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Physical chemistry 108

also be determined if the overall composition is known. When B
is the more volatile component, the vapor is richer in B and liquid
richer in A. Separation of pure A and B can be achieved by
distillation. For some non-ideal systems, there is a low-boiling or
high-boiling azeotropic point on the diagram. In this case
separation of pure A and B by distillation is not possible.

Related topics Fundamentals of equilibria (C1) Colligative properties (D3)
Further acids and bases (C3) Phase equilibria (D4)
Non-electrolyte solutions (D1)

The phase rule

For phase diagrams of mixtures of different chemical species, the phase rule can be used
to determine the number of degrees of freedom, F, in the system (see Topic D4). This is
given by:
F=C−P+2

where C is the number of components and P is the number of phases present. The
number of components is the number of independent chemical species in the system. This
is usually equal to the number of different chemical substances present; for example, a
mixture of benzene and water would have two components. However, in a few cases,
new chemical species are formed by reaction. An example is the ionization of a weak
acid (see Topic C3):

In this case, although there appears to be four chemical species, there are two equations
linking them; the equilibrium constant expression (see Topic C1) and an equation
maintaining the overall electroneutrality of the system, which equates the number of
cations and ions to maintain no overall charge. This means that in reality there are only
two components. Generally C=S−R, where C is the number of components, S is the
number of chemical species present and R is the number of different equations linking
them. For systems involving substances that ionize, the number of components is
generally equal to the number of chemical species present without the complication of
ionization. This is because ionization produces the same number of extra chemical
species as equations linking them and increases both S and R by the same amount.
A phase is rigorously defined as a part of the system that is uniform both physically
and chemically throughout. A pure solid, a pure liquid and a pure gas are each a phase, as
in each the density and chemical composition are identical at all locations. By this
criterion, a mixture of different chemical species can also be one phase, as long as the
mixing is so thorough that at any location the relative amounts of all the species is the
same as any other location. Mixing in gases is very efficient and there is only ever one
gas phase in a mixture. A mixture of two liquids can be either two phases if the liquids