Geoscience Reference
In-Depth Information
temperature and is independent of the vessel volume. The pressure that develops,
called vapor pressure, characterizes any chemical in the liquid or solid state.
When the temperature increases, the proportion of molecules with energy in
excess of the cohesive energy also increases, and an excess vapor pressure is
observed. The Clausius-Clapeyron equation describes the variation of vapor
pressure with temperature as follows:
d
ð
lnp
Þ=
dT ¼ DH
v
=
RT
2
ð
7
:
6
Þ
where p is the vapor pressure, DH
v
is the heat of volatilization, R is the universal
gas constant, and T is temperature (K).
Because the vapor pressure of chemicals is a key factor in controlling their
dissipation within the subsurface, and from the subsurface to the atmosphere,
accurate estimation of this value is required. Comprehensive reviews on this
subject are given by Plimmer (
1976
) and Glotfelty and Schomburg (
1989
). For
contaminants with low vapor pressure that reach the subsurface as a result of a
nonpoint disposal (e.g., pesticides used in agricultural practices), their vapor
pressure is sufficiently low to be below detection limits, which may explain some
discrepancies in the reported results.
Partitioning between phases (corresponding to the maximum of entropy) can be
expressed by equating the chemical potentials in the respective phases (Mackay
1979
). In partitioning between phases, matter flows from high chemical potential
to low chemical potential, and at equilibrium, the chemical potential is the same in
both phases. Due to difficulties in measuring the chemical potential, Mackay
(
1979
) reintroduced the much simpler concept of fugacity, which can be used quite
simply to express distribution of organic contaminants among the various phases
of the subsurface. It is important to stress that high fugacity denotes a greater
tendency for a chemical to escape from a phase. In fact, the role of fugacity in mass
diffusion is similar to the role of temperature in heat diffusion: Mass always flows
from high to low fugacity, just as heat flows from high to low temperature.
Fugacity is linearly related to concentration, given as
C
i
¼ f
i
Z
i
ð
7
:
7
Þ
where i denotes the ith phase, C is the concentration (mol/V), f is fugacity, and Z is
the fugacity capacity of the phase (Mackay
1979
). A phase with large Z accepts a
large amount of chemical, just as a substance with high heat capacity stores much
heat. Each phase has a Z value for each chemical at each temperature; if the Z values
are known, the equilibrium distribution between the phases can be determined.
The maximum vapor pressure value that can be established at the inner surface
of the laminar flow layer in air moving over a soil surface is reached only when the
surface is covered uniformly by the contaminant. This situation is almost impos-
sible to find in the subsurface, where a chemical is partially adsorbed on the
subsurface solid or dissolved in the subsurface water, which reduces the vapor
pressure below the equilibrium value of the pure compound.
