Physical Chemistry Third Edition

12.3 The Temperature Dependence of Rate Constants 539

The activation energies are somewhat smaller than for activation-limited reactions,

often near the values for the energies of activation for diffusion processes.

EXAMPLE12.9

For the reaction

2I→I 2

in carbon tetrachloride, the value of the rate constant at 23◦Cis7. 0 × 106 m^3 mol−^1 s−^1 .At

30 ◦C, the value is 7. 7 × 106 m^3 mol−^1 s−^1. Find the activation energy and compare it with

the activation energy for the viscosity of carbon tetrachloride in Example 10.17.

Solution

Ea

Rln(k 2 /k 1 )

1

T 1

−

1

T 2



(8.3145 J K−^1 mol−^1 )ln

(

7. 7 × 106 m^3 mol−^1 s−^1

7. 0 ×106 m^3 mol−^1 s−^1

)

1

296 K

−

1

303 K

10200 J mol−^1

This value is nearly the same as that of Example 10.17, 10400 J mol−^1.

PROBLEMS

Section 12.3: The Temperature Dependence of Rate
Constants

12.7 The first-order rate constant for the thermal

decomposition of 3-methylcyclobutanone has the values^7

T/K k/ 10 −^4 s−^1 T/K k/ 10 −^4 s−^1

552.24 0.4259 589.05 6.459

561.81 0.8936 596.96 11.201

570.41 1.707 606.14 20.83

579.35 3.207

a.Find the value of the activation energy and the value

of the preexponential factor.

b.Find the value of the rate constant at 600.0 K.

c.Find the time for 80.0% of the reactant to react at

600.0 K.

12.8 The rate constant for the gas-phase thermal

decomposition of ethyl bromide (bromoethane) is equal

to 0.1068 s−^1 at 500◦C and equal to 6.4529 s−^1 at 600◦C.

(^7) H. M. Frey, H. P. Watts, and I. D. R. Stevens,J. Chem. Soc. Faraday
Trans., 2, 83 , 601 (1987).
Find the parametersAandEain the Arrhenius expression
for this rate constant.
12.9For the reaction
H 2 +I 2 −→2HI
at 373.15 K, the rate constant is equal to 8. 74 ×
10 −^15 L mol−^1 s−^1. At 473.15 K, it is equal to
9. 53 × 10 −^10 L mol−^1 s−^1. Find the value of the
parametersAandEain the Arrhenius expression for the
rate constant.
12.10The gas-phase reaction
2N 2 O 5 −→4NO 2 +O 2
obeys first-order kinetics. The half-life of this reaction
equals 89500 s at 273.15 K and equals 795 s at 323.15 K.
a.Find the values of the preexponential factor and the
activation energy in the Arrhenius formula
b.Find the fraction of N 2 O 5 molecules remaining after
1.00 hour in a reaction carried out at 298.15 K.