Physical Chemistry Third Edition

540 12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms

12.11The gas-phase decomposition of acetaldehyde, CH 3 CHO,
obeys second-order kinetics. Some values of the rate
constant are:

T/K k/L mol−^1 s−^1 T/K k/L mol−^1 s−^1

703 0.0110 811 0.79

733 0.0352 836 2.14

759 0.105 865 4.95

791 0.343

a.Find the activation energy and the preexponential

factor.

b.Find the value of the rate constant at 500◦C.

c.If the initial pressure of pure acetaldehyde is equal to

0.500 atm at 500◦C, find the time for 50.0% of the

acetaldehyde to react.

12.12For the reaction of I 2 and N 2 CHCO 2 C 2 H 5 in CCl 4 at
298.15 K,k 3. 28 × 10 −^4 L mol−^1 s−^1 , and at
323.15 K,k 4. 60 × 10 −^3 L mol−^1 s−^1. Find the
activation energy and the preexponential factor in the
Arrhenius expression. Do you think that the reaction is
diffusion-controlled or activation-controlled? Explain
your answer.

12.13The hydrolysis of 2-chlorooctane in 80% ethanol obeys
pseudo first-order kinetics. At 0◦C the rate constant equals

1. 06 × 10 −^5 s−^1 and at 25◦C it equals 3. 19 × 10 −^4 s−^1.
   a. Find the values of the parameters in the Arrhenius
   formula for this reaction.
   b. Find the value ofkat 15◦C.

Find the half-time of the reaction at 15◦C, neglecting

any back reaction.

12.14The decomposition of benzenediazonium fluorborate in

aqueous HCl solution obeys pseudo first-order kinetics.

The rate constant is measured to be equal to 4. 04 ×

10 −^5 s−^1 ± 0. 12 × 10 −^5 s−^1 at 25◦C and equal to

3. 18 × 10 −^4 s−^1 ± 0. 09 × 10 −^4 s−^1 at 40◦C. Calculate

the activation energy and estimate the error in the

activation energy, assuming that the errors in the

temperature are negligible.

12.15 a.The rate constant for the bimolecular elementary

gaseous process

CO+O 2 −→CO 2 +O

is equal to 1. 22 × 105 L mol−^1 s−^1 at 2500 K and is

equal to 3. 66 × 105 L mol−^1 s−^1 at 2800 K. Find the

value of the activation energy and the value of the

preexponential factor.

b.Assuming a hard-sphere diameter of 350 pm for O 2

and a hard-sphere diameter of 360 pm for CO,

calculate the value of the steric factor in the collision

theory.

12.16Apply the collision theory to calculate the rate constant

for the gas-phase reaction

2NO−→N 2 +O 2

at 500.0 K. The effective hard-sphere diameter of NO

molecules is 205 pm. Assume thatEcis equal to

293 kJ mol−^1 and that the steric factor is equal to 1.

12.4 Reaction Mechanisms and Rate Laws

There is no direct way to take an experimentally determined rate law for a chemical

reaction and deduce the correct mechanism from it. For example, the reaction

H 2 +I 2 −→2HI

is second order overall, first order with respect to each reactant. The rate law could

correspond to a bimolecular elementary reaction, and this was once thought to be

the case. The reaction is now thought to proceed by several competing mechanisms,

including the elementary mechanism.^8

Although we cannot directly deduce a mechanism from a rate law, we can often

deduce a rate law from an assumed mechanism and can then compare this equation

with the experimental rate law. If the two do not match, the proposed mechanism must

(^8) K. J. Laidler,op. cit., p. 297ff (note 3); Sullivan,J. Chem. Phys., 46 , 73 (1967).