Physical Chemistry , 1st ed.

constant,k, of the reaction. Using the symbol EAfor activation energy, equa-
tion 20.48 becomes





(

(

l

1

n

/T

k

)

)E

R

A

Rearranging:

(ln k) E

R

A

T

(^1) 

Now both sides of the equation can be integrated:
ln k
R

E

T

A(integration constant) (20.49)

It is common to rewrite equation 20.49 by taking the exponential of both sides
of the expression:

keEA/RTe(integration constant)

The second exponential is some number; it is typically defined as Aand the
above equation is written as

kAeEA/RT (20.50)

This is called the Arrhenius equation.The constant Ais sometimes referred to
as the pre-exponential factor.
Estimates ofEAcan be made using experimental values of rate constants de-
termined at different temperatures. Or, if the activation energy is known, its
value can be used to predict rate constants at new temperatures. Also, the nat-
ural logarithm of equation 20.50 can be taken to generate a new form of the
Arrhenius equation:

ln kln AE

R

A

T

(^1)  (20.51)
yb mx
where the labels indicate how this form of the Arrhenius equation is written
in the form of a straight line. Pre-exponential factors and activation energies
can be estimated graphically.
Example 20.8
In a recent paper (Orkin et al.,J. Phys. Chem.,1997, 101: 174), rate constants
were determined for the reaction between the hydroxyl radical and chloro-
bromomethane:
OHCH 2 BrCl →products
Data that were obtained included the following values of the rate constant k
for the following temperatures:
T(K) k[cm^3 /(moleculesecond)]
298 1.11 10 ^13
313 1.34 10 ^13
330 1.58 10 ^13
Show graphically that the Arrhenius equation is followed (approximately,
since these data are subject to experimental error), and determine Aand EA.
20.6 Temperature Dependence 703

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