Chemistry - A Molecular Science

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

1. 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.

2. 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

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Carolina

State

University