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

misuse) these “over-maximum” fugacities. For example, a chemical may be spilled
into a lake. The fugacity can be calculated as the amount spilled divided by VZ for
water. If the resulting fugacity exceeds the vapor pressure, the water has insufficient
capacity to dissolve all the chemical, and a separate pure chemical phase must be
present. A similar situation can apply when a pesticide is applied to soils.
It is likely that the maximum Z value that a solute can ever achieve is that of
the pure phase Z p. It may be useful to calculate Z P to ensure that no mistakes have
been made by grossly overestimating other Z values.
5.6.6 Solutes of Negligible Volatility
A problem arises when calculating values of the fugacity and fugacity capacity
of solutes that have a negligible or zero vapor pressure. Thermodynamically, the
problem is that of determining the reference fugacity. The practical problem may
be that no values of vapor pressure or air-water partition coefficients are published
or even exist. Examples are ionic substances, inorganic materials such as calcium
carbonate or silica and polymeric, or high-molecular-weight substances including
carbohydrates and proteins. Intuitively, no vapor pressure determination is needed
(or may be possible), because the substance does not partition into the atmosphere,
i.e., its “solubility” in air is effectively zero. Ironically, its air fugacity capacity can
still be calculated as (1/RT), but all the other (and the only useful) Z values cannot
be calculated, since H cannot be determined and indeed may be zero. Apparently,
the other Z values are infinite or at least are indeterminably large.
This difficulty is more apparent than real and is a consequence of the selection
of fugacity rather than activity as an equilibrium criterion. There are two remedies.
The first method, which is convenient but somewhat dishonest, is to assume a
fictitious and reasonable, but small, value for vapor pressure (such as 10 –6 Pa) and
proceed through the calculations using this value. The result will be that Z for air
will be very small compared to the other phases, and negligible concentrations will
result in the air. It is obviously essential to recognize that these air concentrations
are fictitious and erroneous. The relative values of the other concentrations and Z
values will be correct, but the absolute fugacity will be meaningless.
The second method, which is less convenient but more honest, is to select a new
equilibrium criterion. We can illustrate this for air, water, and another phase(s) by
equating fugacities as follows:
©2001 CRC Press LLC
f = C A/Z A = C W/Z W = C S/Z S
We can divide through by P S to give
f = C ART = C wP S /C S = C SP S /(C S K SW)
f/P S = a = C ART/P S = C W/C S = C S/C S K SW
The equilibrium criterion is now a, an activity that is dimensionless and is the
ratio of fugacity to vapor pressure. The new Z values with units of mol/m 3 can be
defined as