# Arrhenius

The Arrhenius equation gives "the dependence of the rate constant k of chemical reactions on the temperature.

## source

This function seems to exist in multiple variants WdW: Falge et al., 1996, lathuile.doc (internal document), FLASTR3 source code.

## details

Falge et al. (1996): The temperature dependency of dark respiration, Rd, as well as of the kinetic constants tau, Kc, and Ko (see Harley and Tenhunen 1991) may each be described by an exponential function,

$\frac{f-Ea}{R \cdot Tk$ (3)

where 'Parameter' may represent Rd, τ, Kc, or Ko, and f and Ea are the scaling constant and activation energy, respectively, for each parameter, Tk is leaf temperature (°K), R is the gas constant.

lathuile.doc: The temperature dependence of the parameters is described following Farquhar & Wong (1984) {not found in publ - WdW) for the parameters KC, KO, Rd, and ? (Eqn 9):

${\displaystyle P(T)=P(298)\cdot e^{\frac {h_{a}\cdot (T\cdot K-298)}{273\cdot R\cdot T\cdot K}}}$(9)

[where] ${\displaystyle P=K_{c},k_{o},R_{d},\tau }$

   (presumably, T*K ought to be Tk? WdW)



Flastr2.for (see below)

${\displaystyle P=f*(e^{\frac {T_{k}-298}{R\cdot T_{k}\cdot 298}})^{h_{a}}}$

## behaviour

The Falge formula and the one from FLASTR3 behave the same, even though the scaling is orders of magnitude different with their original parameters. The one from lathuile.doc seems to be incorrect. In the figure below, all three of them are plotted, scaled to unity at 20°C.

## model

   rtk = basicValues.GAS_CONSTANT * TemperatureKelvin
exponent = (TemperatureKelvin - 298.) / (rtk * 298.)
result = Prefactor * exp(exponent) ** EActivation