2.2.13 (HL)—Arrhenius factor (A)

A is the frequency factor: it represents the frequency of collisions with proper orientation. In the linear Arrhenius form, the y-intercept is ln A.

Read the intercept, find A by exponentiating ln A, and keep A distinct from Ea: Ea describes the energy barrier, while A describes collision frequency and orientation.

From a fitted line, intercept b gives A = eᵇ, while gradient m gives Ea = −mR. Check the pair against k = Ae^(−Ea/RT) at one data temperature. A has the same units as k for the stated rate law; it is not an activation energy or a universal constant.

Worked intercept example: for the same first-order Arrhenius line, use $\ln k=-6.02$, $1/T=0.00296\,\mathrm{K^{-1}}$ and gradient $-E_a/R=-12500\,\mathrm{K}$. From $\ln k=(-E_a/R)(1/T)+\ln A$, $-6.02=(-12500)(0.00296)+\ln A$, so $\ln A=30.98$ and $A=e^{30.98}=2.85\times10^{13}\,\mathrm{s^{-1}}$. The unit is $\mathrm{s^{-1}}$ because this reaction is first order and $A$ has the same units as $k$.