20.7 & 20.8 Mechanisms and Steady States
20.51. (a)Suggest a mechanism for the bromination of
ethane:
Br 2 CH 3 CH 3 →CH 3 CH 2 Br HBr(b)Would you expect that this reaction might go faster or
slower than the chlorination of methane? (Hint:consider the
strengths of the bonds involved in the initial steps of the
mechanism.)
20.52.Derive equation 20.62.
20.53.Explain why a “consecutive reaction” analysis would
not be appropriate for a mechanism in which the second step
is the RDS. That is, why can’t we write that mechanism in
terms of A →B →C in this case?
20.54.Determine a rate law for the chlorination of methane
assuming that the first step is the rate-determining step.
20.55.Determine a rate law for the chlorination of methane
assuming that the second step is the rate-determining step
and that the first step can be approximated by the steady-
state approximation. What is the difference between the an-
swer here and the answer for the previous exercise?
20.56.A proposed mechanism for the gas-phase chlorination
of methane is
Cl 2 CH 4 →CH 4 Cl Cl
CH 4 Cl→CH 3 HCl
CH 3 Cl 2 →CH 3 Cl Cl
ClCH 4 →CH 3 HCl
and so onSuppose the first step is the RDS. What is the expected rate
law in terms of the original reactants, Cl 2 and CH 4? How would
you determine if this mechanism might be a potentially cor-
rect (or, for that matter, a potentially incorrect) one?
20.57.Consider the proposed mechanism in the previous
problem. Now assume that the second step is the RDS. Use
the steady-state approximation to determine a rate law in
terms of the original reactants. Nowhow would you determine
if this mechanism might be correct?
20.58.Many gas-phase reactions require some inert body,
usually represented as M, to absorb or supply energy in a col-
lision in order to proceed. In the spontaneous decomposition
of ozone, O 3 , we can suggest the mechanism
O 3 M→O 3 * MO RDS
3 *→O 2 O
OO 3 →2O 2for the overall reaction
2O 3 →3O 2In the mechanism, O 3 * refers to an ozone molecule in some
energetically excited state that can react spontaneously to form
O 2 and O atoms. Determine the rate law of the proposed
mechanism in terms of O 3 and M, where the second step is the
rate-determining step. Will adding an inert gas like Ar to a sam-
ple of ozone increase or decrease the rate of the reaction?
20.59.Show that equation 20.68 is equivalent to equation
20.64.
20.60.Carbonic anhydrase, an enzyme whose substrate is
CO 2 , has a Kof 12 mM. When the concentration of CO 2 is
1.4 10 ^4 M, the rate of reaction between carbonic anhy-
drase and CO 2 is 2.72 10 ^7 mol/s, and when the concen-
tration of CO 2 is 2.2 10 ^4 M, the rate is 4.03 10 ^7 mol/s.
If the reaction follows Michaelis-Menten kinetics, what is Vfor
this reaction?
20.61.Show that another form of the Michaelis-Menten equa-
tion israte KV[S[]S]
20.62.When [S] K, what is the value of the rate of a reac-
tion that follows Michaelis-Menten kinetics? Considering the
answer, what use do you think this might be?20.9 Chain and Oscillating Reactions
20.63.Most halogenation reactions of hydrocarbons proceed
via a free-radical chain reaction mechanism. Of the halogens
Cl 2 , Br 2 , and I 2 , which initiation reaction should proceed most
easily? Explain your answer.
20.64.The free-radical reaction H 2 I→HI Hhas a pre-
exponential factor of 2.4 1011 M^1 s^1 and an activation
energy of 142 kJ/mol. Predict its rate constant at 400 K.
20.65.Pyrolysis involves heating compounds to break them
into smaller molecules, and typically involves free-radical chain
reactions. Pyrolysis of crude oil fractions is a common method
of making smaller hydrocarbons from large-chain hydrocar-
bons. Pyrolysis of ethane, C 2 H 6 , forms ethylene and hydrogen
gases (C 2 H 4 and H 2 ) as the primary products. Suggest a mech-
anism for this pyrolysis reaction, labeling your reactions as ini-
tiation, propagation, and termination steps.
20.66.Nuclear fission reactions can also proceed by chain re-
action. Consider an ideal nuclear fission reaction as(^235) U (^1) n → (^92) Kr (^141) Ba 21 n
Suggest conditions under which this reaction does not pro-
ceed; conditions under which this reaction maintains a chain
reaction; and conditions under which significant branching
occurs (leading to an explosion).
20.67.Label the elementary processes for the reaction be-
tween H 2 and O 2 (see section 20.7) as initiation, propagation,
branching, or termination reactions.
20.68.Write the rate laws for elementary processes for the
proposed mechanisms 1 and 2 of oscillating reactions.
20.69.What are the rate laws of mechanisms 1 and 2 for
oscillating reactions if the second reactions were the rate-
determining steps?
20.10 Transition-State Theory
20.70.Estimate G* for an elementary process whose rate
constant kis 8.5 10 ^1 M^1 s^1 at 450 K.
Exercises for Chapter 20 729