# Catalysis:Determination of Arrhenius Parameters

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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

(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*, so that we may predict correct rate constants at any given reaction temperature.

_{a}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 *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:

(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 *E _{a}* is equal to the