Physical Chemistry Third Edition

562 12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms

processes. If the diffusion of the reactant molecules is a slow process compared to the

chemical part, the reaction is called a diffusion-limited or diffusion-controlled reaction.

If the rate is limited by the chemical part, the reaction is called activation-limited. In

either a gaseous or liquid-state elementary process, the molecularity of a substance is

equal to its order.

The empirical Arrhenius formula for the temperature dependence of elementary rate

constants was presented. This empirical formula was based on an idea that “activated”

molecules with high energy are necessary for the reaction to occur and that the popu-

lation of molecules with a characteristic activation energy is given by the Boltzmann

probability distribution. We presented the collision theory of bimolecular reaction rates,

using first the assumption that all collisions with a relative kinetic energy greater than

a critical value would lead to reaction.

A set of rate differential equations can be constructed for a mechanism, with one

equation for each elementary step. These simultaneous differential equations cannot

generally be solved analytically. We introduced two approximation schemes, the rate-

limiting-step approximation and the steady-state approximation. These schemes are

used to deduce an approximate rate law corresponding to a given mechanism. Example

mechanisms were studied, including chain reactions, in which propagation steps are

included in the mechanism. Suggestions were made for proposing a mechanism to

correspond to an experimental rate law.

ADDITIONAL PROBLEMS

12.38For the reaction

H 2 +I 2 −→2HI

the value of∆Uis− 8 .2kJmol−^1.

a.Find the value of the activation energy for the reverse

reaction, using information in the chapter.

b.Using thermodynamic data and the Gibbs–Helmholtz

equation, find the value of the equilibrium constant

for the reaction at 373.15 K. State any assumptions.

c.Find the value of the reverse rate constant at 373.15 K,

using your result from part b and data in the chapter.

12.39The thermal decomposition of ethyl bromide
(bromoethane) follows first-order kinetics, and the rate
constant is reported to be equal to 0.1068 s−^1 at 500◦C
and equal to 6.4529 s−^1 at 600◦C.
a.FindEaandAin the Arrhenius formula for this
reaction.
b.Find the value of the rate constant at 550◦C.
c.If the initial pressure of bromoethane at 550◦Cis
1.000 atm, find the partial pressure of bromoethane at
a reaction time of 10.00 s and at a reaction time of
100.0 s.

12.40The decomposition of ethyl bromide (bromoethane),

C 2 H 5 Br, in the gas phase is observed to be a first-order

reaction.

a.Assuming the Lindemann mechanism, write the

steps of the mechanism. The products are ethene,

C 2 H 4 , and hydrogen bromide, HBr. What must

be the case for the first-order rate law to be

observed?

b.The value of the rate constant at 527◦C is reported to

be equal to 0.0361 s−^1. Find the half-life of the

reaction at this temperature. Neglect any reverse

reaction.

c.If the original pressure of pure ethyl bromide is equal

to 1.00 atm, find the partial pressure of each

substance after an elapsed time of 60 seconds.

Neglect any reverse reaction.

d.The rate constant is reported to be equal to 1.410 s−^1

at 627◦C. Find the value ofEaandAin the Arrhenius

formula for the reaction.

12.41The gas-phase recombination of iodine atoms

proceeds in the presence of a second substance,

abbreviated by M:

I+I+M−→I 2 +M