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Arrhenius Reaction Rates#

Arrhenius-like reaction rate constant equations are calculated as 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 (\((\mbox{molecule}\,\mathrm{cm}^{-3})^{-(n-1)}\,\mathrm{s}^{-1}\)),

  • \(n\) 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 equations has the following format:

 type: ARRHENIUS
 A: 123.45
 Ea: 123.45
 B: 1.3
 D: 300.0
 E: 6.0e-06
 time unit: MIN
 reactants:
   spec1:
   spec2:
     qty: 2
   ...
 products:
   spec3:
   spec4:
     yield: 0.65
   ...

 {
     "type" : "ARRHENIUS",
     "A" : 123.45,
     "Ea" : 123.45,
     "B"  : 1.3,
     "D"  : 300.0,
     "E"  : 0.6E-5,
     "time unit" : "MIN",
     "reactants" : {
       "spec1" : {},
       "spec2" : { "qty" : 2 },
       ...
     },
     "products" : {
       "spec3" : {},
       "spec4" : { "yield" : 0.65 },
       ...
     }
 }

The key-value pairs reactants and products are required. Reactants without a qty value are assumed to appear once in the reaction equation. Products without a specified yield are assumed to have a yield of 1.0.

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. The unit for time is assumed to be s, but inclusion of the optional key-value pair time unit = MIN can be used to indicate a rate with minutes as the time unit.

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