# Catalysis:Determination of Arrhenius Parameters

The main effect of temperature on the rate of a chemical reaction comes through the specific rate constant, k. The effect of temperature on k is described by the Arrhenius law, which states

${\displaystyle k=Aexp\left({\frac {-E_{a}}{RT}}\right)}$        (Equation 2)

where A is the pre-exponential factor (related to the entropy changes associated with forming the transition state from the initial reactants) and Ea is the activation energy, or the energy barrier that must be surmounted in order to form products. Part of our goal in performing a reaction engineering analysis of a chemical reaction is to determine the Arrhenius parameters A and Ea, so that we may predict correct rate constants at any given reaction temperature.

The starting point for this analysis is a collection of k versus temperature data. Often, the specific values of k come from non-linear least-squares regression, simultaneous with determining reaction orders.

The determination of A and Ea is often made graphically, through the use of an Arrhenius plot. To create such a plot, one takes the natural log of equation (2) above, to obtain:

${\displaystyle ln(k)=A-{\frac {E_{a}}{RT}}}$        (Equation 7)

Plotting ln(k) versus 1/T according to equation (7) above yields the following linear graph:

(Figure taken from http://www.engin.umich.edu/~cre/course/lectures/three/pics/lec5-26.gif, Elements of Chemical Reaction Engineering by Fogler.)

From this type of plot, A is equal to the intercept and Ea is equal to the ${\displaystyle -R\times (slope)}$