Reaction rate equation
Set
| context | R,J∈N |
| context | ν−,ν+∈Matrix(R,J,Q) |
| context | k∈RR |
| definiendum | [A]∈it |
| j∈range(J) | |
| postulate | [A]:C(R,RJ) |
| range | ::[A](t) |
| postulate | ∂∂t[A]j=∑Rr=1kr⋅(ν+rj−ν−rj)⋅∏Ji=1[A]ν−rii |
The quantities R and J denote the number of reactions and the number of different species. Then ν−rj and ν+rj are stochastic coefficients of the reactants and products and kr is the reaction rate coefficient of the r's reaction.
Physically speaking, for each microscopic particle collision the reaction rate coefficient kr gives the probability that ν−rj of the reactants transform into ν+rj of the products. The rate is moreover proportional to the probability of encounter and hence the product to the momentary concentrations themselves.
Non-time resolved, this reads for all r
∑Jj=1ν(e)rjAjkr⟶∑Jj=1ν(p)rjAj.
For example, the simplest carbon combustion process: CH4+2 O2⟶CO2+2 H2O.
(Or more explicitly: 1 CH4+2 O2+0 CO2+0 H2O⟶0 CH4+0 O2+1 CO2+2 H2O.)
In practice, k depends on the temperature, which, through the equation of state, can again be a nonlinear function of the concentrations.
Reference
Wikipedia: Rate equation
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