First, the standard-state molar enthalpy is given by
 | (2–21) |
so that
 | (2–22) |
where a
mk is the coefficients of the polynomial
that fits the thermodynamic property (in this case, the enthalpy h)
with units [1/K
M-1] and
M is the total number of coefficients of the polynomial
(7). The constant of integration, 
, is the standard heat of formation at 0 K. Normally, however, this
constant is evaluated from knowledge of the standard heat of formation at 298 K, since the
polynomial representations are usually not valid down to 0 K.
Within the thermodynamic data, it is possible to specify the enthalpy of surface species to be dependent on surface coverage of other species. This is an added functionality for addressing surface coverage dependencies, which allows for modification of heat of reaction and therefore reaction rate, based on local surface coverage calculated during a simulation. The theory is explained in Surface-coverage Modification of Rate Expression . The implementation in Ansys Chemkin of the coverage-dependent enthalpy formulation was based on collaborative discussions with researchers at MIT, [4] where the need for this capability was defined for use in estimating thermodynamically consistent and reversible reaction rates for reactions of gas-phase species on metal catalysts.
Coverage dependency is specified in the thermodynamic data using the
HFCOV keyword. This option affects the chemisorption enthalpies.
Equation 2–23
relates the heat of formation
of surface species at any coverage to the heat of formation at zero coverage. The
coverage-dependent coefficient that is input to the model is 
. The 
is calculated using Equation 2–3
in the
Chemkin Input Manual
Input Manual.
 | (2–23) |
The coverage parameters also affect the activation energy of the reverse reaction. Ansys Chemkin calculates the reverse reaction rate constant using the equilibrium constant, and the enthalpy impacts the temperature-dependent equilibrium constant through the Gibbs free energy, as shown below.
 | (2–24) |
The reverse reaction activation energy thus has the following dependence on the coverage-dependent enthalpy.
HFCOV
thus allows for a more complex impact of coverage dependence on the activation energies of surface reactions, especially since coverages will change during the course of the simulation. This option is particularly useful when using approaches such as
Bond Order Conservation (BOC) (also known as Unity Bond Index-Quadratic Exponential Potential approach)[5].
For j th surface species, the coverage dependence on
m th species is specified by 
. Thermodynamic consistency is enforced in the coverage dependent
coefficients for heats of formation in that the partial derivative of heat of formation of
j th species with respect to the coverage of m
th species is same as the partial derivative of heat of formation of the
mth species with respect to the coverage of
jth species:
 | (2–25) |
or
 | (2–26) |
The coverage-dependent coefficients are typically estimated from experimental data on the heat of formation of surface species under various coverages of the same or other species, often measured by Temperature Programmed Desorption (TPD).