Stability studies are important to ensure drugs maintain their efficacy and safety throughout their shelf life. The rate of a chemical reaction determines a drug's stability and can be zero order, first order, or second order. Various factors influence reaction rates, including temperature, pH, moisture, light exposure, and concentration. Understanding reaction kinetics and identifying the order of a reaction allows researchers to predict a drug's shelf life by substituting experimental data into the appropriate rate equation.

1. Stability Studies

2. DRUG STABILITY
STABILITY:
Stability of a pharmaceutical product or a drug is defined as “extent to
which a product retains, within specified limits, and throughout its period
of storage and use (i-e its shelf life) the same properties and
characteristics that is possessed at the time of its manufacture ~ USP.
IMPORTANCE OF STABILITY:
 Chemical and physical degradation of drug substances may change
their PHARMACOLOGICAL effects, resulting in altered efficacy
therapeutic as well as toxicological consequences.
 Because pharmaceuticals are used therapeutically based on their
efficacy and safety, and being stable
 For maintenance of quality until the time of usage or until
their expiration date stability is important.
 The quality should be maintained under the various conditions that
pharmaceuticals encounter, during production, storage in
warehouses, transportation, and storage in hospital and community
pharmacies, as well as in the home.

3.  KINETIC PRINCIPLES:
kinetics in pharmaceuticals, IS defined as the study of physical and
chemical reactions in drugs and dosage forms, FACTORS influencing
these chemical reactions are, ACCELERATED stability testing and
prediction of shelf life of formulations.
 RATES AND ORDER OF REACTION:
To find whether how many constituents of the drug are active and which
primarily cause DEGRADATION AND factors like these, we need to
know the order of reaction
 TYPES OF ORDER OF REACTION:
1. .zero order reaction
2. . First order reaction
3. .second order reaction
4. .pseudo first order reaction
5. .pseudo zero order reaction
 ZERO ORDER REACTION:
If a rate of reaction is independent of concentration of reacting specie
the reaction is zero order reaction.

4.  ZERO ORDER REACTION (continued).
The rate of zero order reaction is given by,
-dA/dt =k
dA is the change in concentration with respect of change in time. “-“ sign
indicates that concentration is decreasing⌠∫
This rate equation can be integrated between initial concentration A®
(original) the At after time “t”.
∫ dA = -k ∫ dt
At -A⁰ = -kt
At = A⁰ - kt
The above equation can also be written as,
K =A⁰ -At/t or
T= A⁰ -At/k
Half life of zero order reaction:
At = ½ A⁰ or
t 1/2= ½ A⁰/K
 The time required for the drug to decompose by 10% (i.e. to 90% of
its original concentration). Thus,
At = 0.9A⁰

5.  ZERO ORDER REACTION (continued).
Substituting above equation we get,
T0.9 = A⁰ -0.9A⁰ /k
When a graph is plotted of concentration against time it gives a straight
line

6.  FIRST ORDER REACTION:
A first-order reaction is a reaction that proceeds at a rate that depends
linearly only on one reactant concentration.
The differential equation describing first order kinetics is:
A→ Product
Rate is the reaction rate (in unites of molar/time) and k is the reaction
rate coefficient (in units of 1/time).
The rate of reaction of first order reaction is given by
-dc/dt = kc
Dc/c = -kdt
Integrating between limits of concentration C⁰ at time t=0 and
concentration c at time t=t
∫ dc/c = -k∫ dt
Or converting to common log we get,
Log c =log C⁰ -kt /2.303 or
K= 2.303/t log c⁰/c or
K=2.303/t log a/(a-x)

7.  FIRST ORDER REACTION (continued):
Where,
‘a’ is the initial concentration equal to C⁰
‘x’ is decrease in concentration in time “t”
‘a-x)’ is concentration remaining after time ‘t’ and equal to c in above
equation.
Here the unit for “k” is sec-1.
HALF LIFE OF FIRST ORDER REACTION:
t 1/2 = 2.303/k log C⁰/1/2 C⁰
= 2.303/k log2
=0.693 /k
SHELF LIFE OF FIRST ORDER REACTION:
T0.9 = 2.303/k log C⁰/0.9 C⁰
=2.303/k × 0.0457
=0.1052/k.
Where dc represents the concentration and dt represents time interval k
is the constant.

8.  FIRST ORDER REACTION (continued):
 These equations can be shown by plotting graph of concentration
against time which is shown in fig (a) and if graph is plotted of log c
against t, a straight line is obtained with a slope equal to –k/2.303
which is shown in figure (b) rate constant can be obtained from the
slope of the line.

9.  SECOND ORDER REACTION:
A reaction is said to be second order when experimentally
determined rate of reaction is proportional to first power of two
reactants
A + B = Product
If a and b represents initial concentrations of A and B and x is the
amount of A and B reacting in time t, the reaction rate dx/dt is given
by,
Dx/dt = (a-x) (b-x)
Where (a-x) and (b-x) are conc. Of A and B.
If initial concentration of two components is equal then equation
becomes
Dx/dt = k (a-x) 2
On integrating x=0 at t=0 and x=dx at t=t we get,
∫ dx/(a – x ) = k∫ dt
Kt =1/at × x / (a-x)
And if the initial concentration is not equal then,

10.  SECOND ORDER REACTION (Continued):
 Kt = 2.303/ (a-b) × log b (a-x) / a (b-x)
x slope = k
a(a-x)
Time
Plot of x/a (a-x) versus time for a second order reaction giving a
diagonal straight line.

11. NOTE:
For instance we have to find the value of "K" or "expiry date of a drug" or "in how
much time the drug will be reduced to half”,we can find all these by substituting
the experimentally found values in a certain order of reaction's equation. That
particular order of reaction is found by graphical method mostly i.e. seeing the
shape of the curve for example straight line is for zero order reaction.
To illustrate the above lines let us take an example.
Consider that the initial concentration of a drug is (c° = 94 unit/ml) and
point/value at which drug was degraded or not suitable for use was ( c= 45
unit/ml ) where k is 2.06 × 10 -5 hr -1, reaction following first order. Find expiry
date?
Here we can put the value in the following equation of first order,
T = 2.303/k log c°/c
T= 2.303/2.06× 10 -5 log 94/45
T= 4 years approx.

12.  PSEUDO FIRST ORDER REACTION:
In a second order reaction ,if concentration of one component is too
large it virtually remains constant and rate of change in concentration
follows first order. Hydrolysis reaction are good example.
 PSEUDO ZERO ORDER REACTION:
A compound decomposing in a solution exhibits first order reaction ,but
if more of it is present in insoluble form. The concentration of the
compound in a solution, thus remains essentially remains constant till
any of insoluble drug remains constant. Such a reaction is pseudo order
reaction. For example in ASPIRIN SUSPENSION it remains zero order
until aspirin is in solid form as it gets dissolved the reaction becomes
first order.
 METHODS FOR FINDING ORDER OF REACTION:
1. Substitution Method
2. Graphical Method
3. Half Life Method
4. Ostwald Isolation Method

13.  Substitution Method:
In this method experimentally obtained data is substituted in relevant
rate equation. The equation that yields a fairly constant value of k
indicates the order of reaction. Table below shows the rate and half life
equation for different order reactions.

14.  GRAPHICAL METHOD:
In this method the data obtained from experiment is plotted to the
relevant form, to determine the particular order of reaction. For example
if a straight line comes it is a zero order reaction.
 Half Life Method:
In this method half life's are determined graphically by plotting a versus t
at two different initial concentrations a1 and a2 .The values of half life
and initial concentration are then substituted in the equation below and
order of reaction is obtained directly.
 Ostwald Isolation Method
This method is introduced by Ostwald and is used to determine the
order of a reaction with respect to one reactant at a time. The total order
of the reaction can be calculated by adding all the orders of there action
for individual reactant.
logt1/2(1)/t1/2(2)
log(a2/a1)
n=

15.  Ostwald Isolation Method (Continued):
The principle behind this method is that if the concentration of all
but one reactant is taken in excess, then during the course of
reaction, the concentration of those reactants taken in excess will
remain constantan the variation in the rate will correspond to the
concentration of that reactant whose concentration is small.
DEGRADATION FACTORS:
1. Temperature: high temperature accelerate oxidation, reduction
and hydrolysis reaction which lead to drug degradation
2. 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

16.  Ostwald Isolation Method (Continued):
pH leads to instability then a way out of this tricky problem is to
introduce a water miscible solvent into the product.
• 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.
3. Moisture:
a. Water catalyzes chemical reactions as oxidation, hydrolysis and
reduction reaction
b. Water promotes microbial growth
4. Light: affects drug stability through its energy or thermal effect which
lead to oxidation.

17. 5. Pharmaceutical dosage forms: solid dosage forms are more
stable than liquid dosage forms for presence of water.
6. 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.
7. UV light: It has a high energy level .it is the cause of many
degradation reactions, exposure to UV illumination may cause
oxidation (photo-oxidation) and scission (photolysis) of covalent
bonds. Yellow-green glass gives the best protection against the UV.
STABILITY TESTING:
First we need to know about the climatic zones .
Zone 1: temperate
Zone 2: Sub tropical with high positive humidity
Zone 3:Hot ,Dry
Zone 4: Hot ,humid

18. It is categorized in three types majorly,
 Accelerated stability testing:
Studies designed to increase the rate of chemical degradation or
physical change of an active substance or drug product by using
exaggerated storage conditions as part of the formal, definitive storage
program.
o Temperature & humidity specifications: In this study ,a storage
condition of 40®c ±2®c and relative humidity of 75±5% for all the four
zones for drug substances to be stored at 25 or 30®c.
o The studies are carried out for 6 months .
o For drug substances recommended to be stored in a refrigerator the
study should be carried out at 25±2®c and 60±5%.
o In general the accelerated storage conditions must be at least 15%
above the expected actual temperature and appropriate relative
humidity.
o Input of heat required to cause product failure is determined. This is
done to subject the product to a condition that accelerates
degradation. This information is then projected to predict shelf life or
used to compare the relative stability of alternative formulations .

19. o Acceleratedstabilitytesting(continued):
This usually provides an early indication of the product shelf life and thus shortening the
developmentschedule.In addition totemperature,stressconditionsapplied duringaccelerated
stability testing are moisture, light, agitation, gravity, pH and package accelerated stability
testing,aproductisstressed at severalhigh temperatures.
Inacceleratedstabilitytesting,aproduct isstressed at severalhigh (warmerthanambient)
temperaturesandtheamount ofheat input requiredtocauseproductfailureisdetermined.
Thisisdonetosubjecttheproducttoaconditionthat accelerates degradation.Thisinformation
isthenprojectedtopredict shelf life orusedtocomparetherelativestabilityofalternative
formulations. Thisusuallyprovidesanearlyindication oftheproductshelf life andthus
shorteningthedevelopmentschedule.In additionto temperature,stressconditionsapplied
duringacceleratedstability testingaremoisture,light,agitation,gravity,pHarealsoapplied.
o Acceleratedstabilitytesting(continued):
This usually provides an early indication of the product shelf life and thus shortening the
developmentschedule.In addition totemperature,stressconditionsapplied duringaccelerated
stability testing are moisture, light, agitation, gravity, pH and package accelerated stability
testing,aproductisstressed at severalhigh temperatures.
Inacceleratedstabilitytesting,aproduct isstressed at severalhigh (warmerthanambient)
temperaturesandtheamount ofheat input requiredtocauseproductfailureisdetermined.
Thisisdonetosubjecttheproducttoaconditionthat accelerates degradation.Thisinformation
isthenprojectedtopredict shelf life orusedtocomparetherelativestabilityofalternative
formulations. Thisusuallyprovidesanearlyindication oftheproductshelf life andthus
shorteningthedevelopmentschedule.In additionto temperature,stressconditionsapplied
duringacceleratedstability testingaremoisture,light,agitation,gravity,pHarealsoapplied.

20.  LONG TERM STABILITY TESTING:
 According to latest guidelines Expiry date is determined from Long-
Term Stability Test Data Accelerated data considered only supportive.
 For long-term studies, frequency of testing should be sufficient to
establish the stability profile of the API.
 For APIs with a proposed re-test period or shelf-life of at least 12
months, the frequency of testing at the long-term storage condition
should normally be every three months over the first year, every six
months over the second year and annually thereafter throughout the
proposed re-test period or shelf-life.
 TEMPERATURE AND HUMIDITY SPECIFICATIONS: In zone 1 and 2
temperature range is 25±2ºc and relative humidity is 60±5%, and in
zone 3 and 4 temperature conditions are 30±2ºc and relative humidity
is 65±5%.

21. Long term stability testing is normally performed for longer
duration of the test period in order to allow significant
product degradation under recommended storage conditions
.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. Stability of the reference material
also includes the stability of reagents as well as consistency of
the performance of the instrument to be used throughout the
period of stability testing. However, system performance and
control for drift and discontinuity resulting from changes in
both reagents and instrumentation must be monitored

22.  LONG TERM STABILITY TESTING (continued):
 Long term testing in substances which are to be stored in refrigerator are
recommended at 5±3ºc and for those who are to be stored in freezer are
recommended at -20±5ºc.
 INTERMEDIATE STABILITY TESTING:
 30±2ºc /60 ±5%.
 Cyclic temperature stress testing:
This is not a routine testing method for marketed products. In this method,
cyclic temperature stress tests are designed on knowledge of the product so
as to mimic likely conditions in market place storage.
 THEORATIC CONSIDERATIONS:
 Stability study requirements and expiration dating are covered in GMP the
USP and FDA.
The main considerations are as follows,
 Product labeling of official articles should provided recommended storage
conditions and expiry date assigned to specific formulation.
 According to FDA guidelines, now registration of pharmaceuticals
worldwide is appreciated.