Consider elementary reversible (or irreversible) reactions involving K chemical species that can be represented in the general form

(3–1)

The stoichiometric coefficients are integer numbers and is the chemical symbol for the k th species. The superscript indicates forward stoichiometric coefficients, while indicates reverse stoichiometric coefficients. Normally, an elementary reaction involves only three or four species; hence the matrix is quite sparse for a large set of reactions. For non-elementary reactions, Equation 3–1 also represents the reaction expression, but the stoichiometric coefficients may be non-integers.

The production rate of the k th species can be written as a summation of the rate-of-progress variables for all reactions involving the k th species

(3–2)

where

(3–3)

The rate of progress variable for the i th reaction is given by the difference of the forward and reverse rates as

(3–4)

where is the molar concentration of the k th species and and are the forward and reverse rate constants of the i th reaction. As indicated in Equation 3–4 , the rate-of-progress of a reaction is evaluated, by default, using the concentration of each reactant or product species raised to the power of its stoichiometric coefficient. Thus, the rate-of-progress of a reaction that includes species with a coefficient of 2 will be second-order with respect to the concentration of . Equation 3–4 is always valid when mass-action kinetics are obeyed, and when the mechanism is written in terms of elementary reactions. As it is often useful to work with reduced chemistry, Gas-phase Kinetics includes an option allowing the user to define an arbitrary reaction order for a species in place of the coefficients used in Equation 3–4 . This option is described further below.

The forward rate constants for the reactions are generally assumed to have the following Arrhenius temperature dependence:

(3–5)

where the pre-exponential factor , the temperature exponent , and the activation energy are specified. These three parameters are required input to the Gas-phase Kinetics package for each reaction.

In Equation 3–5 through Equation 3–10 , refers to the gas temperature, unless auxiliary reaction information is provided to indicate that the reaction depends on a temperature associated with a particular species. Such information would be specified using the auxiliary keyword, TDEP, which is described further in Table 3.7: Alphabetical Listing of Gas-phase Reaction Auxiliary Keywords of the Chemkin Input Manual Input Manual. In the case where the TDEP keyword is included for reaction , represents the temperature of the species whose name follows the TDEP keyword.

In thermal systems, the reverse rate constants are related to the forward rate constants through the equilibrium constants by

(3–6)

Although is given in concentration units, the equilibrium constants are more easily determined from the thermodynamic properties in pressure units; they are related by

(3–7)

The equilibrium constants are obtained with the relationship

(3–8)

The refers to the change that occurs in passing completely from reactants to products in the i th reaction; specifically,

(3–9)

(3–10)

For reactions involving electrons, the use of equilibrium constants to determine reverse rates is usually not appropriate. In some cases, detailed balancing on electron-driven reactions can be applied using the Saha equation (see, for example, Mitchner and Kruger [14]) that relates the ionization and electron-third-body recombination reactions to the species partition functions. While such relations can be used to calculate explicitly reverse rates from forward rates, they are not part of the built-in features of Gas-phase Kinetics. To avoid erroneous results, it is therefore required that all reactions involving electron species must either be specified as forward reactions only, or must include the reverse rate parameters explicitly stated using auxiliary keywords. The specification of reverse-rate parameters is described in more detail in the REV entry in Table 3.7: Alphabetical Listing of Gas-phase Reaction Auxiliary Keywords of the Chemkin Input Manual Input Manual).