Thermodynamics and Chemistry

CHAPTER 13 THE PHASE RULE AND PHASE DIAGRAMS

13.2 PHASEDIAGRAMS: BINARYSYSTEMS 425

whereais a constant equal to the mole ratio of N 2 and O 2 in the dry air. This equation
cannot be changed to a relation between intensive variables such asxN 2 andxO 2 , so thatr
is zero and there are still three degrees of freedom.
Finally, let us assume that we prepare the system with dry air of fixed composition, as
before, but consider the solubilities of N 2 and O 2 in water to be negligible. ThennlN 2 and

nlO 2 are zero and Eq.13.1.13becomesngN 2 =ngO 2 Da, oryN 2 DayO 2 , which is a relation
between intensive variables. In this case,ris 1 and the phase rule becomes

FD 2 CsrPD 2 (13.1.14)

The reduction in the value ofFfrom 3 to 2 is a consequence of our inability to detect any
dissolved N 2 or O 2. According to the components approach, we may prepare the liquid
phase with H 2 O and the gas phase with H 2 O and air of fixed composition that behaves as a
single substance; thus, there are only two components.

Example 5: equilibrium between two solid phases and a gas phase

Consider the following reaction equilibrium:

3 CuO.s/C2 NH 3 .g/ï3 Cu.s/C3 H 2 O.g/CN 2 .g/

According to the species approach, there are five species, one relation (for reaction equilib-
rium), and three phases. The phase rule gives

FD 2 CsrPD 3 (13.1.15)

It is more difficult to apply the components approach to this example. As components,
we might choose CuO and Cu (from which we could prepare the solid phases) and also NH 3
and H 2 O. Then to obtain the N 2 needed to prepare the gas phase, we could use CuO and
NH 3 as reactants in the reaction 3 CuOC2 NH 3! 3 CuC3 H 2 OCN 2 and remove the
products Cu and H 2 O. In the components approach, we are allowed to remove substances
from the system provided they are counted as components.

13.2 Phase Diagrams: Binary Systems

As explained in Sec.8.2, a phase diagram is a kind of two-dimensional map that shows
which phase or phases are stable under a given set of conditions. This section discusses
some common kinds of binary systems, and Sec.13.3will describe some interesting ternary
systems.

13.2.1 Generalities

A binary system has two components;Cequals 2 , and the number of degrees of freedom is
F D 4 P. There must be at least one phase, so the maximum possible value ofFis 3.
SinceFcannot be negative, the equilibrium system can have no more than four phases.
We can independently vary the temperature, pressure, and composition of the system as
a whole. Instead of using these variables as the coordinates of a three-dimensional phase