Page 189 - Introduction to chemical reaction engineering and kinetics

7.4 Problems for Chapter 7 1 7 1

7-4 The oxidation of NO to NOz, which is an important step in the manufacture of nitric acid by
the ammonia-oxidation process, is an unusual reaction in having an observed third-order rate
constant (k~o in (-mo) = k~&oco,) which decreases with increase in temperature. Show
how the order and sign of temperature dependence could be accounted for by a simple mech-
anism which involves the formation of (NO)* in a rapidly established equilibrium, followed
by a relatively slow bimolecular reaction of (NO)2 with 02 to form NOz.
7-5 (a) Verify the rate law obtained in Example 7-3, equation 7.1-3.
(b) For the HZ + Brz reaction in Example 7-3, if the initiation and termination steps involve a
third body (M), Br2 + M -+ 2Bf + M, and 2Br + M -+ Br;! + M, respectively, what effect
does this have on the rate law in equation 7.1-3? (The other steps remain as in Example
7-3.)
7-6 The rate of decomposition of ethylene oxide, C&40(A), to CI& and CO, has been studied
by Crocco et al. (1959) at 900-1200 K in a flow reactor. They found the rate constant to be
given by

kA = 10” exp(-21,00O/T)
in s-l (with Tin K). They proposed a free-radical chain mechanism which involves the initial
decomposition of C&O into radicals (C2HsO’ and HO), and propagation steps which involve
the radicals CzHaO* and CHj (but not HO) in addition to the reactant and products; termination
involves recombination of the chain carriers to form products that can be ignored.
(a) Write the following:
(i) an equation for the overall stoichiometry;
(ii) the initiation step in the mechanism;
(iii) the propagation steps;
(iv) the termination step.
(b) Derive the rate law from the steps of the mechanism, and state whether the form agrees
with that observed. Clearly state any assumption(s) made.
(c) Estimate the activation energy (EAT) for the initiation step, if the sum of the activation
energies for the propagation steps is 126,000 J mol-‘, and E,J for the termination step is
0.
7-7 Suppose the mechanism for the thermal decomposition of dimethyl ether to methane and
formaldehyde

CH30CH3 + CHq + HCHO (4

is a chain reaction as follows:

CH30CH3 2 CH; + OCH; El

CH; + CH30CH3 2 CHq + CH20CH; E2

CH20CH; 2 CH; + HCHO E3
CH; + CH20CHj 2 CH3CH20CH3 E4

(a) Show how the mechanism is consistent with the stoichiometry for (A).
(b) Identify any apparent deficiencies in the mechanism, and how these are allowed for by
the result in (a).
(c) Derive the rate law from the mechanism, clearly justifying any assumption(s) made to
simplify it.
(d) Relate the activation energy, EA. of the reaction (A) to the activation energies of the indi-
vidual steps.