Physical Chemistry Third Edition

26.4 The Activated Complex Theory of Bimolecular Chemical Reaction Rates in Dilute Gases 1115

EXAMPLE26.13

The experimental value of the preexponential factor for the reaction

H 2 +I 2 →2HI

is equal to 1. 65 × 107 L mol−^1 s−^1. Find the value of∆S‡◦at 298.15 K.

Solution

From Eq. (26.4-23)

∆S‡◦Rln

(

hAc◦

ekBT

)

hAc◦

ekBT



(6. 62 × 10 −^34 J s)(1. 65 × 107 L mol−^1 s−^1 )(1 mol L−^1 )

(2.71828)(1. 38 × 10 −^23 JK−^1 )(298 K)

 9. 77 × 10 −^7

∆S‡◦(8.3145 J K−^1 mol−^1 )ln(9. 77 × 10 −^7 )−115JK−^1 mol−^1

Exercise 26.14

a.Explain why the entropy change of activation for a bimolecular gaseous reaction is generally

negative.

b.The collision theory of bimolecular gaseous chemical reactions provides a formula for the

preexponential factor:

ANAvπd 122

(

8 kBT

πμ

) 1 / 2

wheredis the collision diameter (the distance between the centers of the particles at collision)

andμis the reduced mass of the two particles:

μ

m 1 m 2

m 1 +m 2

Estimate the preexponential factor for a typical bimolecular elementary reaction in which two

atoms form a diatomic activated complex. Assume typical values of masses and the collision

diameter.

PROBLEMS

Section 26.4: The Activated Complex Theory of
Bimolecular Chemical Reaction Rates in Dilute Gases

26.31For the gas-phase reaction

CH 3 +CH 4 →CH 4 +CH 3

the Arrhenius preexponential factor equals

5 × 104 m^3 mol−^1 s−^1. Estimate∆S‡◦at 298 K. Explain

your value of∆S‡◦.

26.32Moss and Coady^10 give information about approximate

potential energy surfaces for several reactions,

(^10) S. J. Moss and C. J. Coady,J. Chem. Educ., 60 , 445 (1983).