McKay, Donald. "Front matter" Multimedia Environmental Models ...

1.0. This, then, is the fugacity or vapor pressure of pure liquid solute at the temperature
(and strictly the pressure) of the system.
The activity coefficient g is defined here on a “Raoult’s law” basis such that g is
1.0 when x is 1.0. In most cases, g values exceed 1.0 and, for hydrophobic chemicals,
values may be in the millions.
An alternative convention, which we do not use here, is to define g on a Henry’s
law basis such that g is 1.0 when x is zero.
The activity coefficient is thus a very important quantity. It can be viewed as the
ratio of the activity or fugacity of the solute to the activity or fugacity that the solute
would have if it were in a solution consisting entirely of its own kind. It depends
on the concentration of the solute with a dependence of the type
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log g = log g O (1 – x) 2
where g O is the activity coefficient at infinite dilution, i.e., when x the mole fraction
approaches zero.
Another useful way of viewing activity coefficients is that they can be regarded
as an inverse expression of solubility, i.e., an insolubility. A solute that is sparingly
soluble in a solvent will have a high activity coefficient, an example being hexane
in water. For a liquid solute such as hexane, at the solubility limit, when excess pure
hexane is present, the fugacity equals the reference fugacity f R and
Therefore,
f i = f R = x ig if R
x i = 1/g i or g i = 1/x i
The activity coefficient is thus the reciprocal of the solubility when expressed as a
mole fraction. For solids at saturation, f i is the fugacity of the pure solid f S. Thus,
and
f S = x ig if R
x i = (f S/f R)/g i = F/g i
where F is the fugacity ratio discussed earlier. Solid solutes of high melting point
thus tend to have low solubilities, because F is small.
It is more common to express solubilities in units such as g/m 3 . Under dilute
conditions, the solubility S i mol/m 3 is x i/v S, where v S is the molar volume of the
solution (m 3 /mol) and approaches the molar volume of the solvent. S i is thus 1/g iv S
for liquids and F /g iv S for solids. In the gas phase, the solubility is essentially the
vapor pressure in disguise, i.e.,