Page 123 - Instant notes

Phase diagrams of mixtures 109

are immiscible (do not mix and form two separate liquids) or one phase if they are
completely miscible (each completely soluble in the other). Solid atoms and molecules
are held tightly in the solid lattice and there is often an energy penalty for mixing them,
so there is usually a phase for each solid. However, homogeneous one-phase mixtures
can be formed from two solids consisting of atoms of molecules with comparable size
and structure, such as in metal alloying.

Phase diagrams for two components

Using the phase rule, for a system of two components, F=4−P and as the minimum
number of phases that could be present in a system is one, the maximum value of F is
three. Three intensive variables would be required to define the state of the system, which
would involve plotting and interpreting a three-dimensional phase diagram. This is
complicated to reproduce on paper, so one variable is kept constant to avoid this. The
variable chosen is usually the pressure, which is fixed at one atmosphere, the ambient
pressure in experimental measurements. This reduces the number of degrees of freedom
which remain to be plotted, F′, by one, so that F′=3−P and the maximum value of F′,
when P=1, is F′=2. These remaining two variables are plotted as the axes of the two-
dimensional phase diagram. For a mixture of two species A and B, the two variables
normally chosen are the temperature, T, as the y-axis and x A, the mole fraction of A
(which specifies the overall composition of the mixture) as the x-axis. It is not necessary
to plot x B, as this can be calculated from the relationship x B=1−x A. This results in a
temperature-composition phase diagram.

Partially miscible liquids

A typical temperature-composition phase diagram observed for partially miscible liquids
is shown in Fig. 1a.