Chemical kinetics and surface chemistry

(18PCY302)

Dr.
Dr
rr.. M
Manab Kundu
Research
rch Assistant Professor
Professo
Electrochemical Energy Storage Laboratory
SRM Institute
ute of Science and Technology
Kattankulathur
attankulath
Chennai
 Chemical Kinetics
Chemical kinetics deals with the rates of chemical
reactions and with how the rates depend on factors
such as concentration and temperature.

Thermodynamics – does a reaction take place?

Reaction speed: measured by the change in concentration with time.

Important factors which affect rates of reactions:

– reactant concentration
– temperature
– action of catalysts
– surface area
– pressure of gaseous reactants or products
 Kinetics
• Studies the rate at which a chemical process
occurs.

• Besides information about the speed at which

reactions occur, kinetics also sheds light on the
reaction mechanism (exactly how the reaction
occurs).
 Activation Energy
• There is a minimum amount of energy required for a
reaction: the activation energy, Ea.
• Just as a ball cannot get over a hill if it does not roll
up the hill with enough energy, a reaction cannot
occur unless the molecules possess sufficient energy
to get over the activation energy barrier.
 Activation Energy
• Molecules must possess a minimum amount of energy to
react. Why?
– In order to form products, bonds must be broken in the
reactants. Bond breakage requires energy.
– Molecules moving too slowly, with too little kinetic energy,
don䇻t react when they collide.
• Activation energy, Ea, is the minimum energy required to
initiate a chemical reaction.
− Ea will vary with the reaction.

Next we will look at an example of Ea.

 Activation Energy
• Consider the rearrangement of methyl isonitrile:

– In H3C-N C, the C-N C bond bends until the C N bond

breaks and the N C portion is perpendicular to the H3C
portion. This structure is called the activated complex or
transition state.
– The energy required for the above twist and break is the
activation energy, Ea.
– Once the C-N bond is broken, the N C portion can continue to
rotate forming a C-C N bond.
* Here䇻s what the reaction looks like in terms of a graph of the
energies that are involved in the process…
 Activation Energy
• The change in energy ∆E for the reaction is the difference in
energy between CH3NC (reactant) and CH3CN (product).
• The activation energy Ea is the difference in energy between
reactants, CH3NC, and the transition state.
• The rate depends on Ea. If the 䇾hill䇿 is taller, the reaction rate is
slower. If the 䇾hill䇿 is shorter the rate is faster.
• Notice that if a forward reaction is exothermic… (CH3NC Æ CH3CN),
then the reverse reaction is endothermic… (CH3CN Æ CH3NC).
• The methyl isonitrile molecule needs to gain enough energy to
overcome the activation energy barrier.
• From kinetic molecular theory, we know that as temperature
increases, the total kinetic energy increases and the number of
molecules with energy greater than Ea increases.
• So as long as the temperature is high enough, the reaction can
make it 䇾over the hill䇿 and proceed.
 A+B C+D

Exothermic Reaction Endothermic Reaction

The activation energy (Ea) is the minimum amount of

energy required to initiate a chemical reaction.
 Energy Diagrams

Exothermic Endothermic

(a) Activation energy (Ea) for the forward reaction 50 kJ/mol 300 kJ/mol
(b) Activation energy (Ea) for the reverse reaction 150 kJ/mol 100 kJ/mol
(c) Delta E (change in energy) -100 kJ/mol +200 kJ/mol
 Arrhenius Equation

Svante Arrhenius developed a mathematical

relationship between k and Ea:

where A is the frequency factor, a number that

represents the likelihood that collisions would
occur with the proper orientation for reaction. k
is the rate constant
 Arrhenius Equation

Taking the natural

logarithm of both
sides, the equation
becomes
1
RT
y = mx + b
When k is determined experimentally at
several temperatures, Ea can be calculated
from the slope of a plot of ln(k) vs. 1/T.
Temperature Dependence of the Rate Constant

k = A • exp( -Ea/RT )
(Arrhenius equation)

k is the rate constant

Ea is the activation energy (J/mol)
R is the gas constant (8.314 J/K•mol)
T is the Kelvin temperature
A is the frequency factor
1/T
Collision theory
Theories of reaction rate

How to interpret ???

Collision theory - A is a frequency factor determined

by the rate of collision of molecules in the gas state
Thermodynamic formulation - A is determined in
terms of the free energy of activation
Statistical mechanics - A is determined using
Partition functions
Radiation hypothesis

- Infrared radiation emitted by the walls of reaction

vessel

- Received support from behaviour of unimolecular

gas reactions, since it was argued that the rate of

such reactions could not depend on molecular

collisions.
Four main lines of approach to the problem of
pre-exponential factor

1. Kinetic theory of collision

2. Thermodynamics with an additional hypothesis to

explain the rates of reactions

3. Statistical mechanics with an additional hypothesis to

explain the rates of reactions

4. Molecular dynamics
 Kinetic theory of collisions

For a gas containing only one type of molecule, A, the

number of collision per unit time per unit volume:

……………….1

Where NA is the number of molecule per unit volume, d is the molecular

diameter (equal to the distance between the centre when collision occurs)
and ū is the mean molecular speed given by kinetic theory to be:

……………….2
Where m is the molecular mass, introduction of this expression into the
equation 1, gives

……………….3

This quantity is known as the collision number, and its SI unit is m-3 s-1

The corresponding expres5ion for the collision number ZAB for two unlike
molecules. A and B, of masses mA and mB, is

……………….4

The distance d is now the mean of the molecular diameters, or the sum
of their radii. It is the distance between the centers of A and B when
reaction occurs. A reduced mass μ can be defined by the equation
 ……………….5

The equation 4 can be written as

……………….6

According to the hard-sphere collision theory, the collision number multiplied

by the Arrhenius factor e-EIRT gives the rate of formation of the products of
reaction, in terms of the number of molecules formed per unit volume and
per unit time. Thus, for reaction between two molecules A and B the rate is
expressed as
……………….7
 Division by NA NB gives a rate constant in molecular units (SI unit:-m3s-
1)-lt-can be put into molar units (SI unit: m3 mol-1 s-1) by multiplication by
the Avogadro constant L:

……………….7

The pre-exponential factor in this expression is called the collision

frequency factor and given the symbol ZAB (or ZAA if there is only one type
of molecule):

……………….8

Thus the rate constant is expressed as:

……………….9
 Lewis applied this treatment to the reaction

2HI H2+I2

Calculated pre-exponential factor = 3.5 X10-7 dm3 mol-1s-1 at 556 K

Experimental value = 3.52 X 10-7 dm3 mol-1s-1

The expression of rate constant: ……………….9

Lewis applied this treatment to the reaction:

2HI H2+I2

Calculated pre-exponential factor = 3.5 X10-7 dm3 mol-1s-1 at 556 K

Experimental value = 3.52 X 10-7 dm3 mol-1s-1

Limitations:

¾ For gas reactions between molecules of any complexity the observed

pre-exponential factors are often lower by several powers of 10 than the
factors calculated by the simple collision theory.
¾ Deviations from theory often are encountered with solution reactions
between ions or dipolar substances.
 Simple hard-sphere collision theory is not adequate for chemical
reactions.
™ If two molecules are to undergo a chemical reaction they must not merely
collide with sufficient mutual energy: they must come together with such a
mutual orientation that the necessary bonds can be broken arid made.

™ The. simple kinetic theory counts every sufficiently energetic collision as an

effective one: in reality, the molecules may not approach each other in the right
way for reaction to occur, eyen if there is plenty of energy.

Considering the fraction of the total number of collisions that are effective
from the orientation point of view, rate expression can be expressed as:

P: steric factor ……………….10

9 The evaluation of P cannot be done in a satisfactory manner.

9 Factors other than orientation are involved, and again these cannot be
estimated easily.
The simple hard sphere collision theory of reactions is not consistent with the
fact that at equilibrium the ratio of rate constants in the forward and reverse
directions is the equilibrium constant.
Thus, if the rate constants in the two directions are formulated

……………….11 and 12

The ratio is ……………….13

This expression lacks of entropy term. The equilibrium constant:

……………….14

introducing an entropy term into the kinetic theory expression:

……………….15

Δ#SO and Δ#HO are the standard entropy and enthalpy changes in reaching
the activated state. This procedure is not entirely satisfactory but was useful
in paving the way to transition-state theory.
 Rate theories based on thermodynamics
Thermodynamics is concerned with systems at equilibrium and can give no
complete treatment of reaction rates.
However, if additional hypotheses are made, thermodynamics may make an
important contribution to theories of rates

The expression for rate of reaction in terms of Gibbs free energy change
Δ#GO is the Gibbs free energy change
in going from the initial to the
……………….16
activated state

van't Hoff equation: ……………….17

By splitting the Gibbs free energy change into quantities relating to forward
and reverse reactions
For forward reaction: ……………….18

For forward reaction: ……………….19

 In general: ……………….20

Where ν# is a factor same for over all reactions

Further splitting of Δ#GO into enthalpy and entropy terms:

……………….21

Kohnstamm and Scheffer were the first to introduce the concepts of the
Gibbs energy of activation Δ#GO , the entropy of activation Δ#SO and the
enthalpy of activation Δ#HO .

However, they were unable to interpret the multiplying factor v*.

According to transition-state theory this factor is equal to kT/h. where k

is the Boltzmann constant and h the Planck constant.
1. The infrared radiation emitted by the walls of reaction vessel
determined the rate of a chemical reaction – is known as:

i. Radiation hypothesis ii. Kinetic theory of collision iii. Hard sphere

theory iv. Theories of reaction rate

2. Collision theory of chemical reactions is based on

i. Thermodynamics ii. Statistical mechanics iii. Kinetic theory of gas

iv. Quantum theory

3. The rate constant is given by the equation k=pze−E/RT. Where p

represents

i. number of total collision ii. number of effective collision iii. Pressure

v. steric factor

4. Collision theory considers reacting species to be

i. linear molecules ii. hard sphere iii. Shapeless iv. Tetrahedral

molecules
The expression of rate constant: ……………….9

Lewis applied this treatment to the reaction:

2HI H2+I2

Calculated pre-exponential factor = 3.5 X10-7 dm3 mol-1s-1 at 556 K

Experimental value = 3.52 X 10-7 dm3 mol-1s-1

Limitations:

¾ For gas reactions between molecules of any complexity the observed

pre-exponential factors are often lower by several powers of 10 than the
factors calculated by the simple collision theory.
¾ Deviations from theory often are encountered with solution reactions
between ions or dipolar substances.
 Simple hard-sphere collision theory is not adequate for chemical
reactions.
™ If two molecules are to undergo a chemical reaction they must not merely
collide with sufficient mutual energy: they must come together with such a
mutual orientation that the necessary bonds can be broken arid made.

™ The. simple kinetic theory counts every sufficiently energetic collision as an

effective one: in reality, the molecules may not approach each other in the right
way for reaction to occur, eyen if there is plenty of energy.

Considering the fraction of the total number of collisions that are effective
from the orientation point of view, rate expression can be expressed as:

P: steric factor ……………….10

9 The evaluation of P cannot be done in a satisfactory manner.

9 Factors other than orientation are involved, and again these cannot be
estimated easily.
The simple hard sphere collision theory of reactions is not consistent with the
fact that at equilibrium the ratio of rate constants in the forward and reverse
directions is the equilibrium constant.
Thus, if the rate constants in the two directions are formulated

……………….11 and

The ratio is ……………….13

This expression lacks of entropy term. The equilibrium constant:

……………….14

introducing an entropy term into the kinetic theory expression:

……………….15

Δ#SO and Δ#HO are the standard entropy and enthalpy changes in reaching
the activated state. This procedure is not entirely satisfactory but was useful
in paving the way to transition-state theory.
 Rate theories based on thermodynamics
Thermodynamics is concerned with systems at equilibrium and can give no
complete treatment of reaction rates.
However, if additional hypotheses are made, thermodynamics may make an
important contribution to theories of rates

The expression for rate of reaction in terms of Gibbs free energy change
Δ#GO is the Gibbs free energy change
in going from the initial to the
……………….16
activated state

van't Hoff equation: ……………….17

By splitting the Gibbs free energy change into quantities relating to forward
and reverse reactions
For forward reaction: ……………….18

For forward reaction: ……………….19

 In general: ……………….20

Where ν# is a factor same for over all reactions

Further splitting of Δ#GO into enthalpy and entropy terms:

……………….21

Kohnstamm and Scheffer were the first to introduce the concepts of the
Gibbs energy of activation Δ#GO , the entropy of activation Δ#SO and the
enthalpy of activation Δ#HO .

However, they were unable to interpret the multiplying factor v*.

According to transition-state theory this factor is equal to kT/h. where k

is the Boltzmann constant and h the Planck constant.
1. The infrared radiation emitted by the walls of reaction vessel
determined the rate of a chemical reaction – is known as:

i. Radiation hypothesis ii. Kinetic theory of collision iii. Hard sphere

theory iv. Theories of reaction rate

2. Collision theory of chemical reactions is based on

i. Thermodynamics ii. Statistical mechanics iii. Kinetic theory of gas

iv. Quantum theory

3. The rate constant is given by the equation k=pze−E/RT. Where p

represents

i. number of total collision ii. number of effective collision iii. Pressure

v. steric factor

4. Collision theory considers reacting species to be

i. linear molecules ii. hard sphere iii. Shapeless iv. Tetrahedral

molecules