Chemical kinetics dr. asm

Chemical KineticsChemical Kinetics
Drug stability: Reaction kinetics: zero, pseudo-zero, first &
second order(complex reaction: reversible, parallel and side
reactions), units of basic rate constants, determination of
reaction order.
Physical and chemical factors influencing the chemical
degradation of pharmaceutical product: temperature, solvent,
ionic strength, dielectric constant, specific & general acid base
catalysis, Simple numerical problems.
Stabilization of medicinal agents against common reactions
like hydrolysis & oxidation. Photolytic degradation and its
prevention. Accelerated stability testing in expiration dating of
pharmaceutical dosage forms.
Dr. Atishkumar S. Mundada
Associate Professor

Introduction:Introduction:
• The branch of Physical chemistry which deals with the rate
of reactions is called Chemical Kinetics.
• The study of Chemical Kinetics includes :
(1) The rate of the reactions and rate laws.
(2) The factors as temperature, pressure, concentration and
catalyst, that influence the rate of a reaction.
(3) The mechanism or the sequence of steps by which a
reaction occurs.
• A mechanism describes in detail exactly what takes place at
each stage of an overall transformation. A complete
mechanism must also account for all reactants used, the
function of a catalyst, stereochemistry, all products formed
and the amount of each. 2

Fundamentals of chemical kinetics:Fundamentals of chemical kinetics:
• Reaction rates: Speed of any event is measured by the
change that occurs in any interval of time.
• The speed of a reaction (reaction rate) is expressed as the
change in concentration of a reactant or product over a
certain amount of time.
• Units are usually Mole/sec (M/s).
• Rates are affected by several factors:
• The concentrations of the reactants
• The temperature at which a reaction occurs
• The presence of a catalyst
• The surface area of solid/ liquid reactants/ catalysts 3

• Rate Law: The empirical differential rate equation (or
simply the rate law) is determined experimentally and is
defined as the expression for the rate of reaction in terms of
concentrations of chemical species as indicated by
Equation
• Rate = k[reactant 1]m[reactant 2]n ....
• where k is the rate constant (or rate coefficient) and the
exponents (m) and (n) are determined experimentally and
can be a whole number (positive or negative) or, in complex
reactions, fractions.
• The reaction rate equation (RRE) contains concentration
terms for all species that interact up to and including the
rate-limiting step.
18 March 2020 SNJB's SSDJ College of Pharmacy, Chandwad (Nasik) 4

• Order of Reaction: The order of reaction (or order of the
rate law) is the sum of the exponents in the rate law, that is,
the sum of the partial orders with respect to individual
reagents, for example, (m+n) of rate law Equation.
• However, Zuman and Patel stressed that: “with more
complex reactions the overall kinetic order loses its
meaning, since the reaction rates are not simple functions
of concentration.
• In such cases, systematically planned experiments
enabling the verification of the complete RRE are
necessary”.

• Molecularity: Molecularity is the number of colliding
molecular entities that are involved in a single reaction step.
• While the order of a reaction is derived experimentally, the
molecularity is a theoretical concept and can only be applied
to elementary reactions.
• In elementary reactions, the reaction order, the molecularity,
and the stoichiometric coefficient are numerically the same
but represent different concepts.
• Thus, a reaction involving one molecular entity is called
unimolecular, whereas a bimolecular reaction involves two
molecular entities.
• A reaction involving three molecular entities is called
termolecular or trimolecular; these reactions are rare
because of the improbability of three molecular entities
colliding simultaneously. 6

• Rate Constant: The rate constant, k, is the proportionality
constant that relates the reaction rate to the concentration
(or activity or pressure, for example) of the reacting
substances, as shown in rate law equation.
• Consider a first-order reaction of a reagent (1.0 mol L−1)
whose k=0.01 s−1. This means that each second, 0.01 mol
L−1 of the reactant, is transformed into products.
• The value of k for two reactions of different orders (e.g.,
first, second) cannot be compared directly because their
units are different. For second order reaction it is Ltr Mol s−1
7

• Rate-Controlling Step: A rate-controlling (rate-
determining or rate-limiting) step is the slowest step of a
chemical reaction that determines the rate of the overall
reaction.
• In a simplified model, it can be compared to the neck of a
funnel. The rate at which water flows through a funnel is
limited/determined roughly by the width of the neck of the
funnel and not by the rate at which the water is poured into
the funnel.
• For any multistep reaction, the RLS is taken as the “most
sensitive” step, or the step, which, if perturbed, causes the
largest change in overall rate.

• Reaction Half-Life (t1/2): The half-life (or half-time, t1/2) of a
reaction is the time required for the concentration of a given
reactant to reach a value that is the arithmetic mean of its
initial and final, or equilibrium, values.
• For a reactant that is entirely consumed, it is the time
required for the reactant concentration to fall to one-half of
its initial value.
• This term is used to convey a qualitative idea of the
timescale for the reaction.
• It has a quantitative relationship to the rate constant in
simple cases. For example, an irreversible first-order
reaction is practically complete after five t1/2, corresponding
to 96.9% reactant transformation.

• The half-life of a reaction has an exact quantitative meaning
only in the following cases:
• (i) for a first-order reaction, where the half-life of the
reactant may be called the half-life of the reaction;
• (ii) for a reaction involving more than one reactant, with
their concentrations in their stoichiometric ratios. In this
case, the half-life of each reactant is the same and may
be called the half-life of the reaction.
• If the concentrations of reactants are not in their
stoichiometric ratios, the half-lives for the different reactants
are not the same and use of the term half-life of the reaction
is not warranted.

Types of Reactions:Types of Reactions:
• Chemical reactions may be classed into two types :
(a) Elementary reactions
(b) Complex reactions
• An elementary reaction is a simple reaction which
occurs in a single step.
• A complex reaction is that which occurs in two or more
steps.
• Namely reversible, consecutive, and parallel reactions.
• The simplest case of consecutive reactions is:
A→B→C
• Compounds that undergo reaction via two or more
pathways simultaneously are referred to as parallel or
competitive.

Zero order reaction:Zero order reaction:
• A reactant whose concentration does not affect the reaction
rate is not included in the rate law. In effect, the
concentration of such a reactant has the power 0.
• Thus [A]0 = 1.
• A zero order reaction is one whose rate is independent
of concentration. For example, the rate law for the
reaction
• NO2 + CO ⎯⎯→ NO + CO2 at 200°C is rate = k [NO2]2
• Here the rate does not depend on [CO], so this is not
included in the rate law and the power of [CO] is
understood to be zero.
• The reaction is zeroth order with respect to CO. The
reaction is second order with respect to [NO2]. The overall
reaction order is 2 + 0 = 2.

PseudoPseudo––order reactions:order reactions:
• A reaction in which one of the reactants is present in a large
excess shows an order different from the actual order. The
experimental order which is not the actual one is
referred to as the pseudo order.
• Let us consider a reaction A + B ⎯⎯→ products
• in which the reactant B is present in a large excess. Since it
is an elementary reaction, its rate law can be written as
rate = k [A] [B]
• As B is present in large excess, its concentration remains
practically constant in the course of reaction. Thus the rate
law can be written as rate = k′ [A]
• where the new rate constant k′ = k [B].
• Thus the actual order of the reaction is second-order but in
practice it will be first-order. Therefore, the reaction is said to
have a pseudo-first order. 13

First order reactions:First order reactions:
• Let us consider a first order reaction A→ products
• Suppose that at the beginning of the reaction (t = 0), the
concentration of A is a moles litre–1. If after time t, x moles
of A have changed, the conc. of A is (a – x).
• We know that for a first order reaction, the rate of reaction,
dx/dt, is directly proportional to the concentration of the
reactant.
• The value of k can be found by substituting the values of a
and (a – x) determined experimentally at time interval t
during the course of the reaction.
• Examples of First order Reactions:
(1) Decomposition of N2O5 in CCl4 solution
(2) Decomposition of H2O2 in aqueous solution.
(3) Hydrolysis of an Ester 14

Second order reactions:Second order reactions:
• Let us take a second order reaction of the type 2A →
products
• Suppose the initial concentration of A is a moles litre–1. If
after time t, x moles of A have reacted, the concentration of
A is (a – x).
• We know that for such a second order reaction, rate of
reaction is proportional to the square of the concentration of
the reactant.
• Examples of Second order Reaction
• Hydrolysis of an Ester by NaOH.

How to determine the order of a reaction:How to determine the order of a reaction:
• There are at least four different methods to determine the
order of a reaction.
• (1) Using integrated rate equations: The rate equation
which yields a constant value of k corresponds to the
correct order of the reaction.
• This method of ascertaining the order of a reaction is
essentially a method of hit-and-trial but was the first to be
employed. It is still used extensively to find the order of
simple reactions.
• (2) Graphical method: we can determine the reaction
order by seeing whether a graph of the data fits one of the
integrated rate equations.

• (3) Using half-life period: Two separate experiments are
performed by taking different initial concentrations of a
reactant.
• The progress of the reaction in each case is recorded by
analysis. When the initial concentration is reduced to one-
half, the time is noted. Let the initial concentrations in the
two experiments be [A1] and [A2], while times for
completion of half change are t1 and t2 respectively.
• Calculation of order of reaction. We know that half-life
period for a first order reaction is independent of the initial
concentration, [A].
• We also know : half-life ∝ 1/[A] for 2nd order reaction
• half-life ∝ 1/ [A]2 for 3rd order reaction

• (4) The Differential method: This method was suggested by
van’t Hoff and, therefore, it is also called van’t Hoff’s
differential method.
• According to it, the rate of a reaction of the nth order is
proportional to the nth power of concentration.
• (5) Ostwald’s Isolation method:
• This method is employed in determining the order of
complicated reactions by ‘isolating’ one of the reactants so far
as its influence on the rate of reaction is concerned.
• Suppose the reaction under consideration is : A + B + C ⎯⎯→
products
• The order of the reaction with respect to A, B and C is
determined. The order of the reaction is then determined by
using any of the methods described earlier. 18

Degradation of pharmaceutical product:
• The USP defines the stability of a pharmaceutical product
as “extent to which a product retains, with in specified limits,
and through out its period of storage and use i.e. its shelf
life, the same properties and characteristics that it
possessed at the time of its manufacture”.
Why stability testing is necessary-
• Chemical degradation may lead lowering of concentration
of drug in dosage form
• Toxic product may form due to degradation of active
ingredients.
Stability is used to determine:
• Quality of a drug substance or drug product
• Shelf life for the drug product
• Recommended storage conditions

Degradation Pathways:
• Pharmaceutical products tends to deteriorate on storage,
even though it is expected to retain acceptable chemical,
physical and microbiological stability.
• To get desired effect from any pharmaceutical product has
to be stable throughout its shelf life.
• Drug substances used as pharmaceuticals have diverse
molecular structures, therefore, they are susceptible to
different kinds of degradation pathways.
• Degradation of drugs occur through three principal
pathways namely
• Chemical Degradation
• Physical Degradation
• Microbial Degradation.

Chemical degradation:
• Hydrolysis/Solvolysis: Drugs with the following functional
groups:esters, amides, lactones or lactams, Imides, may be
susceptible to hydrolysis.
• Oxidation: Some functional groups subject to oxidation are
phenols, aldehydes, alcohols and unsaturated fats and oils.
• In order to reduce degradation by oxidation, nitrogen and
carbon dioxide are often used to replace the airspace in
pharmaceutical dosage forms.
• Polymerization: This is the process by which two or more
identical molecules combine together to form a much larger
and more complex molecule. The reactants are called
monomers and the products are called polymers.
• Eg. Aminopenicillin, such as ampicillin sodium in aqueous
solution.
21

• Isomerisation: is the process of conversion of a drug into its
optical or geometric isomers.
• The isomers are often of different therapeutic activity.
• There are two types of isomerization- Optical & Geometric
• Optical isomerism divided into Racemization &
epimerization.
• Racemization is a reversible conversion between optical
isomers also known as enantiomers. Eg. Thalidomide.
• Epimerization is a irreversible conversion. Eg. Tetracyclines
to epitetracycline.
• Geometric isomerism: Forms CIS and Trans isomers of the
compounds. E.g.vitamin A forms the cis–trans isomers.

• Dehydration: Is the elimination of a water molecule from
the molecular structures. Found in the degradation of
prostaglandin E2 and tetracycline.
• Decarboxylation: Occurs sometimes in drugs with
carboxylic acid groups. It is not a common.
• Decarboxylations occur in the following antibiotics:
carbenicillin sodium, carbenicillin free acid, ticarcillin
sodium, and ticarcillin free acid.
• Chemical Incompatibilities: May occur in APIs as well as
between API & Excipients.

Physical Degradation:
• Polymorphism: Polymorphs are different crystal forms of
the same compound caused by exposure to changes in
temperature, pressure, relative humidity, drying,
granulation, milling and compression.
• Polymorphs differ in their crystal energy, insolubility,
dissolution rate and melting point. The metastable seeks to
revert to the most stable form.
• Steroids, sulphamides and barbiturates are notorious for
their propensity to form polymorphs.
• Adsorption: Drug-plastic interaction has been a major
challenge when drugs are stored in plastic materials.
• This compromises the preservative content and
predisposes the drug to microbial degradation.

• Temperature: Increase in temperature degrades
thermolabiles, it enhances degradation chemically and
physically.
• Evaporation of water from liquid preparation will cause the
drug concentration to change with the possibility of
crystallization, if the solubility of the drug in the solvent is
exceeded.
• Water loss from emulsion will cause it to crack or
suspension to cake.
• Volatile components such as alcohol, ether, ketones,
aldehydes, iodine, volatile oils, camphor and cosolvent of
lower molecular weight etc., escape from formulation
through vaporization, even at room temperature, leading to
drug loss.
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SNJB's SSDJ College of Pharmacy, Chandwad (Nasik) 25

• Photodegradation: Degradation of light sensitive drugs or
excipients by room or sunlight.
• Photodegradation occurs when molecules absorb light
wavelength, especially 300–400 nm. UV light causes more
damage than red or orange light and shorter wavelengths
cause more damage than longer ones.
• Photodecomposition involves oxidation mechanism,
although others like polymerization or ring opening may
occur. Once initiated can progress in the absence of light in
a chain reaction.
• It occurs during manufacture, storage and during the use of
the product.
• In susceptible compounds, photodecomposition creates
free radical intermediates, which can perpetuate chain
reactions. 26

• To avoid photochemical reactions, photolabile formulations
are packaged in coloured containers.
• Yellowish green glass is best protector against UV
radiation; amber colour gives only a little protection from
infrared radiation.
• The addition of an antioxidant like sodium thiosulfate or
sodium metabisulfite hinders the photodegradation of
sulfacetamide.
• Nifedipine, nicardipine, nitroprusside, chlorthalidone,
acetazolamide, retinol, riboflavin, furosemide and
phenothiazines are very labile to photo-oxidation.
• Photochemical reactions are common in steroids.
18 March 2020
SNJB's SSDJ College of Pharmacy, Chandwad (Nasik)
27

• pH: Acidic and alkaline pH influence the rate of
decomposition of most drugs.
• Many drugs are stable between pH 4 and 8.
• Weekly acidic and basic drugs show good solubility when
they are ionized and they also decompose faster when they
are ionized.
• So if the pH of a drug solution has to be adjusted to improve
solubility and the resultant pH leads to instability then a way
out of this tricky problem is to introduce a water-miscible
solvent into the product.
• It will increase stability by:
• suppressing ionization
• reducing the extreme pH required to achieve solubility -
enhancing solubility and
• reducing the water activity by reducing the polarity of the
solvent. 20% PG is placed in chlordiazepoxide injection. 28

• Reactions catalyzed by pH are monitored by measuring
degradation rates against pH, keeping temperature, ionic
strength and solvent concentration constant.
• Some buffers such as acetate, citrate, lactate, phosphate
and ascorbate buffers are utilized to prevent drastic change
in pH.
• Sometimes pH can have a very serious effect on
decomposition. As little as 1 pH unit change in pH can
cause a change of ten fold in rate constant.
• So when we are formulating a drug into a solution we
should carefully prepare a pH – decomposition profile and
then formulate the solution at a pH which is acceptable
physiologically and stability-wise also.

• Moisture:
• a. Water catalyses chemical reactions as oxidation,
hydrolysis and reduction reaction
• b. Water promotes microbial growth.
• Concentration: rate of drug degradation is constant for the
solutions of the same drug with different concentration.
• So, ratio of degraded part to total amount of drug in diluted
solution is bigger than of concentrated solution.
• Stock solutions: are concentrated solutions which diluted by
using (i.e. syrup 85%) at high concentration the stability is
high.
SNJB's SSDJ College of Pharmacy, Chandwad (Nasik) 30

Microbiological degradation:
• Micro-organisms are everywhere: air, food, water and
humans, raw materials and finished products.
• Degradation due to micro-organisms can render the
product harmful to the patient or have an adverse effect on
the product properties.
• Once opened, a product degrades microbiologically
shortening the shelf life, except there is addition of
preservatives.
• Injectable need to be used immediately the container is
opened.

Stabilization of medicinal agents:Stabilization of medicinal agents:
• The main chemical reactions that affect the stability of a
drug are oxidation and hydrolysis.
• Temperature control: The most universal approach to
stabilizing drug components is to lower the temperature.
• Reduction of the temperature normally slows down not only
enzymatic but also spontaneous reactions.
• pH adjustment: The second approach, pH control, takes
advantage of the fact that most enzymes have a narrow
range of working pH.
• Albumin possessing weak hydrolase activity in its IIIA
subdomain is the most abundant protein in animal plasma.
• It binds to a number of drug molecules conferring stability to
certain compounds that are otherwise unstable in plasma. 33

• Derivatization: One of the analytical purposes for the
derivatization of pharmaceuticals is to ease the stability
issue in biological samples.
• For example, drug molecules containing a sulfhydryl group
(the thiol compound) are generally not stable in plasma.
• The thiol group is a strong nucleophile that may react with
cystine residues in plasma protein or glutathione to form
disulfide bonds, depending on the solution pH and oxidation
potential.
• Derivatization is one of the useful approaches employed to
stabilize this class of compounds.

Stability testing:Stability testing:
• One of the major reasons for product recalls in past decade
is supply of poor quality drugs and stability data does not
support expiration date of finished pharmaceutical product.
• Additionally to get desired effect from any pharmaceutical
product is has to be stable throughout its shelf life.
• Stability studies are not only indispensible part of any
product development but it also play crucial role in
pharmaceutical research and development.
• For any new drug product or finished pharmaceutical
product, stability analysis not only provides useful
information regarding the degradation of the drug product,
but it also gives an idea about an expiration dating of the
same.
• Alteration in quality will affect safety and efficacy of
pharmaceutical formulation. 35

• The main goal of stability testing is to provide evidence on
how the quality of a drug substance or drug product varies
with time under the influence of a variety of environmental
factors, such as temperature, humidity, and light, and to
establish a retest period for the drug substance or a shelf-
life for the drug product and recommended storage
conditions so that it will remain stable throughout its shelf
life.
• Additionally stability studies help in designing a drug product
and its final packaging material so that the product has
appropriate physical, chemical and microbiological
properties during a defined shelf life when stored and used
as labeled.
36SNJB's SSDJ College of Pharmacy, Chandwad (Nasik)

Regulatory perspective of stability study:
• Various guidelines are available on designing and as well
as conducting stability study of pharmaceuticals.
• Stability testing guidelines by international conference on
harmonization has made remarkable progress in
implementation across the globe.
• From the regulatory prospective main reason to conduct
degradation studies is to support following information:
• Evaluate the intrinsic stability of drug molecule and
identify probable degradation product.
• Predict the degradation pathway for parent drug
molecule.
• Develop and validate suitable stability indicating assay
method.
• Accelerated and stress studies are also conducted to
establish a tentative expiration date.
18 March 2020 SNJB's SSDJ College of Pharmacy, Chandwad (Nasik)
37

Stability testing methods:Stability testing methods:
• Stability testing is a routine procedure performed on drug
substances and products and is employed at various stages
of the product development.
• In early stages, accelerated stability testing (at relatively
high temperatures and/or humidity) is used in order to
determine the type of degradation products which may be
found after long-term storage.
• Testing under less rigorous conditions i.e. those
recommended for long-term shelf storage, at slightly
elevated temperatures is used to determine a product’s
shelf life and expiration dates.
• •The major aim of pharmaceutical stability testing is to
provide reasonable assurance that the products will remain
at an acceptable level of fitness/quality throughout the
period during which they are in market. 38

Real time stability testing:
• Real-time stability testing is normally performed for longer
duration in order to allow significant product degradation
under recommended storage conditions.
• The period of the test depends upon the stability of the
product which should be long enough to indicate clearly that
no measurable degradation occurs and must permit one to
distinguish degradation from inter-assay variation
• During the testing, data is collected at an appropriate
frequency such that a trend analysis is able to distinguish
instability from day-to-day ambiguity.
• The reliability of data interpretation can be increased by
including a single batch of reference material for which
stability characteristics have already been established.

Accelerated stability testing:
• In accelerated stability testing the samples are subjected to
stress, refrigerated after stressing, and then assayed
simultaneously.
• Because the duration of the analysis is short, the likelihood
of instability in the measurement system is reduced in
comparison to the real-time stability testing.
• Further, in accelerated stability testing, comparison of the
unstressed product with stressed material is made within
the same assay and the stressed sample recovery is
expressed as percent of unstressed sample recovery.
• For statistical reasons, the treatment in accelerated stability
projections is recommended to be conducted at four
different stress temperatures.

• The concept of accelerated stability testing is based upon
the Arrhenius equation lnK= lnA + Δ /
•K = degradation rate/s,
•A = frequency factor/s, (Specifically relates to molecular collision,
deals with the frequency of molecules that collide in the correct
orientation and with enough energy to initiate a reaction. It is a
factor that is determined experimentally, as it varies with different
reactions)
•ΔE = activation energy (kJ/mol),
•R = universal gas constant (0.00831kJ/mol),
•T=absolute temperature (K)
• This equation describe the relationship between storage
temperatures and degradation rate.
• Using Arrhenius equation, projection of stability from the
degradation rates observed at high temperatures for some
degradation processes can be determined.
• When the activation energy is known, the degradation rate at
low temperatures may be projected from those observed at
“stress” temperatures.
41

• The stress tests used in the current International Conference
on Harmonization (ICH) guideline (e.g., 40% for products to
be stored at controlled room temperature) were developed
from a model that assumes energy of activation of about 83
kJ per mole.
• It explains the effect of temperature on rate of a reaction.
According to Arrhenius, for every 10º rise in temperature, the
speed of reaction increases about 2-3 times.
• Estimation of k value
• The reaction is conducted at several temperatures.
• Concentration of reactants is determined (log(a-x).
• Appropriate graphs are drawn for the kinetic data.
• Data is processed for all the orders.
• The order of the reaction is identified.
• From the slopes of the lines, k values are calculated for all
temperatures.

• By using Arrhenius relationship, Log k values are plotted
against reciprocal of absolute temperature.
• Extrapolate the straight line to room temperature (k25) and
read the log k value on y-axis.
• With substitution of the k25 value in the equation, the shelf
life of the product is calculated.

Expiration Date/Shelf life:
• An expiration date is defined as the time up to which the
product will remain stable when stored under recommended
storage conditions. Thus, an expiration date is the date
beyond which the product may no longer retain fit for use.
• If the product is not stored in accordance with the
manufacturer’s instructions, then the product may be
expected to degrade more rapidly.
• Shelf life is the time during which the product, if stored
appropriately as per the manufacturer’s instructions, will
retain fitness for use (>90% of label claim of potency).
• The expiration date is also defined as the date placed on the
container/labels of a drug product designating the time
during which a batch of the product is expected to remain
within the approved shelf life specifications, if stored under
defined conditions and after which it should not be used 44

Chemical kinetics dr. asm

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