Page 177 - Introduction to chemical reaction engineering and kinetics

7.1 Simple Homogeneous Reactions 159

Chain mechanisms may be classified as linear-chain mechanisms or branched-chain
mechanisms. In a linear chain, one chain carrier is produced for each chain carrier re-
acted in the propagation steps, as in steps (3) and (4) above. In a branched chain, more
than one carrier is produced. It is the latter that is involved in one type of explosion (a
thermal explosion is the other type). We treat these types of chain mechanisms in turn
in the next two sections.

7.1.3.1 Linear-Chain Mechanisms
We use the following two examples to illustrate the derivation of a rate law from a
linear-chain mechanism.

(a) A proposed free-radical chain mechanism for the pyrolysis of ethyl nitrate,
C,HsONO, (A), to formaldehyde, CH,O (B), and methyl nitrite, CH,NO, (D),
A + B + D, is as follows (Houser and Lee, 1967):
kl
A-+C,H,O’ + NO, (1)
C,H,O’ % CH; + B (2)
k3
CHj + A-D + C,H,O* (3)
2CzH500&H,CH0 + C,H,OH (4)

Apply the stationary-state hypothesis to the free radicals CH; and C,HsO* to derive
the rate law for this mechanism.
(b) Some of the results reported in the same investigation from experiments carried out
in a CSTR at 250°C are as follows:
c,/mol mP3 0.0713 0.0759 0.0975 0.235 0.271
(- rA)/mol rnP3s-r 0.0121 0.0122 0.0134 0.0209 0.0230
Do these results support the proposed mechanism in (a)?
(c) From the result obtained in (a), relate the activation energy for the pyrolysis, EA, to
the activation energies for the four steps, EA1 to EA4.
(d) Obtain an expression for the chain length CL.

SOLUTION

(a) The first step is the chain initiation forming the ethoxy free-radical chain carrier,
C,H,O’, and NO,, which is otherwise unaccounted for, taking no further part in the mech-
anism. The second and third steps are chain propagation steps in which a second chain car-
rier, the methyl free radical, CH;, is first produced along with the product formaldehyde
(B) from C,H,O’, and then reacts with ethyl nitrate (A) to form the other product, methyl
nitrite (D), and regenerate C,H,O’. The fourth step is a chain-breaking step, removing
C,H,O.. In a chain reaction, addition of the chain-propagation steps typically gives the
overall reaction. This may be interpreted in terms of stoichiometric numbers (see Example
7-1) by the assignment of the value 1 to the stoichiometric number for each propagation
step and 0 to the other steps.
To obtain the rate law, we may use (-Y*) or rn or rn. Choosing r,, we obtain, from
step (21,

rB = 'bCc,H50*