Page 43 - Modeling of Chemical Kinetics and Reactor Design

Reaction Mechanisms and Rate Expressions 13

energy. The fraction of collisions having energies in excess of E is
represented by e –E/RT , which can now be substituted in Equation 1-54
to give:

r ∝ e − ERT C C T 05 (1-55)
.
C A B
0.5
The effect of temperature in T is small compared with its effect
in e –E/RT ; therefore, T 0.5 can be combined with the proportionality
constant resulting in:

r = k e − ERT C C (1-56)
C O A B
Generally, r = f (temperature) f (composition) and at a given temperature:
1
i
2
(
r = k f composition) (1-57)
2
i
where
=
kk e − ERT (1-58)
O
where k = reaction rate constant or velocity constant
k = frequency factor or preexponential factor
o
E = activation energy, J/mol or cal/mol
R = gas constant = 8.314 J/mol•K = 1.987 cal/mol•K
T = absolute temperature, K

Equation 1-58 is referred to as the Arrhenius equation.

Effect of Temperature on Reaction Rates

We can evaluate the effect of temperature on the reaction rate from
the Arrhenius equation, k = k e –E/RT , as:
o

ln k = ln k − E (1-59)
O
RT
When plotting experimentally determined reaction rate constants as
a function of temperature (i.e., ln k against 1/T), a straight line is
obtained with –E/R equal to the slope and the intercept as ln k . Figure
o
1-4 shows the linear relationship between the reaction rate constant
and the temperature.