Thermodynamics and Chemistry

CHAPTER 13 THE PHASE RULE AND PHASE DIAGRAMS

13.2 PHASEDIAGRAMS: BINARYSYSTEMS 438

0

0:005

0:4

0:6

0:8

1:0

3:0

3:2

p=10

^2

bar

0 1

CuSO 4 zB H 2 O

A(s) + B(g) 0:003

AB(s) + B(g)

A(s) + AB(s)

0:70

AB(s) + AB 3 (s) AB 3 (s) + B(g)

1:05

AB 5 (s)

+ B(g)

3:09

AB

(s) + AB 3

(s) 5

AB 5 (s)

+ sln

sln

sln + B(g)

Figure 13.12 Pressure–composition phase diagram for the binary system of CuSO 4

(A) and H 2 O (B) at 25 C.a

aRef. [ 107 ]; Ref. [ 169 ], p. 263.

The dissociation pressures of the three hydrates are indicated by horizontal lines in Fig.
13.12. For instance, the dissociation pressure of CuSO 4
5H 2 O is1:05 10 ^2 bar. At the
pressure of each horizontal line, the equilibrium system can have one, two, or three phases,
with compositions given by the intersections of the line with vertical lines. A fourth three-
phase equilibrium is shown atpD3:09 10 ^2 bar; this is the equilibrium between solid
CuSO 4
5H 2 O, the saturated aqueous solution of this hydrate, and water vapor.
Consider the thermodynamic equilibrium constant of one of the dissociation reactions.
At the low pressures shown in the phase diagram, the activities of the solids are practically
unity and the fugacity of the water vapor is practically the same as the pressure, so the equi-
librium constant is almost exactly equal topd=p, wherepdis the dissociation pressure of
the higher hydrate in the reaction. Thus, a hydrate cannot exist in equilibrium with water va-
por at a pressure below the dissociation pressure of the hydrate because dissociation would
be spontaneous under these conditions. Conversely, the salt formed by the dissociation of
a hydrate cannot exist in equilibrium with water vapor at a pressure above the dissociation
pressure because hydration would be spontaneous.

If the system contains dry air as an additional gaseous component and one of the dis-

sociation equilibria is established, the partial pressurepH 2 Oof H 2 O is equal (approx-

imately) to the dissociation pressurepdof the higher hydrate. The prior statements

regarding dissociation and hydration now depend on the value ofpH 2 O. If a hydrate

is placed in air in whichpH 2 Ois less thanpd, dehydration is spontaneous; this phe-

nomenon is calledefflorescence(Latin:blossoming). IfpH 2 Ois greater than the vapor

pressure of the saturated solution of the highest hydrate that can form in the system,