Kinetics and Examples

1. Presented By
Nargis Ara
Ph. D Scholar (Pharmaceutics)
Integral University, Lucknow
SATBILITY CALCULATION

2. Contents
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 Introduction to Drug Stability Studies
 Drug Kinetics
 Prediction of Half-Life (t½)
 Prediction of Self-Life (t90)
 Zero-Order Rate Reaction
 First-Order Rate Reaction
 Second-Order rate Reaction

3. Introduction
 Drug stability refers to the capacity of a drug
substance or product to remain within
established specifications of identity, strength,
quality, and purity in a specified period of time.
 Purpose of Stability Studies:
Quality of a drug product
Self life of the drug product
Recommended storage condition
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4. Drug Kinetics
 It is defined as how drug changes with time
i.e., study of rate of change.
 The rate, velocity or speed of a reaction is
expressed as dc/dt where, dc is small
changes in the concentration within a given
time interval dt.
 Importance of Drug Kinetics
It helps to predict stability of drug (half-life).
It helps to predict the expiry period (shelf-
life) of product.
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5. Prediction of Half-Life
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 The half life (t½) is defined as the time
required for one-half of a reactant to
disappear, as [A] has decreased to ½[A].
 Because [A] at t½ is one-half of the original
[A],
[A]t = 0.5 [A]0
 The average ‘k’ value is calculated using the
data for appropriate order of reaction either by
substitution or graphical method and then the
t1/2 values for each time period in the kinetic
study is estimated.

6. Prediction of Self-Life
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 Shelf life (t90%) is defined as the time at which the
concentration of reactant [A], decreased to 90% of its
original concentration.
 As per definition the term equation becomes,
C =90a/100
or, t =t90
 The mathematical prediction of self-life is based
on Arrhenius equation.
 Substitution of ‘k’ value into the appropriate order
of reaction allows the amount of decomposition
after a given time to calculated.

7. Zero-Order Rate Reaction
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 Rate is constant and is independent of the concentration of
the reactant.
dc/dt=k0 k0= c0 – c /t
Where, c = drug concentration at time t
c0 = initial concentration of the drug
k0 = zero-order rate constant (concentration/time)
t = time
Calculation of t1/2
Let c = co /2 and t1/2 = t
substitute in equation;
c = co – k t
co /2= co - k t1/2
t1/2 = co / 2k
Calculation of t90
Let c = 0.9 co and t= t90
substitute in equation;
c = co –k t
0.9 co = co - k t90
t90 = 0.1 co / k
c
t

8. First-Order Rate Reaction
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 The reaction rate of change is proportional to drug
concentration.
dc/dt=-k.c c=c0.e-kt ln c =
ln c0-k.t
Where, c= drug concentration at time, t
c0= initial concentration of the drug
k =first-order rate constant (concentration/time)
t =time
Calculation of t1/2
let c = c0 /2 and t = t1/2
substitute in equation;
ln c = ln c0 – k.t
ln c0=ln c0-k.t1/2
t1/2 = ln 2/ k
t1/2 = 0.693 / k
Calculation of t0.9
Let c = 0.9 c0 and t = t0.9
substitute in equation;
ln c = ln c0 – k.t
t0.9 = 0.105 / k
lnc = lnco – kt
Slope = c1 – c2 / t1 – t2
Slope = -k
ln c
t
ln
c0

9. Second Order Rate Reaction
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 When two components reacting with each
other or one component reacting with itself.
Half life: t1/2 = 1 / kc0
Shelf life: t0.9 = 0.11 /
kc0

10. Graphical Determination of the
Reaction Order for the decomposition
of N2O5
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11. A Plot of [N2O5] Vs. Time for Three
Reaction Half-Life
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12. Examples
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 Example 1:
(k[A]=k0 )

13. • Example 2:
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(k=2.303/t . log c0/c)

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 Example 3:

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 Example 4:

16. An Overview of Rate, Half-life and
Self-life Equation
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Reaction
Order
Rate equation Half –life
Equation ( t½ )
Self-life
Equation ( t90% )
Zero-order k0 = c0 – c /t c0 / 2k c0 / 10k
First-order k1= 2.303/t . ln .
c0/c
0.693/k 0.105/k
Second-order
(a=b=c0)
1/c – 1/c0 = kt 1/c0k 0.11/c0k
Here, c = concentration of the drug at time, t ; c0 = initial concentration ; k=
rate constant
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17. References
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 Patrick J. Sink. (2006). Martin’s Physical Pharmacy
and Pharmaceutical Sciences: Physical Chemical and
Biopharmaceutical Principles in the Pharmaceutical
Sciences. Lippincott William and Wilkins, 5, 400-432.
 Gilbert S. Banker and Christopher T. Rhodes. (2002).
Modern Pharmaceutics. Marcel Dekker, Inc., New
York, 4, 154-160.
 Tembhare E. et.al. (2019). An Approach to Drug
Stability Studies and Self-Life Determination. ACRI,
19(1), 1-20.
 https://mysite.science.uottawa.ca/sgambarotta/sites/d
efault/files/CHM%201311F/slide%20show/ch14-
kinetics/Ch14-kinetics-lecture.pdf 01/02/2021.

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