Kinetic Theory and Reaction Kinetics - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 273

In words, we describe the process as initiated by the decomposition of acetaldehyde to
form the methyl radical

CHO. Then methyl attacks the parent
molecule acetaldehyde and abstracts an H atom to formmethane and leave the acetyl radical
$

$ CH 3 and the formyl radical $

CH 3 CO, which dissociates to form another methyl radical and CO. Finally, two methyl radi-
cals combine to form the stable molecule ethane. Two formyl radicals react to form HCHO
and CO.
Reaction (6.61) is the initiation step, where free radicals are generated as a start. Reac-
tions (6.62) and (6.63) are propagation steps, where new free radicals are generated from
the “old:” ones. Reactions (6.64) and (6.65) are termination steps, where free radicals are
consumed.
This is a set of four elementary reactions. Examination of these four steps shows that they
do involve the reaction of acetaldehyde and that methane is formed by step 2 and CO by
step 3. If we add steps 2 and 3, we get

/

4 þ

(6.59)

CH CHO CH CO

3

but this occurs by a sequence of two steps.
Note also that stable products C 2 H 6 and HCHO are formed, alongside the free radi-
cals. Ethane C 2 H 6 and formaldehyde HCHO are not among the products we said were
formed. These species are minor products (no more than 1% of the amount of CH 4
and CO), which can be ignored and perhaps not even measured. When you are uncover-
ing the kinetics though, the detection of trace products, especially the stable products, is
paramount.
This reaction system is an example of a chain reaction. The only reactant is acetaldehyde,
and there are seven products listed: CH 4 , CO,

,C 2 H 6 , and HCHO. The
first two, CH 4 and CO, are the major products, and the last two, C 2 H 6 and HCHO, are the
minor products. The other species,

$ CH 3 , $ CHO, CH 3 CO $

$ $ $

CH 3 , CHO, CH 3 CO , are free radicals that are very

active and never build up to high concentrations.
To show that the above kinetics or mechanism can yield this empirical rate expression of
3/2 order, let us apply the PSS approximation on all the free radicals:

0 ¼ r

CH 3 ¼

r

1

r

2 þ

r

3 2

r

$ 4

CH 3 2

0 ¼ k

1 ½

CH CHO k

2 ½$

CH

3 ½

CH CHO þ k

3 ½

CH CO $2 k

4 ½$

(6.66)

3 3 3

0 ¼ r ¼ r

1 2

r

$ CHO 5

2 0 ¼ k

1 ½

CH CHO 2 k

5 ½$

CHO (6.67)

3

0 ¼ r ¼ r

2

r

$ CH 3 CO 3

0 ¼ k

2 ½$

CH

3 ½

CH CHO k

3 ½

CH CO $ (6.68)

3 3

And the overall rate of reaction,

r ¼ r CH 4 ¼ r

2 ¼

k

3 ½$

CH

3 ½

CH CHO (6.69)

3