2.3.1. Specific Heat Capacity at Constant Pressure

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:

  1. 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).

  2. 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.