The source of chemical species due to reaction, , is computed as the sum of the reaction sources over the
reactions that the species may participate in:
(19–8) |
where |
|
| |
|
Note that in Equation 19–8,
| for the reactants of the forward reaction |
| for the products of the forward reaction |
The individual reaction rates
are themselves functions of the form
(19–9) |
where is a rate "constant", the terms
are the molar concentrations of the reactant species
, and
are a set of exponential powers.
The values of the rate constant and the exponential orders are dictated by a reaction mechanism that is an elementary step-by-step description of a chemical interaction.
The exponential orders may be different from the stoichiometric coefficients of the reaction itself.
For a given reaction mechanism, the influence of temperature on the rate constant
can be expressed in terms of an Arrhenius type relationship involving the universal
gas constant and the absolute temperature
:
(19–10) |
A change in temperature, however, may modify the reaction mechanism. Equation 19–10 holds as long as a change in the system does not change the reaction mechanism. It is a subtle fact that a change in composition can also change the reaction mechanism.
Considering an unknown rate constant at any temperature
, and a reference rate constant
at a reference temperature
, the pre-exponential factor can be eliminated from Equation 19–10 to yield
(19–11) |
represents a shift in temperature. It is set to 0 by default.
This relationship has proven useful to relate to
from appropriate reference values
and
. The temperature can also be expressed in a relative scale in
conjunction with the absolute temperature with respect to the zero of the relative
scale (
).
Chemical reactions are either exothermic or endothermic (that is, they either generate or consume energy). Energy (positive or negative) associated with the chemical reaction acts as a source term of the energy equation as follows:
(19–12) |
where is the heat of reaction
.
where is the heat of reaction
. Note that the temperature of the system strongly affects the rate
of reaction; as a general rule, a change in temperature of about ten degrees changes
the reaction rate by a factor of two.