Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 52

TABLE 3.5
Criteria for Equilibrium between Two Phases a
and b
Property Criteria

G i = G i Gibbs free energy

a
i = μ

b
i

Chemical potential μ

f i
Note: In terms of chemical potentials, at constant temperature and
either at constant V or P , the criteria for irreversible and
reversible processes are:
Δμ i < 0 (irreversible, spontaneous process)
Δμ i = 0 (reversible, equilibrium process)
Δμ i > 0 (nonspontaneous process).

f i Fugacity =

TABLE 3.6
Definition of Fugacity Capacities for Environmental
Compartments
Compartment Definition of Z (mol/m 3 /Pa)

Air 1/ RT
Water 1 /K aw
Soil or sediment K sw ρ s /K aw
Biota K bw ρ b /K aw
Source: From Mackay, D. 1991. MultimediaEnvironmentalModels . Chelsea,
MI: Lewis Publishers.
Note: R is the gas constant ( = 8.314 Pa m 3 /mol/K), K aw is Henry's con-
stant for species (Pa m 3 /mol), K sw is the partition constant for species
between the soil or sediment and water (dm 3 /kg), K bw is the biocon-
centration factor (dm 3 /kg), and ρ s and ρ b are the densities (kg/dm 3 ) of
soil/sediment and biota, respectively. 1 dm 3 = 1L.

The value of Z depends on a number of factors, such as identity of the solute, nature of
the environmental compartment, temperature T , and pressure P . A fugacity capacity
can be defined for each environmental compartment (Table 3.6). In order to obtain the
value of Z , a knowledge of other equilibrium relationships between phases ( partition
coefficients ) is required. These relationships will be described in detail in Chap-
ter 4. Suffice it to say at this point that the partition coefficients are to be either
experimentally determined or estimated from correlations.
Once the fugacity capacities are known for individual compartments, the mean Z
value can be determined by multiplying the respective Z j value with the volume of
the compartment ( V j ) and summing over all compartments. If the total mass of the
compound or chemical input or inventory in all the compartments is known, then the