Chemical Kinetics
Learning Objectives
At the end of this lecture, students will be able to:
• Define rate, order of a reaction and molecularity
• Explain the use of apparent zero-order kinetics in the practice of pharmacy
• Describe the concept and applications of half-life 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 first-order kinetics to the practice of pharmacy
• Describe half-life and shelf life of pharmaceutical products and drugs
• Describe the principles and concepts of second-order reaction kinetics
• Calculate the half-life and shelf life of pharmaceutical products and drugs
• Determine the order of a reaction
Chemical Kinetics
• Chemical kinetics involves 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 that is equal to the number of molecules or atoms that must collide simultaneously to give the products
• Unimolecular reactions- one type of molecule stoichiometrically participates in the reaction
Example-Isomerisation of trans-stilbene to cis-stilbene
• 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 the 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 multi sulfonamide 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 color fading
• Integrating equation (1) between initial absorbance, A0 at t=0 time, and absorbance, At at t=t
or, k0= A0−At / 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 – k0t………….(4)
• The units for k0 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 half-life can be derived as follows:
c= a/2 and t=t1/2
Substituting the values in the equation (3) gives:
• The unit for the half-life 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) / k0 =
0.1a / k0 ………(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 the concentration of undecomposed drug at time t, and k1 is the first order rate constant
• When [A] is maintained constant due to the 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 catalyzed 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 ct – ln c0 = -k1(t-0)
ln ct = ln c0-k1t………………(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, hours-1, minutes-1
• 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 represents 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
ct= c0/2
and t=t1/2
• Substituting the terms in equation (4) gives:
Shelf life
The term in equation (4) can be changed to
ct= (90/100) c0 and t=t90
Substituting the terms in equation (4) and rearranging gives:
Pseudo First Order Reaction Reaction
• It is a reaction that 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 = k2[A][B]…………..(10)
• Where A and B are the reactants in the reaction and k2 is the second order rate constant
• In pseudo first order the concentration of one of the reactants is in large excess, and considered to be constant
−dc / dt = k2[A][constant]…………..(11)
Examples
• Hydrolysis of esters catalyzed by H+ ions
• Base catalyzed oxidative degradation of prednisolone in an aqueous solution
• Acid catalyzed 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 concentrations of A and B
k2 is the specific rate constant for second-order
Examples
• Alkaline hydrolysis of esters such as methyl acetate or ethyl acetate
• Hydrolysis of chlorobutanol in the 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 half-life- time/ conc.
Determination of Order of a Reaction
• The order of a reaction can be determined experimentally
• The methods employed to determine the order of a reaction are:
Graphical method
• The kinetic experiment is conducted and the data are collected
• The data are plotted on 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 data are collected
• The data 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
Half-life method
• Initially the t1/2 is calculated by using the equation for each order
• The relationship between half-life and initial concentration is as follows:
T1/2 = 1 / an−1 ………….(6)
Where n is the order of the reaction
• Alternatively an experiment is conducted at two different initial concentrations a1 and a2
• The half-life t1/2(1) and t1/2 (2) are related as follows
Where n is the order of the reaction
Chemical Kinetics Summary
• Rate- The 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 that is equal to the number of molecules or atoms that must collide simultaneously to give the products
• Order – The 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 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 behavior
• The half-life of first-order reaction kinetics is given by
t1/2 =0.693 / 1
• Shelf life of first-order reaction kinetics is given by
t90 =0.105 / 1
• Pseudo-first-order reaction- It is a reaction that is originally a second-order but made to behave like a first-order
• Pseudo-first-order reaction is represented by
−dc / dt = k2[A][constant]
• Example for pseudo-first-order reaction kinetics- Hydrolysis of esters catalyzed 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 of one
• Example- Alkaline hydrolysis of esters such as methyl acetate or ethyl acetate
• Rate equation when a= b
• Rate equation when a ‡ b
• Half-life equation for second-order
t1/2 = 1 / ak2
• There are three methods of determining of order of a reaction:
– Graphical method
– Half-life method
– Substitution method
Chemical Kinetics FAQs
- What is the Arrhenius equation, and how does it relate to chemical kinetics?
- The Arrhenius equation relates temperature, activation energy, and the rate constant of a reaction. It helps us understand how temperature influences reaction rates.
- What is the role of catalysts in chemical kinetics?
- Catalysts increase reaction rates by providing an alternative reaction pathway with lower activation energy, allowing reactions to occur more quickly.
- How do concentration and temperature affect reaction rates?
- Higher concentrations and temperatures generally lead to faster reaction rates by increasing the frequency of collisions and the energy of reactant molecules.
- What distinguishes chemical kinetics from thermodynamics?
- Chemical kinetics deals with reaction rates and mechanisms, while thermodynamics focuses on the energy changes during reactions.
- What are some real-world applications of chemical kinetics?
- Chemical kinetics is applied in pharmaceuticals, environmental science, and materials science to predict and control reaction behavior for practical purposes.
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