Physical Chemistry , 1st ed.

into account the molecular orientations that are thought necessary to promote

a reaction (and so take into account what collision theory calls the steric fac-

tor) as well as the energy barrier that reactants must overcome to become

products (taking into account what collision theory calls the activation en-

ergy). Two new concepts are needed to understand transition-state theory. The

reaction coordinateis the conceptual pathway taken as the two reactant mole-

cules become products. Plots of total energy of the bimolecular system versus

the reaction coordinate are called reaction profiles,illustrated in Figure 20.24.

The maximum on the reaction profile curve represents the potential energy

barrier the reactants must overcome to react. The transition state(or activated

complex) is the intermediate structure of the two molecules that exists at the

potential energy maximum.†

A key point in transition-state theory is to calculate a theoretical rate con-

stant kfor the bimolecular elementary process. In terms of transition-state

theory, the bimolecular elementary process given as

A B →products

can be further broken down into two steps involving the transition state C*:

k

A B→C* (a)

k*

C*→products (b)

where kand k* represent the rate constants of the two imaginary steps,kfor

the bimolecular step a and k* for the unimolecular step b. If the reaction con-

sidered is in fact an elementary process, then from the ideas in section 20.7,

the rate laws can be written in terms of the stoichiometry of the reaction:

rate k[A][B] k*[C*] (20.70)

The second equality in equation 20.70 is a basic assumption that species A and

B become some transition state C* on their way to forming products, so the

rate of the elementary process can be expressed in terms of the concentrations

of original reactants orin terms of the amount of the transition state. We can

rewrite equation 20.70 in terms of the elementary process rate constant kas

k

k

[A

*[

]

C

[B

*

]

]

 (20.71)

The concentrations in equation 20.71 correspond to a concentration-based

equilibrium constant of the first reaction in the hypothetical two-step process,

so we define a dimensionless Kc* as



K

c°

c*

[A

[C

][

*

B

]

]

 (20.72)

where c° represents the standard concentration unit (that is, 1 M or a1) to

make the expression unitless. We rewrite the expression for k, equation 20.71, as

k

Kc*

c



°

k*



720 CHAPTER 20 Kinetics

Hrxn

EA

Progress of reaction (“reaction coordinate”)

Reactants

Products

Activated

complex/transition

state

Energy

Figure 20.24 A reaction profile is a diagram
illustrating the relationship between the energy of
the reactants, the energy of the products, and the
energy of the proposed intermediate species called
the activated complex or the transition state. The
difference between the energies of the reactants
and the transition state is Arrhenius’s proposed
activation energy.

†Although many references use the terms transition stateand activated complexinter-

changeably, other references define them differently. For example, some references refer to

the point on the reaction profile as the transition state, and to the molecular species at that

point as the activated complex itself. We will not worry about such subtleties here.