Physical Chemistry , 1st ed.

which is a rate law in terms of A, a species whose concentration is knowable

(as supposed a few paragraphs above).

Now: does this rate law agree with the experimentally determined rate law?

If it does, then this mechanism—and the identification of the rate-determin-

ing step—is plausible. (Not proven, just plausible.) If this rate law does not

agree with the experimentally determined rate law, then the mechanism is

probably incorrect.By using approximations such as the steady-state one, we

can try to judge whether a proposed mechanism is consistent with experi-

mental observations.

In a more detailed approach, we recognize that the forward and reverse re-

actions in the equilibrium have their own characteristic rate constants and rate

laws. For the reaction

k 1

A B

k 1

the forward reaction has the rate law

rate k 1 [A]

The reverse reaction has the rate law

rate k 1 [B]

If we consider the fact that the intermediate B has a steady-state concentra-

tion, then its concentration is not changing over time. The way to write this

using the tools of calculus is



d[

d

B

t

]

 0

The concentration of B increases due to the first step’s forward reaction, but

decreases due to the first step’s reverse reaction as well as the rate-determining

step’s forward progress. Since the overall change in [B] is zero by the steady-

state approximation, we can write (using k 2 for the rate constant of the second,

rate-determining step)



d[

d

B

t

]

 0 k 1 [A] k 1 [B] k 2 [B] (20.60)

(Recall that the RDS is B →k^2 C, so the rate of disappearance of B from this

process is simply k 2 [B].) For a reaction whose rate-determining step gives us

the rate law

rate k 2 [B] (20.61)

we can use equation 20.60 to substitute for the concentration of the interme-

diate B:

[B] 

k

k

1

1 [



A]

k 2



k 1

k



1

k 2

[A] (20.62)

Substituting for [B] in equation 20.61, we get for the rate law

rate k 2 

k 1

k



1

k 2

[A]

constant

Recognizing that the collection of constants equals some other constant, we

again combine them into a constant kand write the above rate law as

rate k[A] (20.63)

JQPJ

712 CHAPTER 20 Kinetics

