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

$k = Aexp \left ( \frac{-E_a}{RT} \right)$        (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 E_a 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 E_a, 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](Catalysis/Determination of Rate Law Parameters).

The determination of A and E_a 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:

$ln(k) = A - \frac{E_a}{RT}$        (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 ¹)

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

---

1. Fogler, H. S., Elements of Chemical Reaction Engineering, 4th Edition, Prentice-Hall, Inc., Englewood Cliffs (2005).↩