Chemical Kinetics
Contents
• Introduction to chemical kinetics
• Concept of molecularity and order of a reaction
• Different types of order of a reaction including rate
constants, halflife, shelf life, apparent or pseudo order
• First order reaction kinetics examples, derivation,
halflife and shelf life
• Pseudo first order reaction kinetics
• Second order reaction kinetics examples, derivation,
halflife and shelf life
• Determination of order of a reaction
Learning
Objectives
At the end of this lecture,
student will be able to:
• Define rate, order of a reaction and molecularity
• Explain the use of
apparent zeroorder kinetics to the practice of pharmacy
• Describe the concept and applications of halflife and
shelf life in the formulation and production of different pharmaceutical
products and drugs
• Describe the principles and concepts of first order
reaction kinetics
• Explain the importance of apparent firstorder kinetics to
the practice of pharmacy
• Describe halflife and shelf life of pharmaceutical
products and drugs
• Describe the principles and concepts of second order
reaction kinetics
• Calculate halflife and shelf life of pharmaceutical
products and drugs
• Determine the order of a reaction
Chemical Kinetics
• Chemical kinetics involve the study of the rate of a
chemical process
• The rate, velocity or speed of a reaction is given by ± (dc/dt)
• dc is the small change in the concentration within a given
time interval
• Negative sign indicates the decrease in concentration over
a period of time
• Law of mass action explains the rate of a chemical
reaction is proportional to the product of the molar concentration of the
reactants each raised to a power equal to the number of molecules of the
substance undergoing reaction
Molecularity of a Reaction
• Molecularity is defined in terms of a number which is
equal to the number of
molecules or atoms
that must collide simultaneously to give the products
• Unimolecular reactions one type of molecule stoichiometrically
participate in the reaction
ExampleIsomerisation of transstilbene to cisstilbene
• Bimolecular reaction Two types of molecules stoichiometrically
involved in the reaction
Example Oxidation of hydrogen peroxide
• Termolecular reaction Termolecular and other higher molecularity
are seldom observed
• Three or more molecules having sufficient kinetic energy
meeting simultaneously in the same region of space is unlikely
Order of a Reaction
• Order of a reaction is defined as the number of
concentration terms on which the rate of a reaction depends
• The overall order of reaction is equal to the powers of
the concentration terms affecting the experimentally determined rate
• In contrast to molecularity, it is possible for the order
of a reaction to assume fractional or zero values
Zero Order Reaction
• Zero order reaction is defined as a reaction in which the
rate does not depend on the concentration terms of the reactants
• Mathematically expressed as:
−dc / dt =k0
Where, k0 is the specific rate constant
• Examples:  Colour loss of liquid multisulfonamide
preparation
 Oxidation of vitamin A in an oily solution
 Photochemical degradation of chlorpromazine in aqueous
solution
• Mechanism: The
rate must depend upon some factor other than the concentration term
Derivation:
• The rate
equation for zero order can be written as
−dA / dt =k0…………..(1)
Where A is the absorbance (optical density) of the
preparation
• The concentration is measured in terms of optical density
• Negative sign indicates colour fading
• Integrating equation (1) between initial absorbance, A_{0}
at t=0 time, and absorbance, At at t=t
or, k0= A_{0}−A_{t} / t
…………..(2)
• The initial concentration is expressed as ‘a’ and the concentration
at any time t, is ‘c’, then equation (2) becomes
k0=(a− c) / t ………………(3)
• Equation (3) may be written as
c= a  k_{0}t………….(4)
• The units for k_{0} are conc/time, if the conc. Is
expressed in moles/liter, then k0 will be moles/liter.sec
Half life
• It is the time required for the concentration of the
reactant to reduce to half of its initial concentration
• The halflife can be derived as follows:
c= a/2 and t=t1/2
Substituting the values in the equation (3) gives:
• The unit for halflife period is sec/conc., min/conc.
hr/conc. etc.
• Shelf life
• It is the time required for the concentration of the
reactant to reduce 90% of its initial concentration
• Terms in equation (3) change to
C = 90a / 100 and t= t90
• Substituting the values in equation (3) gives:
t90=(a− 0.9a) / k_{0 }=
0.1a / k_{0 }………(6)
• Units time/conc
Apparent Zero Order Reaction
• Pseudo zero order is a reaction, which may be a first
order, but behaves like a zero order
• In suspensions, drug degradation is a chemical reaction
and follows an apparent zero order
• The rate equation can be written as:
d[A] / dt =k1[A]…………..(7)
Where [A]is concentration of undecomposed drug at time t,
and k1 is the first order rate constant
• When [A] is maintained constant due to reservoir of solids
in the suspension, the rate equation (7) changes to
d[A]

 =
k1 X constant = k0 …………..(8)
dt
First Order Reaction
• First order reaction is defined as a reaction in which the
rate of reaction depends on the concentration of one reactant
• The first order rate equation can be written as:
−dc / dt α c , therefore, −dc /
dt = k1c
Where c is the concentration
of the reactant
and k1 is
the specific rate constant for first order
Examples
• Decomposition of hydrogen peroxide catalysed by 0.02 M potassium
iodide
• Acid hydrolysis of ethyl acetate and methyl acetate
• Diffusion of drugs across biological membranes
Derivation
• Rate expression is written as:
−dc / dt = k1c………(1)
Integrating equation (1) between concentration c0 at time
t=0 and concentration ct at time t=t gives:
ln c_{t} – ln c_{0} = k_{1}(t0)
ln c_{t} = ln c_{0}k_{1}t………………(2)
Converting equation (2) to logarithm to the base 10 gives:
Rearranging the above equation,
• Graphically the equation may be represented as:
• The unit for k1 is reciprocal time, hours1, minutes1
• Equation (4) can also be written as
• The exponential form of the first order rate equation is
The equation in logarithms to base 10
• The exponential form of first order kinetics represent
that the curve will be asymptotic
Half life
• Time required to reduce the concentration of the reactant
to half of its initial concentration the term in equation (4) can be changed to
c_{t}= c_{0}/2
and t=t_{1/2}
• Substituting the terms in equation (4) gives:
Shelf life
The term in equation (4) can be changed to
c_{t}= (90/100) c_{0 } and t=t_{90}
Substituting the terms in equation (4) and rearranging
gives:
Pseudo First Order Reaction Reaction
• It is a reaction which is originally a second order but
made to behave like a first order
• In second order reaction, the rate depends on the concentration
terms of two reactants, the rate equation would be:
−dc / dt = k_{2}[A][B]…………..(10)
• Where A and B are the reactants in the reaction and k_{2}
is second order rate constant
• In pseudo first order the concentration of one of the
reactant is in large excess, and considered to be constant
−dc / dt = k_{2}[A][constant]…………..(11)
Examples
• Hydrolysis of esters catalysed by H+ ions
• Base catalysed oxidative degradation of prednisolone in aqueous
solution
• Acid catalysed hydrolysis of digoxin
Second Order Reaction Reaction
• It is defined as a reaction in which the rate depends on
the concentration terms of two reactants each raised to the power one
• The rate equation can be written as
Where [A] and [B] are the concentration of A and B
k_{2} is the specific rate constant for second order
Examples
• Alkaline hydrolysis of esters such as methyl acetate or
ethyl acetate
• Hydrolysis of chlorobutanol in presence of sodium
hydroxide
Derivation: As
per the definition the rate equation is
• Let ‘a’ and ‘b’ be the initial concentration of A and B,
respectively, and ‘x’ be the concentration of each species reacting in time t
• Substituting the above terms in equation (1) gives:
• Considering a=b, the above equation changes to
• Integrating equation (2) employing the conditions x=0 at
t=0 and x = x at t=t
• Equation (3) is the integral equation for second order
reaction kinetics when a=b
• When a ‡ b, the integral equation is :
• Graphical representation of second order kinetics
Half life
• As per the definition the terms in equation (3) can be
changed to
• Unit for halflife time/ conc.
Determination of Order of a Reaction
• The order of a reaction can be determined by
experimentally
• The method employed to determine order of a reaction are:
Graphical method
• The kinetic experiment is conducted and the datas are
collected
• The datas are plotted on a graph paper
• The graph which gives a better fit for the straight line,
the reaction is considered to be of that order
Substitution method
• The kinetic experiment is conducted and the datas are
collected
• The datas are substituted in the integral equation of
zero, first and second order to get the k values
• The order in which the k values at different time period
remain constant, the reaction is considered to be of that order
Halflife method
• Initially the t_{1/2 }is calculated by using the
equation for each order
• The relationship between halflife and initial
concentration is as follows:
T_{1/2} = 1 / a^{n−1 }………….(6)
Where, n is the order of the reaction
• Alternatively an experiment is conducted at two different initial
concentration a1 and a2
• The halflife t_{1/2}(1) and t_{1/2 }(2)
are related as follows
Where n is the order of the reaction
Summary
• Rate Rate of a
reaction is given by ± (dc/dt) dc is the small change in the concentration
within a given time interval
• Molecularity 
It is defined in terms of a number which is equal to the number of molecules or
atoms that must collide simultaneously to give the products
• Order – Order
of a reaction is defined as the number of concentration terms on which the rate
of a reaction depends
• Zero order
reaction It is defined as a reaction in which the rate does not depend on
the concentration terms of the reactants
• Pseudo zero order
reaction It is a reaction, which may be a first order, but behaves like a
zero order
• First order
reaction It is defined as a reaction in which the rate of reaction depends
on the concentration of one reactant
• Example Acid
hydrolysis of ethyl acetate and methyl acetate
• First order
reaction kinetics equation
• First order reaction kinetics is monoexponential in nature
• The curve of a first order reaction kinetics shows
asymptotic behaviour
• The halflife of
first order reaction kinetics is given by
t_{1/2 }=0.693 / 1
• Shelf life of first
order reaction kinetics is given by
t_{90} =0.105 / 1
• Pseudo first order
reaction It is a reaction which is originally a second order but made to
behave like a first order
• Pseudo first order reaction is represented by
−dc / dt = k_{2}[A][constant]
• Example for pseudo
first order reaction kinetics Hydrolysis of esters catalysed by H+ ions
• Second order
reaction  It is defined as a reaction in which the rate depends on the
concentration terms of two reactants each raised to the power one
• Example
Alkaline hydrolysis of esters such as methyl acetate or ethyl acetate
• Rate equation when a= b
• Rate equation when a ‡ b
• Halflife equation
for second order
t_{1/2 }= 1 / ak_{2}
• There are three methods
of determination of order of a reaction:
 Graphical method
 Halflife method
 Substitution method
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