Page 376 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.2 Searching for a Mechanism 347

For constant concentrations of CS2 and the third body, M, we take a ratio of Equa-
tion (E7-1.10) to (E7-1.9):
(E7-1.11)

which is of the same form as that suggested by Figure E7-1.1. Equation (E7-1.11)
and similar equations involving scavengers are called Stem-Volmer equations.

Now, let us proceed to some slightly more complex examples involving
chain reactions. A chain reaction consists of the following sequence:
1. Initiation: formation of an active intermediate.
Steps in a chain :2. Propagation or chain transfer: interaction of an active intermediate
reaction with the reactant or product to produce another active intermediate.
3. Termination: deactivation of the active intermediate.

Example 7-2 PSSH Applied to Thermal Cracking of Ethane

The thermal decomposition of ethane to ethylene, methane, butane, and hydrogen is
believed to proceed in the following sequence:
Init(iation:

>
(1) C2H6 bH6 2CH3* - r1C2H6 = klC2H6 [C2H61
Let kl = kIC2H6
Propagation:
k2
(2) CH,. +CZH6 * CH,+C,H,* -r2~~~~ I[c2H[61
[CH3*
k2
=
(3) C2H5* k3 ) C,H4+H* ‘3C2H, = k3 [C2H50 1
k4
(4) He fClH6 * C2H5. +H2 -r4C2H6 = k4 cHo I[c2H6jl
Temnination:

kS
(5) 2C2 H, ’ C4H10 -r5C2Hj. = kSCZHj[C1H50 I-’
Let k5 k5C2Hj.
(a) Use the, PSSH to derive a rate law for the rate of formation of ethylene.
(Ib) Compare the PSSH solution in Part (a) to that obtained by solving the com-
plete set of ODE mole balances.

Solution
Part (a) Developing the Rate Law
The rate of formation of ethylene is

(E7-2.1)