8

CHAPTER CHAPTER CHAPTER CHAPTER ---- I I I I

Introduction to Chemical Kinetics

9

CHAPTER I

1.0 INTRODUCTION

Science may be defined as describing, creating and understanding

facts of human experience (Lindsey). It would be impossible to

achieve this object unless we evolve a ‘system’ or ‘method’ to

study the countless natural phenomena.

Perhaps it would be better to say that science is an ‘activity

pursued by means of scientific methodology’.

By the view of physical sciences life it self is a complex set of

coordinated and interdependent chemical reactions that sustained

for a time.

Investigating rates of reactions and trying to understand such

processes at the molecular level have formed an important part of

chemistry.

Chemistry is science of matter, its chemical reactions, and also its

composition, structure and properties.

Chemistry is related with atoms and their interactions with other

atoms, and particularly with the properties of chemical bond.

The word chemistry comes from the word alchemy which in turn

is derived from the Arabic word al-kimia (greek word) meaning

cast together.

An alchemist was called a 'chemist' in popular speech, and later

the suffix "-ry" was added to this to describe the art of the chemist

as "chemistry".

The birth of Chemical Kinetics often is taken to have occurred in

1850, when the German Scientist Ludwig Ferdinand Wilhelmy

studied the rate of inversion of sucrose.1

10

French chemists followed Wilhelmy’s work, who in 1862

published the result of the reaction between ethanol and acetic

acid to give ethyl acetate and water.2

The rapidness with which a chemical reaction velocity is

influenced by change in concentration and temperature etc. and

whether reaction occurs in one step or in a sequence of steps are

all such problems which fall in periphery of the subject called,

Chemical Kinetics.3

Chemical kinetics is also known as reaction kinetics, is the study

of rates of chemical processes.4-8 Chemical kinetics comprises of

investigations of how different experimental conditions can

influence the speed of a chemical reaction and yield information

about the reaction's mechanism and transition states, as well as

the construction of mathematical models that can describe the

characteristics of a chemical reaction.9-15

Chemical kinetics concerns with the experimental determination

of reaction rates from which rate laws and rate constants are

derived.

Kinetics study is important as it provides essential evidences to

the mechanisms of chemical processes.16-19 Relatively simple rate

laws exist for zero-order reactions (for which reaction rates are

independent of concentration), first-order reactions, and second-

order reactions, and can be derived for others. In consecutive

reactions, the rate-determining step often determines the kinetics.

11

Kinetics may be considered as a more fundamental science than

Thermodynamics in the sense that the later tells us about the

extent of reaction but the former tells about the rate of the

reaction.20

Chemical Kinetics fundamentally deals with

(i) The details of process where by a system passes from one

state to another,

(ii) With the rate of chemical reactions21, and

(iii) With all factors which influence them as well as probable

reaction mechanism.22

Valuable evidence about mechanisms also is provided by

nonkinetic investigations, such as the detection of reaction

intermediates and isotope exchange studies. But knowledge of a

mechanism can be satisfactorily only after a careful kinetic

investigation has been carried out.

It is a modern tool in development and progress of chemistry.

The sequence of elementary reaction which comprise the reaction

is termed as reaction pathway or mechanism which is reasonable

and consistent with the kinetic data.23 Kineticiscts want to know

how reaction occurs.24

The significance and importance of this field is realized by the

fact that understanding of reaction mechanism may make it

possible to select reaction condition leading to higher yield of

desired products and a lower yield of undesired ones.

12

The chemical reactions may be divided into two classes:25

(a) Homogeneous Reactions – are those in which all the reactants

and the products are present in a single phase i.e., the reactants

and products are physically indistinguishable. Such reactions

take place in gas mixtures or liquids.

(b) Heterogeneous Reactions – are those reactions in which

reactants and products are present in two or more phases. Such

reactions take place in solid and gas, solid and liquid, two

immiscible liquid, or even two solids.

1.1 KINETIC TERMS :

The terms which will be used further in our study are discussed as

follows:

1.1.0 Reaction stoichiometry:

A chemical reaction of known stoichiometry in general can be

written as

aA + bB + cC + ……….. → ……….. + yY + zZ

Earlier letters of alphabets are used for reactants and later letters

for products, the letter X is reserved for reaction intermediate.26

‘ν’ is the stoichiometric coefficient of a species in a balanced

chemical equation, it is negative for reactants and is positive for

products.

In above reaction stoichiometric coefficients of reactants are –a, -

b, -c and for products is y and z.

13

1.1.1 Molecularity of Reaction:

The stoichiometry of the reaction can give us some information

regarding the minimum number of molecules of reactants leading

to the formation of products. This is known as Molecularity of

Reaction.27

Assuming the reaction to occur through molecular collisions, it

can be defined as number of atoms or molecules which collide

together at one and the same time for the reaction to occur.

1.1.2 Order of Reaction:

The power to which the concentration of a species (a product or a

reactant) is raised in a rate law is the Order of the Reaction with

that species.28 The term order with its present meaning, was

introduced by W. Ostwald.29

1.1.3 Rate of Reaction:

Rate of reaction means the speed with which the reaction takes

place.30 It can be defined as the change in concentration of anyone

of the reactants or products per unit time.

Rate of Reaction = decrease in conc. of reactant or increase in conc. of product Time taken

Mathematically it can be written as

For reactant

Rate of Reaction = - d[A] dt

And for products

14

Rate of Reaction = d[B] dt

This can be combined as follows:

Rate of Reaction = - d[A] = d[B] dt dt

As the concentration of the reactant is decreasing with time

therefore d [A] is negative.

1.1.4 Rate Constant:

For the reaction

A + B → Products

Here, Rate of Reaction:

r = dx/dt = k CACB

CA and CB are concentration of reactants A and B, and x denotes

the concentration of product formed at a time ‘t’ where constant

‘k’ is called the Rate Constant or the Specific Rate of the

Reaction.31

It’s a fundamental kinetic parameter and as the reaction rate

increases the value of rate constant increases.

1.1.5 Rate Expression or Rate Law:

The expression which describes the reaction rate in terms of the

molar concentrations of the reactants as experimentally

determined is called Rate Law.32

It’s a mathematical relation between rate and concentration of

reactants and products. It is in the form of products of power of

concentration such as

-dc/dt = k CAn

1 CBn

2 CCn

3

15

The Rate Law can be determined by following methods:

1. Integration method

In this method, the initial concentrations of all the reactants

taking part are determined. The concentration of the

reacting substance is then determined at different intervals

of time. The different values of ɑ and x are thus

determined, and are substituted in various order rate

expressions.

2. Van’t Hoff method

In this method, the initial rate of reaction is measured when

the concentration of one reactant is varied and all others are

kept constant. Initial reaction rates are determined by

measuring the slopes of concentration-time curves at zero

time.

From the equation:

ln[dx/dt]0 = ln k’ + x ln [A]0

a plot between ln[dx/dt]0 against ln [A]0 gives a straight line

whose slope gives the value of x, the order of reaction with

respect to A.

3. Graphical method

This method is used when there is only one reactant and the

order is a positive whole number. The stepwise procedure

to obtain rate law by this method is given as below:

16

(a) The concentration of the reactant is measured at

different time intervals by some suitable method.

(b) A graph is plotted between concentration (along Y-

axis) and time (along X- axis).

(c) From the graph of concentration versus time, the

instantaneous rates corresponding to different

concentrations are determined by drawing tangents to

the curve and subsequently finding their slopes.

(d) Different graphs are now plotted as follows between:

(i) Rate versus concentration, or

(ii) Rate versus (concentration)2, or

(iii) Rate versus (concentration)3 and so on.

This process is continued till the graph obtained is a

straight line. If a straight line is obtained in first case the

reaction is of first order, in second case the reaction is of

second order, and in third case the reaction is of third order

and so on.

4. Half-life method

t0.5 = 1/ɑn – 1

when we start with two independent reactions with initial

concentrations ɑ1 and ɑ2, on rearranging this reaction we

get the equation:

n = 1 + [{log(t1/t2)} / {log( ɑ2/ɑ1)}]

from this equation the order of reaction, n can be

calculated.

17

5. Ostwald’s isolation method (Initial rate method)

This method was given by Ostwald in 1902. When there

are more than one reactant than such reactions are

determined by Ostwald’s isolation method. By initial

reaction rate we mean the rate at the beginning of the

reaction. In this method, the concentration of all reactants

except one is taken in excess and the order of reaction is

then determined by any method with respect to that reactant

which is not taken in excess. The reactant which is not

taken in excess is said to be isolated from other reactants

which are taken in excess. The total order of the reaction

will be the sum of the order of all isolated reactions.

In the reaction:

n1A + n2B + n3C � products

the reaction velocity is given as follows:

dx/dt = k. CnA

1 . CnB

2 . CnC

3

the order of the reaction will be n1 + n2 + n3

Advantage of this method is that mode of action of each

component can be determined separately and disturbing

effects can be traced to the origin.

From the above methods fifth one that is Ostwald’s isolation

method is important one. This method is implemented in the

present work.

18

1.2 Activation Parameters:

It has been known for many years that with increase in

temperature rate of reactions increases simultaneously. Thus the

study of temperature variation for a given reaction is much

beneficial for the interpretation of a possible reaction mechanism.

This interpretation of reaction mechanism requires the calculation

of kinetic and activation parameters such as temperature

coefficient, energy of activation, frequency factor, enthalpy of

activation, entropy of activation, free energy activation and

frequency factor and steric factor.

1.2.0 Activation Energy and Frequency Factor:

The molecules require a discrete minimum energy before the end

products are formed. Thus the reactants must pass through an

energy rich or activated state before they can react. The quantity

of energy required by the reactants to overcome this activated

state or energy barrier is known as the Activation Energy.

Arrehenius proposed the empirical equation for calculating the

energy of activation of a reaction having the rate constant k at

temperature T:

k = Ae –Ea/RT

where,

‘Ea’- is Activation Energy

‘A’- is pre-exponential factor or frequency factor.

Since the pre-exponential factor in the above equation is

dimensionless, the pre-exponential factor has the same unit as the

rate constant k.33

19

Experimentally, the energy of activation may be calculated or

obtained graphically from the study of reaction at two or more

temperatures.34

1.2.1 Enthalpy of Activation:

Enthalpy is a thermodynamic function of a system, equivalent to

the sum of the internal energy of the system plus the product of its

volume multiplied by the pressure exerted on it by its

surroundings.

∆H# = ∆E# + P∆V#

The change ∆H is positive in endothermic reactions.

∆H# is Negative in heat-releasing exothermic processes.

∆H# of a system is equal to the sum of non-mechanical work done

on it and the heat supplied to it.

1.2.2 Entropy of Activation:

It is thermodynamic property which measures randomness or

disorder of a system. The more disorder or randomness, higher

will be entropy, e.g. solid < liquid < gas.

Entropy of a system is state function, i.e., it depends upon initial

and final states of the system. When the state of a system changes,

the entropy also changes.

∆S = qrev /T = ∆ Trev/T

Where q is heat supplied isothermally, T is absolute temperature.

∆S = positive, for irreversible spontaneous process

20

∆S = zero, for change at equilibrium

Entropy increases with temperature, decreases with decrease in

temperature.

The concept of entropy is much related with the probability. To

correlate the above term, the expression is given as below-

∆ S# = 2.303 R [log PZ - log (kT/h)]

∆ S# = 4.5761 [log PZ - log (kT/h)]

Since, log (kT/h) = 13 at room temperature and the

expression can be written as :

∆ S# = 4.5761 [log PZ - 13]

This equation indicates that the positive or negative value of ∆ S#

will depend upon whether (Pz) frequency factor is greater or

smaller then 1013, positive entropy corresponds to a more

probable complex formation and the reaction is faster than the

normal one. If ∆S# is negative i.e. if Pz is less than 1013 then there

is lesser probability of complex formation giving rise to a slower

reaction than the normal one. 35,36

1.2.3 Gibbs Free Energy:

It is maximum amount of energy available to a system during the

process that can be converted into useful work. It is measure of

capacity to do useful work.

G = H - TS

G is free energy.

Change in free energy is given by the equation,

∆G# = ∆H# - T∆S#

∆G# is change in free energy.

If ∆G# is negative, process is spontaneous,

21

When ∆G# is zero, process is in equilibrium, and

If ∆G# is positive, the process does not take place.

1.2.4 Frequency Factor and Steric Factor:

Rate of chemical reaction is related with collision properties of

the reactant molecules. Frequency factor A in a bimolecular

reaction should be equal to the bimolecular frequency Z which

can be calculated from kinetic theory, if the dimensions and

masses of molecules are known.

Specific rate k for a bimolecular reaction can be given by the

following expression.37

k = Ae-Ea/RT

where A is the frequency factor.

The pre-exponential factor or the steric factor P is supposed to

represent the fraction of the total number of collisions that are

effective from the orientation point of view.38

The rate constant can then be written as

k = PzABe-E/RT

here P is the Steric factor.

1.2.5 Temperature Coefficient:

In homogeneous reactions, the rate becomes double or triple for

each 10o rise of temperature, which is sometimes expressed in

terms of temperature coefficient.

22

Temperature coefficient of a chemical reaction is defined as the

ratio of rate constant of a reaction at two different temperatures

separated by 10oC. Thus,

temperature coefficient =kt+10

kt

Where kt = specific rate constant at toC.

Kt+10 = specific reaction rate constant at (t + 10) oC.

1.3A KINETIC THEORY OF REACTION RATES:

There are two important theories of reaction rates, described as

follows:

1.3.0 Collision Theory of Bimolecular Gases:

This is the earliest theory of reaction rates. A treatment of

reactions in terms of the kinetic theory of collisions, was given by

Trautz39and Lewis.40

The reaction between two species takes place only when they are

in contact, it is reasonable to suppose that the reactant species

must collide before they react.

In order for reaction to occur, the energy of collision must equal

or exceed the threshold energy. The effective energy is the kinetic

energy corresponding to the component of the relative velocity of

the two molecules along the line of their centres at the moment of

collision. It is the energy with which the two molecules are

pressed together.

The rate constant can be expressed as:

k = ZABe-E/RT

23

The activation energy Ea is thus identified with the relative

kinetic energy E along the line of centre of the two colliding

molecules which is required to cause the reaction between them.

The collision theory can be generalized by introducing the steric

factor P, into the equation for the bimolecular rate constant in

order to take account of the orientational requirement.

Accordingly equation is:

k = PZABe-E/RT

The steric factor is supposed to be equal to the fraction of

molecular collisions in which the molecules A and B possess the

relative orientations necessary for the reaction.

1.3.1 Transition State Theory:

This theory is also known as Absolute reaction rate theory or

commonly as Activated complex theory developed by Eyring,41

Evans and Polanyi. 42

According to this theory, the bimolecular reaction between two

molecules progresses through the formation of activated complex

which then decomposes to yield the product.

Activated complex is a special molecule in which one vibrational

degree of freedom has been converted to a translational degree of

freedom along the reaction coordinate.

Activated complex is unstable because it is situated at the

maximum of the potential energy barrier separating the products

from the reactants. The difference between the energy of the

24

activated complex and the energy of the reactants is the activation

energy, Ea.

The rate constant may be expressed as follows:

k = (k T/h)K#

The equilibrium constant K# can be expressed in terms of the

standard Gibbs free energy change for the activation process,

(∆G˚)#, called the standard Gibbs free energy of activation. After

substituting its value we get the rate constant as:

k = (k T/h)e(∆S˚)#/R e-(∆H˚)#/RT

This is the well known Eyring equation for the rate constant of a

simple bimolecular gaseous reaction. This equation holds for

reactions in solutions too.

1.3B FACTORS INFLUENCING RATE OF REACTION

There are various factors which influence the rate of reaction.

They are mentioned below:

A. Nature of Reactants

Different reactants have different activation energies. Reaction

between polar or ionic molecules is very fast. Redox reactions are

slower than ionic reactions because they involve transfer of

electrons and bond rearrangement. The physical states of

reacting substances are important in determining their

reactivities. The reaction in which ionic solutions are involved

also take place at high speed.

25

B. Temperature:

Increase of temperature has a marked effect on the rate of a

chemical reaction. Temperature is a measure of the kinetic energy

of a system, so higher temperature implies higher average kinetic

energy of molecules and more collisions per unit time. The ratio

of the rate constants of a reaction at two temperatures differing by

10˚C is known as the temperature coefficient of the reaction.

C. Concentration Effect:

A higher concentration of reactants leads to more effective

collisions per unit time, which increases the reaction rate (except

for zero order reactions). Similarly, a higher concentration of

products tends to be associated with a lower reaction rate.

D. Catalysts:

A catalyst is a substance that can increase the rate of a reaction

but which itself remains unchanged in amount and chemical

composition at the end of the reaction. When a catalyst is added, a

new reaction path with a lower energy barrier is provided. Since

the energy barrier is reduced in magnitude, a larger number of

molecules of the reactants can get over it. This increases the rate

of the reaction. A catalyst does not alter the position of

equilibrium in a reversible reaction. It simply hastens the

approach of the equilibrium by speeding up both the forward and

the backward reactions.

26

1.4 TYPES OF REACTIONS

1.4.0 Elementary Reaction

It is a reaction that occurs in a single step, with no experimentally

detectable reaction intermediates. In this one or more chemical

species react directly to form products in a single step with one

transition state.

The Molecularity of an elementary reaction is the number of

reactant particles (atoms, molecules, free radicals, or ions) that are

involved in each individual chemical event. When the

Molecularity is unity, the reaction is said to be Unimolecular

reaction. When the Molecularity is two, reaction is said to be

Bimolecular reaction.

1.4.1 Composite Reaction

It involves more than one elementary reaction, also it’s called as

Complex or Stepwise reactions.43 In this reaction rate constants of

more than one elementary reactions are involved for the rate of

appearance or disappearance of a reactant. It is convenient to

number the elementary reactions that occur in a composite

mechanism in such a way that reverse reactions are identified

easily.

1.4.2 Chain Reactions

A Composite reaction mechanism sometimes occur includes a

cycle of reactions, such that certain reaction intermediates

consumed in one step are regenerated in another step. If such a

27

cycle is repeated more than one time the reaction is known as

Chain Reaction.44

1.4.3 Oxidation-Reduction Reactions

The change in higher oxidation state due to electron transfer is

regarded as the oxidation, where as lowering of oxidation state is

treated to be reduction.

Rose Stewart has proposed the following general definition-

“ An oxidation and a reduction has occurred in a chemical

reaction if the products differ from the reactants in a way that can

not be accounted for simply by an exchange of protons, hydroxide

ions, alkali metal ions etc. or what is equivalent by an exchange

of water, hydrogen, halide, ammonia etc. “

1.4.4 Electron-Transfer Reactions

The essential step in any redox process is the transfer of electrons.

Fe++ → Fe+++ + e-

Electron transfer reactions involving metal ions and their

complexex are of two types, e.g.

(i) Outer sphere type

(ii) Inner sphere type

In Outer sphere processes, the co-ordination shells of the metal

ions remain intact during electron transfer.

Also, for outer sphere reactions we find that,

28

a) The rate law is of the first order in both reactants, activated

complex composes the intact co-ordination shells of both metal

ions.

b) Co-ordination shell of either metal being inert to substitution,

rate of electron transfer is faster than that of substitution.

The other existing possibility of electron transfer is that reductant

releases the electron to the solvent which in turn transfers it to the

oxidant. The possibility of this mechanism in aqueous solution is

lessened due to evidential scarcity.

In inner sphere processes, electron transfer takes place through a

bridging group common to the co-ordination shells of both metal

ions.

In inner sphere reactions45-50 substitution of the co-ordination

shell of one of the metal ions occurs prior to electron transfer.

Application of the Franck-Codon principle, which states that

electronic transitions are virtually instantaneous in comparison

with atomic rearrangements, has some interesting repercussions.

1.5 Catalyst and Inhibitor:

1.5.0 Catalyst

It is a substance that is both a reactant and a product of reaction,

its concentration enters into the kinetic equation but not in the

equilibrium constant for the reaction. Catalysts can be classified

as follows:51

29

(a) Homogeneous catalyst in which only one phase is involved.

(b) Heterogeneous or surface catalyst in which reaction occurs

at an interphase between the phases.

(c) Auto catalyst is the product of the reaction, catalyzing the

reaction.

(d) Intramolecular catalyst is a group of reactant molecule

catalyzing the reaction itself .

1.5.1 Inhibitor

It is a substance that diminishes the rate of a chemical reaction.

Inhibitors have sometimes been called as “negative catalyst”, but

since their action is quite different from that of catalysts this

usage is not recommended. In contrast to catalysts, inhibitors are

consumed during the course of the reaction.

1.6 Reaction Mechanism:

The mechanistic approach of chemical reactions was proposed in

the 1950’s as an effort to provide a theoretical model of a

chemical reaction. Before that, reactions were studied and

approached from the standpoint of reactants, conditions for the

reaction, and products formed. This net reaction approach sought

only to ask question of what the end results of a process would be.

The mechanistic theory sought to ask a further more important

question. How the reactions proceed in explaining the products

formed?

a) Mechanistic Concept

According to this, a reaction is proceeded along a certain pathway

called a reaction mechanism. This pathway is consisted of one or

30

more steps called “elementary reactions” that take place in a

specific sequence. One of the steps would be the slowest step in

the process, and is represented as the “rate determining” step.

b) Transition State

Each elementary step would have a hypothetical species which

was too short lived to be detected using instruments. This species

was called the activated complex or the transition state. It is the

transition state that involves the breaking of chemical bonds and

the reforming of other bonds to produce the product molecules.

This process of bond breaking and formation is so fast that

transition state has very short live.

c) Intermediate

The species form during the reaction and has very short life is

called intermediate. Not all elementary reactions within a

proposed reaction mechanism would have an intermediate. A

reaction mechanism is like a theory or model explaining how a

reaction occurs. Such a reaction mechanism is capable of

predicting results under some specified environmental conditions.

d) The purpose of a reaction mechanism

Reaction mechanism has been enormously useful in organic

chemical reactions. A reaction mechanism gives the chemist a

degree of control over the reaction process. For example some

reaction occurs with a certain degree of specificity where only

one isomer product is produced to the relative exclusion of

another isomer. If one knows this via knowledge of the reaction

31

mechanism than the chemist has more control over which product

will form. Other reactions involve the formation of one isomer

product under a different set of conditions. If a reaction

mechanism for each result is proposed and validated, than one

could choose the major product by adjusting the conditions under

which the reaction proceeds.

Edwards52 defined reaction mechanism as ‘Reaction mechanism

means the detailed stepwise pattern of atomic and electronic

motions that take place while reactants change to products’.

Bertlett53 defined reaction mechanism as ‘The study of reaction

mechanism is an attempt to describe the conversion of reactants

into products in a chemical reaction’.

The series of reaction steps in which a reaction occurs is called

Reaction Mechanism.

The law of mass action54 is true for each separate step, but not for

the reaction as a whole. The observed reaction rate is determined

by the slowest reaction in the reaction mechanism which is,

therefore called the ‘rate determining step’.

All the steps of the reaction will be having certain rate, but the

rate will be determined by the slowest reaction.

The reaction mechanism may make it possible to select reaction

condition leading to higher yield of desired products and a lower

yield of undesired ones.

32

REFERENCES:

1. L.Wilhelmy; Pogg. Ann.; 81, 413, 499 (1850).

2. P.E.M Berthelot and L.P de Saint-Gilles; Ann. Chim.

Phys.; 63(3), 385 (1862).

3. E.L King; ‘How the Chemical Reaction occur’, W.A

Benjamin, Ind., N,Y; P.6,11,18 (1964).

4. J.Zhou, W.Li, W.Xiao; chem. Eng. Sci.; 55(23), 5637,

(2000).

5. L.Wang, Y.Zhao, J.Fu; J. Hazard. Mater.; 160(2-3), 608,

(2008).

6. J.Xin, H.Imahara, S.Saka; Fuel; 88(2), 282, (2009).

7. F.Maab, H.Elias, K.J. Wannowius; Atmosph. Environ.;

33(27), 4413, (1999).

8. N.Radic, B.Grbic, A.T. Baricevic; Appl. Catal. B: Environ.;

50(3), 153, (2004).

9. G.S. Nunes, I. Mayer, H.E. Toma, K. Arabi; J. Catal.;

236(1), 55, (2005).

10. K. Sharma, R.N. Mehrotra; Polyhedr.; 28(7), 1336, (2009).

11. J.B. Parsa, M.Rezaei, A.R. Soleymani; J. Hazard. Mater.;

168(2-3), 997, (2009).

12. B. Schumacher, Y.Denkwitz, V. Plzak, M. Kime, R.J.

Behm; J. Catal.; 224(2), 449, (2004).

13. J.M. Haschke, T.H. Allen, J.C. Martz; J. Alloys. Comp.;

271, 211, (1998).

14. H.A. Ewais, M.K. Ismael, A.A.A. Khalek; J. Saudi. Chem.

Soc.; 13(2), 219, (2009).

33

15. R.M. Mulla, H.M. Gurubasavaraj, S.T, Nandibewoor;

Appl. Catal. A: General; 314(2), 208, (2006).

16. V.A. Guerrero, B.C. Gates; J. Catal.; 260(2), 351, (2008).

17. M. Moreno, G.T. Baronetti, M.A. Laborde, F.J. Mariano;

Int. J. Hydr. Ener.; 33(13), 3538, (2008).

18. H. Wang, A. Pring, Y. Xie, Y. Ngothai, B. O’neill;

Thermochim. Acta; 427(1-2), 13, (2005).

19. E. Gasana, P. Westbroek, K.D. Wael, E. Temrnerman, K.D.

Clerck, P. Kiekens; J. Electroanal. Chem; 553, 35, (2003).

20. A. Frost and R.G Pearson; ‘Kinetics and Mechanism’, John

Wiley and Sons; p.1 (1961).

21. William F. Sheehan; ‘Physical Chemistry, Prentice Hall of

India Pvt. Ltd. New Delhi; p.539 (1966).

22. (a) V. Kirrer; ‘Physical Chemistry’, Mir Publishers,

Moscow; 415 (1979).

(b) G.M. Barrow; ‘Physical Chemistry’ Int. Student

Edition McGrew Hills, Konga Kusha Ltd, Tokyo;

419.

23. J.O Edwards; ‘Inorganic Reaction Mechanism’, W.A

Benjamin, Inc.; p.2 (1965).

24. P.Groggins; ‘Unit Process in Organic Synthesis’, McGraw

Hill, N.Y.; p.1 (1958).

25. V.B Patania; Chemical Kinetcs; p. 12 (2004).

26. Keith J. Laidler; Chemical Kinetics, third edn., Harper &

Row, N.Y.; p.4 (1987).

27. J.N Gurtu, A.Gurtu; Advanced Physical Chemistry,

eleventh edn.; p.345 (2009).

34

28. Peter Atkins; Julio de Paula, Atkins Physical Chemistry,

seventh edn.,Oxford University Press; p.868 (2002).

29. Keith J. Laidler; Chemical Kinetics, third edn., Harper &

Row, N.Y.; p.10 (1987).

30. V.B Patania; Chemical Kinetcs; p. 3-4 (2004).

31. M.J Walter; Physical Chemistry, Lowe and Brydone

Printers, Great Britain; p. 253 (1966).

32. V.B Patania; Chemical Kinetcs; p. 17 (2004).

33. B.R Puri, L.R Sharma, M.S Pathania; Principles of Physical

Chemistry; p.689 (2003).

34. H.Erying, E.M Erying; Modern Chemical Kinetics,

Chapman and Hall; p.7 (1965).

35. K.J Laidler; Reaction Kinetics, Pergamon Press; p.85,

(1963).

36. A.S.Frost, R.G Pearson; Kinetics and Mechanism, John

Wiley and Sons; p.11, (1961).

37. B.I Robinwitsch; Photosynthesis and related Process,

Interscience Publ.Inc., N.Y.; p.1, (1959).

38. Keith J. Laidler; Chemical Kinetics, third edn., Harper &

Row, N.Y.; p.83 (1987).

39. M. Trautz; Z. Anorgan. Chem.; 96, 1, (1916).

40. W.C. McC. Lewis; J. Chem. Soc.(London); 113, 471,

(1918).

41. H. Erying; J. Chem. Phys.; 3, 107 (1935).

42. M.G, Evans, M. Polanyi; Trans. Faraday. Soc.; 31, 875

(1935).

43. Keith J. Laidler; Chemical Kinetics, third edn., Harper &

Row, N.Y.; p.17 (1987).

35

44. Keith J. Laidler; Chemical Kinetics, third edn., Harper &

Row, N.Y.; p.14 (1987).

45. R.J. Campion, T.J. Conocchioli, N. Sutin; J. Am. Chem.

Soc.; 86, 4591 (1964).

46. J.H. Espenson, J.P. Birk; J. Am. Chem. Soc.;87, 3280

(1965).

47. A. Haim, N. Sutin; J. Am. Chem. Soc.; 88, 5343 (1966).

48. A. Haim, W.K. Wilmarth; Proc. Roy. Soc.(London); 14,

470 (1865).

49. H. Taube, H. Myess, R.L. Rich; J. Am. Chem. Soc.; 75,

4118 (1953).

50. H. Taube, E.L. King; J. Am. Chem. Soc.; 4118 (1953).

51. Keith J. Laidler; Chemical Kinetics, third edn., Harper &

Row, N.Y.; p.14-15 (1987).

52. J.D Edward; Inorganic Reaction Mechanism, John Wiley &

Sons. Inc., N.Y.; (1961).

53. P. Bertlett; Prspective Inorganic Chemistry, Ed. Todd:

Interscience Publisher; p. 12, (1956).

54. C.M. Guldberg, P.Waage; Forh. Vid. Selsk. Christiana; 35,

92, 111 (1864).