Physical Chemistry , 1st ed.

By defining Vand Kas

Vk 2 [E 0 ] and K

k 1

k



1

k 2

 (20.67)

we can write the reciprocalof the rate, 1/rate, as



ra

1

te



V

1



k 2 [

K

E 0 ]



[

1

S]

 (20.68)

A plot of 1/rate versus 1/[S], the inverse of the substrate concentration, gives a

straight line with slope K/(k 2 [E 0 ]) and y-intercept 1/V. Equation 20.68 is called

the Michaelis-Menten equation,and a plot of 1/rate versus 1/[S] is called a

Lineweaver-Burk plot.An example of such a plot is shown in Figure 20.18.

This is one common application of the steady-state approximation to enzyme

kinetics.

20.9 Chain and Oscillating Reactions

The kinetics of certain kinds of reactions are interesting enough that they de-

serve special attention. In this section, we will consider two interesting kinds

of reaction kinetics.

Consider a gas-phase reaction in which one or two reactant species are con-

verted into species that are very reactive themselves. For example, a molecule

of bromine can be broken into two individual bromine atoms, each with an

unpaired electron:

Br–Br →BrBr (a)

In turn, each of these bromine atoms, which are free radicals, can react with

another species, say a hydrogen molecule:

BrH 2 →H–Br H (b)

A new free radical, in this case a hydrogen atom with an unpaired electron, is

generated. This reactive free radical can now react with an unreacted bromine

molecule to make a product molecule and another free radical:

HBr 2 →H–Br Br (c)

The newly generated bromine atom, a free radical, can react with another hy-

drogen molecule as shown in reaction b, after which the new hydrogen atom

can react with another bromine molecule as given in reaction c, and so forth.

Such a reaction cycle can continue undiminished until one reactant is virtually

depleted, or until two free radicals combine to make a molecule that is rela-

tively unreactive, like each of these:

BrBr→Br–Br

BrH→H–Br (d)

HH→H–H

This series of kinetic steps typifies a chain reaction. A chain reactionis a reac-

tion whose mechanism consists of steps whose products are intermediates that

react to form other intermediates, usually in an apparently cyclical fashion.

Reaction a, which started the chain reaction in this example, is called an initi-

ation reaction(or initiation step). Reactions b and c of this example react one

intermediate and produce another intermediate. They are called propagation

714 CHAPTER 20 Kinetics

1

[S]

(^1) rate
Slope k
2 [E 0 ]
K
Intercept V^1
Figure 20.18 A Lineweaver-Burk plot of a re-
action that follows the Michaelis-Menten equa-
tion. A graph of 1/rate versus 1/[S] should give
a straight line with slope K/(k 2 [E 0 ]) and inter-
cept 1/V.