Environmental Engineering Reference
In-Depth Information
collisions that occur irrespective of the energy. The product
A
exp
(
−
E
a
/RT)
is a
measure of the
productive
collisions.
E
XAMPLE
5.8 A
CTIVATION
E
NERGY FOR THE
D
ECOMPOSITION OF AN
O
RGANIC
M
OLECULE IN
W
ATER
Consider the organic molecule (dibromosuccinic acid) in water. Its rate of decomposi-
tion is a first-order process, for which the following rate constants were determined at
varying temperatures:
k
hr
−1
T
(
K
)
1.08
×
10
−
4
323
7.34
×
10
−
4
343
45.4
×
10
−
4
362
138
×
10
−
4
374
A plot of ln
k
versus 1
/T
can be made as shown in Figure 5.9. The straight line has
a slope
−
E
a
/R
of
−
11,480 and an intercept of 26.34. The correlation coefficient is
0.9985. Therefore,
E
a
=
95 kJ/mol and
A
=
2.76
×
10
11
hr
−
1
for the given reaction.
-4
y
= 26.349 - 11480
x
R
= 0.99934
-5
-6
-7
-8
-9
-10
0.0026
0.0027
0.0028
0.0029
0.003
0.0031
(1/
T
)/(1/
K
)
FIGURE 5.9
Temperature dependence of the rate constant for the decomposition
of dibromosuccinic acid in aqueous solution (data from Laidler, 1965). The plot of
ln
k
versus 1
/T
is the linearized form of the Arrhenius equation. The slope gives the
logarithm of the pre-exponential factor (ln A) and the slope is
−
E
a
/R
, where
E
a
is the
activation energy.
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