The
fugacity
In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas ...
capacity constant (Z) is used to help describe the concentration of a chemical in a system (usually in mol/m
3Pa). Hemond and Hechner-Levy (2000) describe how to utilize the fugacity capacity to calculate the
concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'' ...
of a
chemical
A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wit ...
in a system. Depending on the chemical, fugacity capacity varies. The concentration in media 'm' equals the fugacity capacity in media 'm' multiplied by the fugacity of the chemical.
For a chemical system at equilibrium, the fugacity of the chemical will be the same in each media/phase/compartment. Therefore equilibrium is sometimes called "equifugacity" in the context of these calculations.
:
where Z is a proportional constant, termed ''fugacity capacity''. This equation does not necessarily imply that C and f are always linearly related. Non-linearity can be accommodated by allowing Z to vary as a function of C or f.
For a better understanding of the fugacity capacity concept,
heat capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity ...
may provide a precedent for introducing Z as a capacity of a phase to absorb particular quantity of chemical. However, phases with high fugacity capacity do not necessarily retain high
fugacity
In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas ...
.
In calculations of fugacity capacity key factors would be (a) the nature of the solute (chemical), (b) the nature of the medium or compartment, (c) temperature.
Expressions for fugacity capacity
The expression for Z
m is dependent on the media/phase/compartment. The following list gives the fugacity capacities for common medias:
[Donald MacKay. 2001. Multimedia Environmental Models: The Fugacity Approach, 2nd Ed. CRC Press.]
* Air (under
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...
assumptions): Z
air = 1/RT
* Water: Z
water = 1/H
* Octanol: Z
oct = K
ow/H
* Pure phase of target chemical: Z
pure = 1/P
sv
Where: R is the
Ideal gas constant (8.314 Pa·m
3/mol·K); T is the absolute temperature (K); H is the
Henry's law
In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formul ...
constant for the target chemical (Pa/m
3mol); K
ow is the
octanol-water partition coefficient
The ''n''-octanol-water partition coefficient, ''K''ow is a partition coefficient for the two-phase system consisting of ''n''-octanol and water. ''K''ow is also frequently referred to by the symbol P, especially in the English literature. It is ...
for the target chemical (dimensionless ratio); P
s is the vapor pressure of the target chemical (Pa); and v is the molar volume of the target chemical (m
3/mol).
Notice that the ratio between Z-values for different media (e.g. octanol and water) is the same as the ratio between the concentrations of the target chemical in each media at equilibrium.
When using a fugacity capacity approach to calculate the concentrations of a chemical in each of several medias/phases/compartments, it is often convenient to calculate the prevailing fugacity of the system using the following equation if the total mass of target chemical (M
T) and the volume of each compartment (V
m) are known:
:
Alternatively, if the target chemical is present as a pure phase at equilibrium, its vapor pressure will be the prevailing fugacity of the system.
See also
*
Multimedia fugacity model
References
{{Reflist
Chemical thermodynamics
Environmental chemistry
Equilibrium chemistry