Page 117 - Instant notes

Phase equilibria 103

point, equilibrium is established. Thus the melting and freezing temperatures of a pure
substance are identical and in this case the terms can be used interchangeably. (However
this is often not the case for a mixture, as the freezing temperature, where solid first starts
to appear from a solid mixture, is often not the same as the melting temperature, where
solid first starts to melt in a solid mixture (see Topic D5).)
At the melting point, the equilibrium for a pure species A is:

and as for all equilibria, the change in Gibbs free energy for the forward reaction, ∆G, is
zero under all conditions (see Topic C1). For each phase, for a small change in free
energy, dG (see Topic B6), dG=Vdp−SdT and therefore d∆G=∆Vdp−∆SdT, where ∆G,
∆V and ∆S are the changes in Gibbs free energy, volume and entropy during the forward
reaction, so that at equilibrium, ∆G=G (1)−G (s)=0, ∆V=V (1)−V (s) and ∆S=S (1)−S (s), with ∆G,
∆V and ∆S being the change in the Gibbs free energy, volume and entropy on melting
respectively. This means that:

The change in entropy on melting is always positive, as liquid species have more freedom
of movement than solid species. The change in volume is also usually positive, as melting
a solid produces a liquid in which the molecules move around more (have more
translational energy), and as a consequence occupy more space. In this case, dp/dT is
positive, and increasing the pressure increases the melting temperature. A notable
exception to this is water, as solid water (ice) has an open, hydrogen-bonded structure,
which occupies more volume than liquid water. This is why icebergs float, and as a
consequence ∆V is negative; in this case dp/dT is negative (Fig. 1b).

Boiling point

At the boiling point of a liquid A, an equilibrium is established for the physical transition
of A between liquid and vapor:

Again, the equation can be applied to this equilibrium, but in this case with
the changes in volume and entropy being ∆V=V (g)−V (1) and ∆S=S (g)−S (1), for the
transformation between liquid and vapor. ∆S always has a positive value, as molecules
have more freedom of movement in the vapor than in the liquid. Furthermore, ∆V is
always positive and is usually much larger than that observed in a melting transition, as
the volume occupied by a mole of gas is much larger than a mole of liquid, whereas the
difference in the volumes of liquid and solid are comparatively small. As a result, dp/dT
is positive, but has a smaller value than for the melting transition, which means that