Chemistry 4511
Problem Set 4
1.
For the reaction A + B
Æ
AB, the following data are collected:
T (K)
k (s
-1
)
300
5.71E-13
400
5.78E-08
500
5.82E-05
600
5.85E-03
700
0.158
800
1.862
What is the activation energy for this reaction? If it adheres to the hard sphere collision
rate, what is the sum of their radii if their masses are m
A
= 36.4 amu and m
B
= 19.5 amu?
First, we have the relationship k = Ae
-Ea/RT
so we can generate a plot of the data – ln (k)
vs. 1/T:
Arrhenius Plot
y = -13830.42694x + 17.90986
R
2
= 1.00000
-30
-25
-20
-15
-10
-5
0
5
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
1/T (1/K)
ln (k)
From here, the slope = Ea/R which gives an Ea of 115 kJ. For the second part,
assuming hard sphere collision theory accurately represents the prefactor A, we have
the intercept = lnA:
(
)
2
1
2
8
red
b
AB
AB
Tm
k
Ld
Z
A
π
=
=
where
B
A
B
A
red
m
m
m
m
m
+
=
and then solving for d
AB
(
)
4
1
2
2
8
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
=
B
A
b
B
A
AB
m
m
TL
k
m
m
A
d
π
which works out to (watch your units!!!)
d
AB
= 2.098 x 10
-10
m or 2.098 angstroms @ 300 K
d
AB
= 1.64 angstroms @ 800 K

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