-phase Type I diagram, pressure is taken as constant. Setting

p=const reduces the number of degrees of freedom by 1: f= 3 −P=2for

1 phase. (Please do not confusepandP.) The system can be represented in two

dimensions as in Fig. 9.8. If one phase is present, the system can exist at a temperature

and mole fraction represented by any point(T,XB)in either area above or below the

coexistance curves. The upper and lower curves represent the locus of mole fractions

of the vapor (upper) and liquid (lower), respectively, in equilibrium with one another

at a temperature specified on the vertical axis. A system at any temperature and mole

fraction between the coexistence curves splits into two phases, a vapor (upper curve)

and a liquid (lower curve).

When there are two phases in equilibrium (liquid and vapor), the number of

degrees of freedom is further reduced (f= 3 −P= 3 − 2 =1); and specifyingXB

of the system, as the mole fraction in the liquid phase or the mole fraction in the

vapor, automatically specifies the temperature on one of the two coexistence curves.

These two temperatures will not be the same. The lower curve in Fig. 9.8 is the locus

of points at which a trace of vapor is in equilibrium with liquid. The upper curve in

Fig. 9.8 is the locus of points at which a trace of liquid is in equilibrium with vapor.

The horizontal lines connecting them represent thel→vorv→lphase change at

any specific temperature,T(K).

Fractional distillation is one of our most important laboratory and industrial meth-

ods of chemical purification. The separation between the upper and lower curves in

a Type I diagram makes fractional distillation possible. At any temperature, the mole

fraction of component B in the mixture can be read along the horizontal in Fig. 9.8.

As seen from the figure, the mole fractions are different for coexisting liquid and

vapor phases except at the end points of the curves. If we allow a liquid mixture of

XB

T (K)

FIGURE 9.8 A Type I phase diagram. Liquid–vapor equilibriums are expressed by each of

the three horizontal lines.