Page 190 - Introduction to chemical reaction engineering and kinetics

172 Chapter 7: Homogeneous Reaction Mechanisms and Rate Laws

7-8 A possible free-radical chain mechanism for the thermal decomposition of acetaldehyde (to
CH4 and CO) is the Rice-Herzfeld mechanism (Laidler and Liu, 1967):

CH3CH0 2 CHj + CHO*

CHO’ 2 CO + H’
H’ + CHsCHO 2 CH3CO’ + H2

CHj + CHsCHO 2 CH4 + CH&O*
CH3CO’ 5 CHj + CO
ks
2CH; + CZHe

(a) Which species are the chain carriers?
(b) Classify each step in the mechanism.
(c) Derive the rate law from the mechanism for CHsCHO + CH4 + CO, and state the order
of reaction predicted. Assume Hz and CzH6 are minor species.
7-9 From the mechanism given in problem 7-8 for the decomposition of acetaldehyde, derive a
rate law or set of independent rate laws, as appropriate, if Hz and CzH6 are major products
(in addition to CH4 and CO).
7-10 From the mechanism given in Section 6.1.2 for the dehydrogenation of CzH6, obtain the rate
law for CzH6 + Cz& + Hz (assign rate constants ki, . . , kg to the five steps in the order
given, and assume C& is a minor product).
7-11 Repeat problem 7-10 for a rate law or set of independent rate laws, as appropriate, if CH4 is
a major product.
7-12 (a) For the C& oxidative-coupling mechanism described in Section 7.2, verify the rate laws
given in equations 7.2- 1 and -2, and show that 7.2-3 is consistent with these two equations.
(b) Show (i) that equation 7.2-1 reduces to 7.2-3 if CO2 is not formed; and (ii) that 7.2-2
reduces to 7.2-3 if CzH6 is not formed.
v
(c) From the rate laws in (a), derive an expression for the instantaneous fractional yield (se-
“OF
0 7-13 In a certain radical-addition polymerization reaction, based on the mechanism in Example
lectivity) of C2H6 (with respect to CH4).
(d) Does the selectivity in (c) increase or decrease with increase in coo?
7-4, in which an initiator, 1, is used, suppose measured values of the rate, (-rM), at which
monomer, M, is used up at various concentrations of monomer, CM, and initiator, ct, are as
follows (Hill, 1977, p. 125):

c&m01 mm3 ct/mol m-3 (- &/mol mm3 s-l
9.04 0.235 0.193
8.63 0.206 0.170
7.19 0.255 0.165
6.13 0.228 0.129
4.96 0.313 0.122
4.75 0.192 0.0937
4.22 0.230 0.0867
4.17 0.581 0.130
3.26 0.245 0.0715
2.07 0.211 0.0415

(a) Determine the values of k and n in the rate law (-TM) = kci’2c&.