 Modified Arrhenius equation

The Modified Arrhenius equation allows a power of thermodynamic temperature in the pre-exponential factor:Here $A_{\ast }$, $E_0$, $n$, and $T_{\ast }$ are constant model parameters. Using the dimensionless quantity $T/T_{\ast }$ leaves $A_{\ast }$ with the same units as $k$; in the equivalent convention $B{T}^n\exp [-E_0/(RT)]$, $B$ instead has units of $k$ multiplied by ${\mathrm{K}}^{-n}$. The power exponent $n$ here is not an order of reaction. The IUPAC definition uses that equivalent $B{T}^n$ convention.^[ref]

Applying the apparent activation energy definition yields the original short calculationFor the orange synthetic Arrhenius plot, $n=2$, $T_{\ast }=300\mathrm{K}$, and $E_0=60\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. Its pre-exponential factor changes by $(310/300{)}^2\approx 1.06778$ from $300$ to $310\mathrm{K}$; combined with the exponential function, $k(310\mathrm{K})\approx 0.231991{\mathrm{s}}^{-1}$, compared with $0.217266{\mathrm{s}}^{-1}$ for the constant-pre-exponential factor model. The diagram uses those models only to reveal the difference between an exponent parameter and a slope-derived activation energy.