9.10
RATES OF REACTION AND THE RATE LAW
I
H
H C H
- OH
x
(a)
I
H
H
C
H
- OH
x
(b)
I
H
H C H
HO
(c)
The
rate of a reaction
(R) is the rate at which a reactant is consumed or the rate at which
a product is produced. Reaction rates frequently
have units of molarity per unit time. The
rate of reaction depends on the rate at which
the transition state is reached, which in turn
depends on the following two factors:
Figure 9.7 Not all collisions lead to the transition state
- The
collision frequency
is the number of collisions between reactant particles per second in
a liter of solution. It is proportional to the product of their
molar concentrations
. Thus, the
frequency of collisions between CH
I molecules and OH 3
1- ions is proportional to [CH
I][OH 3
1- ].
Collisions (a) and (b) do not lead to the transition state because the reactants are not aligned correctly. Only collision (c) can lead to a C-O bond and the transition state.
- The
fraction of collisions leading to the transition state
depends upon the orientation of
the molecules at collision, their kinetic ener
gies, and the activation energy for the reaction
. As
shown in Figure 9.7, the reactants have the corre
ct orientation to achi
eve the transition state
in only a fraction of their collisions. In additio
n to having the correct orientation, the molecules
must have sufficient thermal energy to overco
me the activation energy for the reaction.
The collision frequency and the fraction of collis
ions that result in the transition state
are combined into a
rate law
for the reaction,
which is a mathematical expression that
describes the rate of the reaction. For a one-st
ep process,* the rate law is the product of the
concentrations of the reactants (the collision frequency) times a
rate constant
(the fraction
of collisions leading to the transition state). Thus, the rate law for CH
I + OH 3
1-^ →
CH
OH 3
- I
1- is R
= k[CH
I][OH 3
1-
] where
k is the rate constant for the forward reaction. The
rate
constant is a function of the activation
energy and the thermal en
ergy (temperature); it
always increases with temperature
. For two reactions with comparable orientation
requirements, the one with the larger rate
constant has the smaller activation energy.
* The processes discussed in this section are all simple, one-step
reactions that can be treated in
the manner discussed here.
However, most chemical reactions occur in more than one step, and the rate law of such reactions
must be determined experimentally.
Example 9.8 What is the ratio of collision frequencies for CH
OH + I 3
1- collisions to CH
I + OH 3
1-^
collisions in a solution that is 1.0 M in CH
OH, 3.0 M in I 3
1-, 0.1 M in CH
I and 0.2 M in 3
OH
1-? Each collision frequency is proportional to the product of the conc
entrations of the
colliding particles, so the ratio is obtained as follows:
frequency of CH^
OH + I 3
1- collisions
frequency of CH
I + OH 3
1- collisions
=
[CH
OH][I 3
1-]
[CH
I][OH 3
1-]
=
(1.0)(3.0)(0.1)(0.2)
= 150
At these concentrations, CH
OH and I 3
1- collisions occur 150 times more frequently than
those between CH
I and OH 3
1-.
Chapter 9 Reaction Energetics
201
© by
North
Carolina
State
University