Physical Chemistry Third Edition

12.3 The Temperature Dependence of Rate Constants 533

reaction of part a and the value of the rate constant at

40 ◦C. State any assumptions.

12.5 For the reaction of C 2 H 5 Br and (C 2 H 5 ) 2 S at 20.00◦Cin
benzyl alcohol, the rate constant is equal to 1. 44 ×
10 −^8 L mol−^1 s−^1. The viscosity of benzyl alcohol at this
temperature is 5. 8 × 10 −^3 kg m−^1 s−^1.
a.Find the value that the rate constant would have if the
reaction were diffusion-controlled. Assume a diameter
of 500 pm5.0 Å for each reactant.
b. What fraction of the encounters leads to reaction?

12.6 For the reaction at 25.00◦C in methanol

CH 3 Br+I−−→CH 3 I+Br−

the rate constant is equal to 9. 48 × 10 −^4 L mol−^1 s−^1.

The viscosity of methanol at this temperature is

5. 47 × 10 −^4 kg m−^1 s−^1.

a. Find the value that the rate constant would have if the

reaction were diffusion-controlled. Assume a diameter

of 400 pm 4 .0 Å for each reactant.

b.What fraction of the encounters leads to reaction?

12.3 The Temperature Dependence

of Rate Constants

The Arrhenius Relation

Reaction rates depend strongly on temperature, nearly always increasing when the

temperature is raised. The first quantitative studies of the temperature dependence of

rate constants were published in the last half of the 19th century, and various empirical

formulas were proposed.^5 TheArrhenius relation, which was proposed in 1889, is

widely used because it is based on a physical picture of elementary processes and

because it usually fits experimental data quite well.

Svante Arrhenius, 1859–1927, was a
Swedish chemist who won the 1905
Nobel Prize in chemistry for his theory
of dissociation and ionization of
electrolytes in solution.

Arrhenius postulated that only “activated” molecules (those with high energy) can

react and that the numbers of such activated molecules would be governed by the

Boltzmann probability distribution of Eq. (9.3-41). This assumption leads to the Arrhe-

nius relation:

kAe−εa/kBT (12.3-1)

The quantityεais the energy that the molecules must have in order to react and is called

theactivation energy. The temperature-independent factorAis called thepreexponen-

tial factor. We can express Eq. (12.3-1) in the form

kAe−Ea/RT (12.3-2)

whereEaNAvεais themolar activation energyand whereRkBNAvis the ideal

gas constant. Experimental molar activation energy values are usually in the range from

50 to 200 kJ mol−^1 , somewhat smaller than energies required to break chemical bonds.

These magnitudes seem reasonable if we picture the activation process as partially

breaking one bond while partially forming another.

(^5) K. J. Laidler,op. cit., p. 40ff. (note 3).