Page 191 - Introduction to chemical reaction engineering and kinetics

7.4 Problems for Chapter 7 173

(b) What is the order of the dependence of the efficiency (f) of radical conversion to Pl
on CM?
7-14 In the comparison of organic peroxides as free-radical polymerization initiators, one of the
measures used is the temperature (T) required for the half-life (ti,z) to be 10 h. If it is desired
to have a lower T, would ri/2 be greater or smaller than 10 h? Explain briefly.
7-15 Starting from equations 7.3-3 to -6 applied to a constant-volume RR, for polymerization rep-
resented by the step-change mechanism in Section 7.3.2, show that the product distribution
can be calculated by sequentially solving the differential equations:

+ 2kcM* + k2c; = 0
dt

dcp,
- + k%m, = kcM+-, ; r = 2,3, . . (7.3-17)
dt

7-16 This problem is an extension of problems 7-10 and 7-11 on the dehydrogenation of ethane to
produce ethylene. It can be treated as an open-ended, more realistic exercise in reaction mech-
anism investigation. The choice of reaction steps to include, and many aspects of elementary
gas-phase reactions discussed in Chapter 6 (including energy transfer) are significant to this
important industrial reaction. Solution of the problem requires access to a computer software
package which can handle a moderately stiff set of simultaneous differential equations. E-Z
Solve may be used for this purpose.
(a) Use the mechanism in Section 6.1.2 and the following values of the rate constants (units
of mol, L, s, J, K):
(1) C2H6 ---) 2CH; ; kl = 5 X 1014exp(-334000/RZ’)
(2) CHj + C2H,j + C2H; + CH4 ; k2 = 4 X 1013 exp(-70300/RT)
(3) C2H; + C2& + H* ; k3 = 5.7 X 10” exp(-133000/RT)
(4) H’ + C2H6 --z C2H; + Hz ; k4 = 7.4 X 1014exp(-52800/RT)
(5) H’ + C2H; --f C2H6 ; k5 = 3.2 X 1013
(i) Solve for the concentration of CsHs radicals using the SSH, and obtain an expression
for the rate of ethylene production.
(ii) Obtain a rate expression for methane production as well as an expression for the
reaction chain length.
(iii) Integrate these rate expressions to obtain ethane conversion and product distribution
for a residence time (t) of 1 s at 700°C (1 bar, pure C2H6). Assume an isothermal,
constant-volume batch reactor, although the industrial reaction occurs in a flow sys-
tem with temperature change and pressure drop along the reactor.
(iv) From initial rates, what is the reaction order with respect to ethane?
(v) What is the overall activation energy?
(b) Integrate the full set of differential equations.
(i) Compare the conversion and integral selectivities in this calculation with those in
pati (4.
(ii) Compare the ethyl radical concentrations calculated in the simulation with those
predicted by the SSH.
(iii) Approximately how long does it take for the ethyl radicals to reach their pseudo-
steady-state values in this calculation?
(iv) Run two different simulations with different ethane pressures and take the initial
rates (evaluated at 100 ms) to obtain a reaction order. Compare with part (a).
(v) Run two different simulations with two different temperatures: take the initial rates
(evaluated at 3% conversion) and calculate the activation energy. Compare with the
answer from part (a).