Page 381 - Physical Chemistry

lev38627_ch12.qxd 3/18/08 2:41 PM Page 362

362
Chapter 12 to heat and chemicals. Some examples of ceramics are sand, porcelain, cement, glass,
Multicomponent Phase Equilibrium bricks, diamond, SiC, Si N , Al O , MgO, and MgSiO ; many ceramics are silicates.
3
3
4
2
4
A composite material is made of two or more materials and may possess properties
not present in any one component. Bone is a composite of the soft, strong, polymeric
protein collagen and the hard, brittle mineral hydroxyapatite [approximate formula
3Ca (PO ) Ca(OH) ]. Fiberglass is a composite containing a plastic strengthened by
4 2
2
3
the addition of glass fibers.
12.6 TWO-COMPONENT LIQUID–VAPOR EQUILIBRIUM
Instead of plotting complete phase diagrams, we shall usually consider only one por-
tion of the phase diagram at a time. This section deals with the liquid–vapor part of
the phase diagram of a two-component system, which is important in laboratory and
industrial separations of liquids by distillation.

Ideal Solution at Fixed Temperature
Consider two liquids B and C that form an ideal solution. We hold the temperature
fixed at some value T that is above the freezing points of B and C. We shall plot the
system’s pressure P against x , the overall mole fraction of B in the system:
B
l
n B,total n n v B
B
x (12.34)
B
v
l
l
n total n n n n v C
B
C
B
v
l
where n and n are the number of moles of B in the liquid and vapor phases,
B
B
l
v
respectively. For a closed system x is fixed, although n and n may vary.
B
B
B
Let the system be enclosed in a cylinder fitted with a piston and immersed in a
constant-temperature bath (Fig. 12.8a). To see what the P-versus-x phase diagram
B
looks like, let us initially set the external pressure on the piston high enough for the
system to be entirely liquid (point A in Fig. 12.8b). As the pressure is lowered below
that at A, the system eventually reaches a pressure where the liquid just begins to va-
l
l
porize (point D). At point D, the liquid has composition x , where x at D is equal to
B
B
the overall mole fraction x since only an infinitesimal amount of liquid has vaporized.
B
v
What is the composition of the first vapor that comes off? Raoult’s law P x P
B
B
l
x P* [Eq. (9.52)] relates the vapor-phase mole fractions to the liquid composition as
B
B
follows:
l
v
l
v
x x P*>P and x x P*>P (12.35)
C
C
B
B
B
C
where P* and P* are the vapor pressures of pure B and pure C at T, where the system’s
B
C
l
l
l
l
pressure P equals the sum P P of the partial pressures, where x n /(n n ),
B
B
B
C
B
C
and the vapor is assumed ideal.
P
A (only liquid)
D (first vapor appears)
System F (last liquid vaporizes)
Figure 12.8 Constant-T bath
0 1
(a) A system held at constant T.
(b) Points on the P-versus-x B x B
phase diagram of the system in (a). (a) (b)