Atkins’ Physical ChemistryEighth Edition

Chapter 22 – Lecture 3

The Rates of Chemical Reactions

Copyright © 2006 by Peter Atkins and Julio de Paula

Peter Atkins • Julio de Paula

Rate Law: An experimentally determined law of nature

Mechanism: A theory of the sequence of events that may be occurring at the molecular level

The mechanism must agree with the rate law!!

Example of a mechanism once believed to be correct

H2 (g) + I2 (g) ⇌ 2 HI (g)

Rate law proposed in 1894:

ratef = kf [H2] [I2]

rater = kr [HI]2

Mechanism: Step (1) H2 + I2 ⇌ H2I2

Step (2) H2I2 → 2 HI

Rate law proposed in 1967:

]I[]HI['k

1

]I][H[krate

2

222

1

appears to be a simplebimolecular mechanism

Reaction Mechanisms

The overall progress of a chemical reaction can be represented at the molecular level by a series of simple elementary steps or elementary reactions

The sequence of elementary steps that leads to product formation is the reaction mechanism.

2NO (g) + O2 (g) 2NO2 (g)

N2O2 is detected during the reaction!

Elementary step: NO + NO N2O2

Elementary step: N2O2 + O2 2NO2

Overall reaction: 2NO + O2 2NO2

+

Elementary step: NO + NO N2O2

Elementary step: N2O2 + O2 2NO2

Overall reaction: 2NO + O2 2NO2

+

Intermediates - species that appear in a reaction mechanism but not in the overall balanced equation

An intermediate is always formed in an early elementary step and consumed in a later elementary step.

Molecularity of a reaction - the number of molecules reacting in an elementary step.

• Unimolecular reaction – elementary step with 1 molecule

• Bimolecular reaction – elementary step with 2 molecules

• Termolecular reaction – elementary step with 3 molecules

Unimolecular reaction A products rate = k [A]

Bimolecular reaction A + B products rate = k [A][B]

Bimolecular reaction A + A products rate = k [A]2

Rate Laws and Elementary Steps

Writing plausible reaction mechanisms:

• The sum of the elementary steps must give the overall balanced equation for the reaction.

• The rate-determining step should predict the same rate law that is determined experimentally.

Rate-determining step - the slowest step in the sequence of steps leading to product formation.

Fig. 22.16 Diagrams of possible reaction schemes

Fig. 22.17 Reaction profile when 1st step is RDS

The experimental rate law for the reaction between NO2 and CO to produce NO and CO2 is rate = k[NO2]2. The reaction is believed to occur via two steps:

Step 1: NO2 + NO2 NO + NO3

Step 2: NO3 + CO NO2 + CO2

What is the equation for the overall reaction?

NO2+ CO NO + CO2

What is the intermediate?

NO3

What can you say about the relative rates of steps 1 and 2?

rate = k[NO2]2 is the rate law for step 1 so step 1 must be slower than step 2

Fig. 22.8 Approach of concentrations to their equilibrium values

For the reaction: A ⇌ B

• In practice, most kineticstudies are on reactionsfar from equilibrium

• ∴ Reverse reactionsare unimportant

Fig. 22.13 Concentrations of A, I and P with time

A → I → P

Consumption of A is ordinary1st-order decay:

tko

ae]A[]A[

Note that the concentration of Irises to a maximumthen falls to zero...

Fig. 22.14 Basis of steady-state approximation

[I] remains negligibly small

A → I → P

Assumption:

0dt

]I[d

Fig. 22.15 Comparison of the exact result for the concentrations

of a reaction and concentrations from steady-state approximation

How do we postulate a plausible mechanism?

• Common approach is to use the kinetic isotope effect

• Process facilitates identification of bond-breaking events

• Decrease in reaction rate is observed when an atom isreplaced with a heavier isotope

• Primary kinetic isotope effect – the RDS requires scissionof a bond involving that isotope

• Secondary kinetic isotope effect – bond scission occursin a bond NOT involving that isotope

How do we postulate a plausible mechanism?

• Effect arises from change in activation energy when atomis replaced with a heavier isotope

• Change is in zero-point vibrational energy of bond

νh)v(E 21

vib

Fig. 22.18 Changes in reaction profile when a C−H

bond is replaced with C−D

Fig. 22.19 Protons can tunnel through the activation barrier

• Effective barrierheight is reduced

• Important only atlow temperatureswhen most of thereactant moleculesare left of the barrier

• More important inelectron transferreactions even at roomtemperature

Fig. 22.20 Difference in zero-point vibrational energies to describe the secondary kinetic isotope effect

λe)H(k

)D(k

where λ is anexperimentallydetermined parameter

• If λ > 1 then the deuteratedform reacts more slowly

• If λ < 1 then the undeuteratedform reacts more slowly