Using arbitrary-order polynomial fits, the molar heat capacities at constant pressure are defined as:
(2–18) |
The superscript o refers to the standard-state. For gas-phase species, the standard state is an ideal gas at 1 atmosphere. For perfect gases, however, the heat capacities are independent of pressure, and the standard-state values become the actual values.
For surface species the standard state of species refers to the case of a chemical
potential for a surface of pure species
(that is,
) with a fixed standard-state site density,
. Moreover, a perfect
solution (that is, non-interacting) is assumed for the
surface phase,
which is independent of the system pressure. Under these assumptions the chemical potential
for surface species
on surface site
may be written as
(2–19) |
The activity of a bulk species is defined in terms of the following equation for the chemical potential:
(2–20) |
where is the standard state chemical
potential of species k at
temperature T and at the standard
pressure P, 1 atm, and ak is the species activity.
The vector X represents an array of the
mole fractions of
the species. Two conventions are normally used to
complete the specification of the activity coefficient:
If the standard state is defined as a pure bulk phase of k at temperature T and 1 atm, then ak is further defined to approach
as
approaches 1 at 1 atm ( Raoult's Law).
If the standard state is defined as the hypothetical state of species k in infinite dilution in bulk-phase species j at temperature T and 1 atm, then is further defined to approach
as
approaches 0 at 1 atm ( Henry's Law).
Both conventions for the standard state work with Surface
Kinetics, as do any other definitions that conform to the formalism
expressed by Equation 2–20
for .
is specified through the entry for species
in the thermodynamics data file. The value of
is required as input to all Surface
Kinetics subroutines that calculate bulk phase thermodynamic quantities
and reaction rates. Therefore, if desired, advanced users can construct their own
subroutines to calculate
, possibly incorporating models for
non-ideality of the bulk phase, and can have the consequences properly incorporated into the
surface kinetics mechanism. Although the activities of all components of an
ideal solution
must sum to 1, this condition is not enforced in Surface
Kinetics. (It is, however, enforced in many of the
Ansys Chemkin program
executables that employ Surface
Kinetics.)
Other thermodynamic properties are given in terms of integrals of the molar heat capacities.