Arrhenius Reaction Rates#

Arrhenius-like reaction rate constants handle the formal Arrhenius equation, but include additional temperature and pressure dependent terms that are commonly found in atmospheric chemical mechanisms. The full equation follows:

\[A e^{-\frac{E_a}{k_bT}} \left(\frac{T}{D}\right)^B (1.0 + E \cdot P)\]

where:

  • \(A\) is the pre-exponential factor (\((\mbox{mol}\,\mathrm{m}^{-3})^{-(n-1)}\,\mathrm{s}^{-1}\)),

  • \(n\) is the number of reactants,

  • \(E_a\) is the activation energy \((\mathrm{J})\),

  • \(k_b\) is the Boltzmann constant \((\mathrm{J}/\mathrm{K})\),

  • \(D\) \((\mathrm{K})\), \(B\) (unitless), and \(E\) (\(\mathrm{Pa}^{-1}\)) are reaction parameters,

  • \(T\) is the temperature \((\mathrm{K})\), and \(P\) is the pressure \((\mathrm{Pa})\).

The first two terms are described in Finlayson-Pitts and Pitts (2000) [FPJ99]. The final term is included to accommodate CMAQ EBI solver type 7 rate constants.

Input data for Arrhenius rate constants have the following format:

 type: ARRHENIUS
 A: 123.45
 Ea: 123.45
 B: 1.3
 D: 300.0
 E: 6.0e-06
 gas phase: gas
 reactants:
   - species name: foo
     coefficient: 2.0
 products:
   - species name: bar
   - species name: baz
     coefficient: 1.3
 name: my_reaction
 __custom property: 32.4

 {
   "type": "ARRHENIUS",
   "A": 123.45,
   "Ea": 123.45,
   "B": 1.3,
   "D": 300.0,
   "E": 6.0e-06,
   "gas phase": "gas",
   "reactants": [
     {
       "species name": "foo",
       "coefficient": 2.0
     }
   ],
   "products": [
     {
       "species name": "bar"
     },
     {
       "species name": "baz",
       "coefficient": 1.3
     }
   ],
   "name": "my_reaction",
   "__custom property": 32.4
 }

The key-value pairs reactants and products are required. If the coefficient is not specified for a reactant or product, it is assumed to be 1.0.

The gas phase key is required and must be set to the name of the phase the reaction takes place in. Each reactant and product must be present in the specified phase.

Optionally, a parameter C may be included, and is taken to equal \(\frac{-E_a}{k_b}\). Note that either Ea or C may be included, but not both. When neither Ea nor C are included, they are assumed to be 0.0. When A is not included, it is assumed to be 1.0. When D is not included, it is assumed to be 300.0 K. When B is not included, it is assumed to be 0.0. When E is not included, it is assumed to be 0.0.

Rate constants are in units of \(\mathrm{(m^{3}\ mol^{-1})^{(n-1)}\ s^{-1}}\) where \(n\) is the total number of reactants.

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