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

Another useful quantity is the ratio of fugacity to some reference fugacity such
as the vapor pressure of liquid benzene. This is a dimensionless quantity and is
termed activity.
Activity can also be used as an equilibrium criterion. This proves
to be preferable for substances such as ions, metals, or polymers that do not appreciably
evaporate and thus cannot establish vapor phase concentrations and partial
pressures.
Our task, then, is to start with a concentration of solute chemical in one phase,
from this deduce the chemical potential, fugacity, or activity, argue that these equilibrium
criteria will be equal in the other phase, and then calculate the corresponding
concentration in the second phase. We therefore require recipes for deducing C from
f and vice versa. This approach is depicted at the bottom of Figure 5.1.
The partition coefficient approach contains the inherent assumption that, whatever
the factors are that are used to convert C1
to f1
and C2
to f2,
the ratio of these
factors is constant over the range of concentration of interest. Thus, it is not actually
necessary to calculate the fugacities; their use is sidestepped. In the fugacity
approach, no such assumption is made, and the individual calculations are undertaken.
We can illustrate these approaches with an example.
Worked Example 5.1
Benzene is present in water at a specified temperature and a concentration C
of 1 mol/m3
(78 g/m3).
What is the equilibrium concentration in air C ?
1. Partition coefficient approach
Therefore,
©2001 CRC Press LLC
K21
is 0.2, i.e., C2/C1
C2
= K21C1
= 0.2 ¥ 1 = 0.2 mol/m3
= 15.6 g/m3
1. Fugacity approach
Using techniques devised later, we find that, for water under these conditions,
f
1
C
2
= C1/Z1
= Z2f2
= C1/0.002
= 500 Pa = f2
= 0.0004f
2
= 0.2 mol/m3
2
= 15.6 g/m3
Clearly, the problem is to determine the conversion factors Z2
and Z1,
or K21,
which is their ratio. Care must be taken to avoid confusing K21
with its reciprocal
K12
or C1/C2,
which in this case has a value of 5.
We therefore face the task of developing methods of estimating Z values that
relate concentration and fugacity, and partition coefficients that are ratios of Z values.
The theoretical foundations are set out in Section 5.3 and result in a set of working
equations applicable to the air-water-octanol system. The three solubilities (or
1