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212 PHASE EQUILIBRIA

5.5 Phase equilibria and colligative properties

Why does a mixed-melting-point determination work?

Effects of impurity on phase equilibria
in a two-component system

The best ‘fail-safe’ way of telling whether a freshly prepared compound is identical
to a sample prepared previously is to perform a mixed-melting-point experiment.
In practice, we take two samples: the first comprises material
A ‘mixed melting point’ whose origin and purity we know is good. The second is fresh
is the only absolutely from the laboratory bench: it may be pure and identical to the
fail-safe way of deter- first sample, pure but a different compound, or impure, i.e. a mix-
mining the purity of ture. We take the melting point of each separately, and call them
asample. respectively T (melt, pure) and T (melt, unknown) . We know for sure that
the samples are different if these two melting temperatures differ.
Ambiguity remains, though. What if the melting temperatures are the same but, by
some strange coincidence, the new sample is different from the pure sample but has
the same melting temperature? We therefore determine the melting temperature of a
mixture. We mix some of the material known to be pure into the sample of unknown
compound. If the two melting points are still the same then the two materials are
indeed identical. But any decrease in T (melt, impure) means they are not the same. The
value of T (melt, mixture) will always be lower than T (melt, pure) if the two samples are
different, as evidenced by the decrease in T (melt) .We callit a depression of melting
point (or depression of freezing point).

Introduction to colligative properties: chemical potential

The depression of a melting point is one of the simplest manifestations of a colliga-
tive property. Other everyday examples include pressure, osmotic pressure, vapour
pressure and elevation of boiling point.
‘Colligative properties’ For simplicity, we will start by thinking of one compound as the
depend on the num- ‘host’ with the other is a ‘contaminant’. We find experimentally
ber, rather than the that the magnitude of the depression T depends only on the
nature,of the chem- amount of contaminant added to the host and not on the identity of
ical particles (atoms the compounds involved – this is a general finding when working
or molecules) under with colligative properties. A simple example will demonstrate how
study.
this finding can occur: consider a gas at room temperature. The
ideal-gas equation (Equation (1.13)) says pV = nRT, and holds
reasonably well under s.t.p. conditions. The equation makes it clear that the pressure
p depends only on n, V and T , where V and T are thermodynamic variables, and
n relates to the number of the particles but does not depend on the chemical nature
of the compounds from which the gas is made. Therefore, we see how pressure is a
colligative property within the above definition.