Physical Chemistry , 1st ed.

which can be rearranged to

k

e

c

2

°

k

h

T

eEA/RTeS*/R (20.84)

Equating the activation-energy exponentials in equation 20.84 and the Arrhenius

equation, the rest of the terms in equation 20.81 must be related to the pre-

exponential factor. Thus, using an experimentally known pre-exponential fac-

tor, we can estimate the entropy change that accompanies the formation of the

transition state using the equation

A

e

c

2

°

k

h

T

eS*/R (20.85)

Thus, we do find some connections between kinetics and thermodynamics

after all.

Example 20.13

For the two-step process

H H 2 →H 3 →H 2 H

H 3 is the transition state for this hydrogen transfer reaction. If the pre-expo-

nential factor were found to be 5.4 107 m^3 /(mols) at 25.0°C, predict the

value ofS*. Comment on its sign and magnitude. Use a standard concen-

tration of 1 M 1 mol/L (1000 mol)/m^3.

Solution

The pre-exponential factor has been expressed in standard units, but as al-

ways we should be careful about the units we use. Using equation 20.85, we

have

5.4 107 

m

m

ol

3

s

e

c

2

°

k

h

TeS*/R

All the fundamental constants have known values, so substituting:

5.4 107 

m

m

ol

3

s



exp

8.314



J/

S

(m

*

olK)



We get, with initial canceling of the joule and kelvin units on the right side:

5.4 107 

m

m

ol

3

s

4.589 1010 

m

m

ol

3

s

exp

8.314



J/

S

(m

*

olK)



The units m^3 /(mols) appear on both sides, so they cancel. Rearranging:

1.2 10 ^3 exp

8.314



J/

S

(m

*

olK)



Taking the natural logarithm of both sides and solving:

6.75

8.314



J/

S

(m

*

olK)



S*56.1 

mo

J

lK



e^2 (1.381 10 ^23 J/K)(298 K)(m^3 )



1000 mol(6.626 10 ^34 Js)

724 CHAPTER 20 Kinetics