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Physical chemistry 96

equilibrium with the liquid mixture. Generally the vapor pressure, p, of the vapor mixture
is given by p=Σ ip i.
The origin of Raoult’s law is that the partial vapor pressure of i is due to an
equilibrium at the surface between the molecules of i in the liquid vaporizing and the
molecules of i in the vapor condensing. This reaction occurs over that fraction of the
surface covered by i, which is x i, and so , and when x i=1 (for pure i) .

Non-ideal solutions

Raoult’s law only applies to a very few systems at all compositions. Generally, it is very
rare for the interactions between A and B to be exactly the same or even similar. This
greatly complicates the situation for high concentrations of solute. However, for all
solutions where the solute (B) is at a very low concentration, nearly the entire surface
consists of solvent molecules (A) and the presence of molecules of B affects only a small
number of solvent molecules. In this case, the vast majority of A interactions are with
other A molecules, which means that Raoult’s law applies to the solvent vapor. Solutions
under these conditions are called ideal-dilute solutions. The chemical potential of the
solvent in the liquid phase is then given by (see Topic D1):

and is the standard chemical potential of the solvent, when a A=x A=1, which is the
chemical potential of pure liquid A. By definition, the activity of a pure liquid is unity
(see Topic C1). As x A=1−x B, adding a solute decreases x A below unity, and it follows that
the chemical potential of an impure solvent is always less than a pure one. This means
that an impure solvent is more stable than a pure one, as it has a lower molar Gibbs free
energy (see Topic B6), so that adding a solute decreases the tendency for a solvent to
vaporize or freeze. This is the origin of the colligative properties of the solvent.
Under these very dilute conditions the solute molecules, B, are surrounded almost
entirely by molecules of A; very different conditions from those which are present in pure
liquid B. However, experimentally its partial vapor pressure, p B, is still found to be
proportional to its mole fraction, x B:

where K B is a constant (not to be confused with the base dissociation equilibrium
constant, see C1). This equation is called Henry’s law and K B is often called the Henry’s
law constant. Its value is constant for a particular solute, B, but also depends on the
nature of the solvent, A, as dissolution of B involves the formation of B–A interactions
and the disruption of A–A interactions. Strong B–A interactions relative to A–A
interactions will tend to favor B being in the liquid and reduce p B (resulting in a small K B)
whilst relatively weak B–A interactions will lead to a larger K B. Although Henry’s law
applies only to dilute solutions, many real systems such as gases dissolved in water or in
blood are just such dilute solutions. In this case, knowledge of the K B values of the gas
for these systems allows the mole fraction (and from this the concentration) of these
gases to be determined at any partial vapor pressure or partial pressure.