LESSON 9.3. - Enzymatic kinetics, microbial kinetics and ...
Introduction to Chemical Kinetics -...
Transcript of Introduction to Chemical Kinetics -...
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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
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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.
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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.
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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.
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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
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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
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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:
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(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.
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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.
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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
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∆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,
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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.
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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
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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
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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.
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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.
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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
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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,
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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
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(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
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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.
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