5. In the reaction of oxygen atoms with benzene the following data was found experimentally:
k(M-1s-1)
T(K)
1.44 x 107
300
3.03 x 107
341
6.9 x 107
392
a) What is the order of this reaction and how do you know that?
b) Calculate the activation energy and the Arrhenius preexponential factor. You do not need to plot the data.
c) Estimate the reactive cross section at 340K
d) Estimate the steric effect , p.
Take the radii to be r(O) = 78pm and r(benzene) = 265pm (1pm = 10-12m) and m(O) = 16amu and
m(benzene) = 78amu.
Arrhenius equation: k = Ae-Ea/RT
Collision Theory
rate of reaction = f x collision density
1
 8k T  2 n
collision frequency z =   b 
N A (per molecule)
   V
1
 8k T  2 n n
collision density ZAB =   b  A B N A2
   V V
f = fraction of successful collisions = e
E NA
 o
RT
(per molecule)
where EoNA = Ea
Activated Complex Theory
k T RT 2
e e
k= b
h P
 S
R
e

Ea
RT


k T RT RS  RTH
e e
= b
h P
Constants
Atomic mass unit, mu = 1.66 x 10-27 kg
h = 6.626 x 10-34 Js
kb = 1.380 x 10-23 J/K
NA = 6.022 x 1023/mol
G = H – TS
J = kgm2/s2
R = 8.314 J/Kmol
1.987cal/Kmol
0.08206 atmL/Kmol
0.08314barL/Kmol
k
14400000
30300000
69000000
Ea
A
T
300
341
392
ln k
16.48
17.227
18.050
16641.30 slope*R
11164444865.0 exp(23.136)
1/T
0.00333
0.00293
0.00255