Page 170 - Introduction to chemical reaction engineering and kinetics

152 Chapter 6: Fundamentals of Reaction Rates

(1) Almost all chemical reactions involve a sequence of elementary steps, and do not
occur in a single step.
(2) The elementary steps in gas-phase reactions have rate laws in which reaction
order for each species is the same as the corresponding molecularity. The rate
constants for these elementary reactions can be understood quantitatively on
the basis of simple theories. For our purpose, reactions involving photons and
charged particles can be understood in the same way.
(3) Elementary steps on surfaces and in condensed phases are more complex be-
cause the environment for the elementary reactions can change as the composi-
tion of the reaction mixture changes, and, in the case of surface reactions, there
are several types of reactive sites on solid surfaces. Therefore, the rate constants
of these elementary steps are not really constant, but can vary from system to
system. Despite this complexity, the approximation of a single type of reaction
step is useful and often generally correct.
In the following chapter, rate laws based on reaction mechanisms are developed.
Although some of these are of the simple “generic” form described in Chapters 3 and
4, others are more complex. In some cases of reactor design, only an approximate fit
to the real reaction kinetics is required, but more often the precision of the correct law
is desirable, and the underlying mechanistic information can be useful for the rational
improvement of chemical processes.

6.8 PROBLEMS FOR CHAPTER 6

6-1 In each of the following cases, state whether the reaction written could be an elementary reac-
tion, as defined in Section 6.1.2; explain briefly.
(a) SO2 + iO2 + SO3
(b) I’ + I’ + M --f Iz + M
(c) 2C3H6 + 2NHs + 302 + 2CsHsN + 6Hz0

(d) C2H4 + HZ + C2H; + H*
6-2 Calculate the fraction of ideal-gas molecules with translational kinetic energy equal to or greater
than 5000 J mol-’ (a) at 300 K, and (b) at 1000 K.
6-3 Show that, for the bimolecular reaction A + B --f products, ksCT is given by equation 6.4-17.
6-4 Some of the results obtained by Hinshelwood and Askey (1927) for the decomposition of
dimetbyl ether, (CHs)20 (A), to CI&,, CO and Hz at 777.2 K in a series of experiments in
a constant-volume batch reactor are as follows:
P,/kFa 7 . 7 12.1 22.8 34.8 52.5 84.8
1500 1140 824 670 590 538
t31ls
Each pair of points, P, and tst, refers to one experiment. P, is the initial pressure of ether (no
other species present initially), and t31 is the time required for 31% of the ether to decompose.
(a) If the reaction is first-order, calculate the value of the rate constant ku,ilS-’ for each exper-
iment.
(b) Test, using the differential method, whether the experimental data conform to the Linde-
mann hypothesis for a unimolecular reaction, and, if appropriate, calculate the values of
the rate constants in the unimolecular mechanism as far as possible; use units of L, mol, s.
6-5 Repeat problem 6-4 using an integral method. For this purpose, substitute the rate law into the
material balance for a constant-volume BR, and integrate the resulting expression to relate f~
and t. Then, with CA0 as a parameter (corresponding to P, in problem 6-4) show that, for a