By
A. S. Adebayo, Ph. D.
4/11/2020 9:09 PM
1

 Applications
 Chemical reactions such as decomposition of medicinal compounds
 Processes of drug absorption, distribution and elimination from the body
 Shelf life determination.
4/11/2020 9:09 PM
2

 In determining the shelf life of a preparation, tests are carried out on the active ingredient, the additives and the finished product to determine:
 Whether decomposition will occur
 The type of decomposition
 Factors that affect the rate of decomposition such as light, air, moisture, temperature, etc.
 The influence of formulation additives
 The rate at which breakdown occurs.
4/11/2020 9:09 PM
3

Expressing speed of a reaction:
 as the decrease in concentration of any reacting substance
 as the increase in concentration of the product per unit time.
 If C is the concentration, then the rate of reaction: dC 
C n dt
 where n=0,1 or 2 for zero, first & second order reactions respectively
4
4/11/2020 9:09 PM

 Manner in which the rate of reaction varies with the concentration of the reactants
 Most processes involving ADME can be treated as first- order processes
 Some drug degradation processes can be treated as either First or zero order processes
 Some drug substances obey Michaelis-
Menten kinetic process
4/11/2020 9:09 PM
5



 n=1 and the reaction rate is dependent on the concentration of one of the reactants in the formulation.
 dC
 kC dt
C is the concentration remaining undecomposed, unabsorbed, yet to be distributed, metabolized or excreted at time t as the case may be
 k is the first order rate constant.
4/11/2020 9:09 PM
6

 On integration, the equation above gives: ln C
 ln C o
  k t
 
 On rearrangement and conversion to log in base 10: log C
 log C o
 kt
2 .
303
7
4/11/2020 9:09 PM

4/11/2020 9:09 PM
.
Log
Conc
Slope = -k/2.303
Time
8

 Determine the expression for rate constant, k
 Determine the expression for process half-life, t
1/2
 Write the exponential forms of the equation in natural log and log in base
10.
 What is the significance of process halflife?
4/11/2020 9:09 PM
9

 In this type of reaction, n=o and the reaction rate is independent of the concentration of the reacting substance.
 The rate of change is constant.
 Here, factors other than concentration of reactants constitute the limiting factor e.g. solubility or absorption of light
(photochemical reactions).
10
4/11/2020 9:09 PM

 When solubility is the limiting factor, only the proportion of drug in solution undergoes degradation:
 As the drug is consumed in the degradative reaction, more drug goes into solution until all solid (C) has reacted.
 Until this has happened, the degradation process will not be dependent on the total conc. of drug but on the proportion in solution, thereby producing a zero order process .
11
4/11/2020 9:09 PM

 Zero order Equation:
 dC o dt
 k
 C o
= original concentration of reacting material, k=reaction rate constant, dt= change in time.
4/11/2020 9:09 PM
12

 Expression of zero order equation:

C t

C o
 kt
 C t
=conc. at time t, C o
=conc. at time o.
 Plot of C against t gives a straight line with slope of -k o
4/11/2020 9:09 PM
13

Concentration versus time (Zeroorder plot)
Conc
Slope = -k
0
Time
4/11/2020 9:09 PM
14

 For a zero order reaction, the time for
50% reaction, t
½, is given as: t
1 / 2

1
2
C o k o

C o
2 k o
4/11/2020 9:09 PM
15

Apparent Zero Order Reaction
Kinetics



Suspensions are a special case of zero order kinetics, in which the concentration of drug in solution depends on its solubility.
As the drug in solution decomposes, more of it is released from a reservoir of suspended particles thereby making the concentration in solution constant.
The effective concentration is the drug equilibrium solubility in the solvent of formulation at given temperatures
4/11/2020 9:09 PM
16

Apparent Zero Order Reaction
Kinetics (Cont.)
 Ordinarily, the equation for decomposition is first order:
 d dt
   
 C=the conc. of drug remaining undecomposed at time t
 k=the known first order rate constant.
4/11/2020 9:09 PM
17

Apparent Zero Order Reaction
Kinetics (Cont.)
 When concentration is rendered constant by suspended particles offering replacement, then k
 
 k o
 thereby turning the first order rate law
 into;  d dt
 k o
18
4/11/2020 9:09 PM

 Can present as;
 Loss of potency
 Accumulation of toxic degradative products
 Degrardation of excipient responsible for product stability e.g. emulsifying agents, preservatives
 Conspicuous colour change e.g. marked discoloration of adrenaline although very slight change in adrenaline content, is unacceptable to patients, pharmacists, physicians and the nurses.
4/11/2020 9:09 PM
19

Solid state versus solution stability
 Generally, chemical reactions proceed more readily in liquid state than in solid state
 Serious stability problems are more commonly encountered in liquid medicines e.g. order of dosage form stability is generally: solution < suspension < tablet.
4/11/2020 9:09 PM
20

Determination of Order of Reaction


Use of rate equation – The data collected in a kinetic reaction should be substituted into the integrated form of equations of various orders.
The process under test should be considered to be of that order where the calculated k value remains constant within limits of experimental error.
21
4/11/2020 9:09 PM

Determination of Order of Reaction..


Half life method – For a zero order or pseudo first order reaction, t ½ is proportional to initial concentration of reactant (Co),
 t½ for a first order reaction is independent of
Co, .
Graphical method – For a zero order or pseudo first order reaction, plot of C vs. t is linear; for first order reaction, plot of log (Co-
Ct) vs. t is linear.
22
4/11/2020 9:09 PM

Factors Affecting Rate of Reactions
 The rate of reaction (degradation of pharmaceutical products) can be influenced
 temperature,
 moisture,

 solvent (pH, dielectric constant, etc), light (radiation),
 catalysts,
 oxygen and
 concentration of reactant (s).
4/11/2020 9:09 PM
23

 Temperature – Rate of most chemical reactions increase with rise in temperature up to 2 to 3 times with each
10 ° rise in temperature.
 The relationship is expressed by
Arrhenius equation: k

Ae
 E a
RT
24
4/11/2020 9:09 PM

 Log transformation gives:



 log k
 log A

E a
1
2 .
303 RT k is the rate of reaction
A is a constant known as the frequency factor
E a is the activation energy,
R is the gas constant (1.987 calories deg -
1 mole -1 OR 8.314 J mole -1 )
T is the absolute temperature.
4/11/2020 9:09 PM
25

 Plot of log k against 1/T gives a straight line with slope of –Ea/2.303R and intercept of log A.
 For a reaction carried out at 2 diff. temp.,
(subtracting eqn. 1 from 2 gives: log k
2 k
1

E a
2 .
303 R

T
2

T
1

T
2
T
1
26
4/11/2020 9:09 PM

Activation Energy: Arrhenius
Equation
 The degradation of a new cancer drug follows first-order kinetics and has degradation rate constants of 0.0001 H -1 at 60 ºC and 0.0009 H -1 at 80 ºC. What is its Ea?
27
4/11/2020 9:09 PM

Stability Projection for Shelf Life
 The time required for 10 % of the drug to degrade with 90 % of intact drug remaining is based on Arrhenius equation: log k
2 k
1

E a
( T
2

T
1
2 .
303 RT
1
T
2
)
 k = reaction rate, T = temperature,
 R = gas constant, Ea = activation energy
28
4/11/2020 9:09 PM

10
Q
10
 k
( T

10 )
K
T
 Q values of 2 (Ea ≈ 12.2 kcal/mole), 3
(Ea ≈ 19.4 kcal/mole), and 4 (Ea ≈24.5 kcal/mole) are commonly used
 They represent the energies of activation of the reactions around room temperature.
29
4/11/2020 9:09 PM

10…..





Q
10 estimates can be made with the equation: where t
90T2 is the estimated shelf life t
90T1 is the shelf life at a given temperature
∆T is the difference in temperature between T and T
2
(i.e. T
2
– T
1
Increase in ∆T will
)
1 decrease shelf life while a decrease in ∆T will increase shelf life t
90
( T
2
)
 t
90
Q
10
( T
1

T
)
 
10
4/11/2020 9:09 PM
30






Shelf-life at different storage temperature can be estimated as: t
90T2 t
90
( T
2
) is the estimated shelf life
 t
90
Q
10
( T
1

T
)
 
10 t
90T1 is the shelf life at a given temperature
∆T is the difference in temperature between T
1 and T
2
Increase in ∆T will decrease shelf life while a decrease in ∆T will increase shelf life
31
4/11/2020 9:09 PM

1
2
3
An ophthalmic solution has a shelf life of 6 hours at room temperature (25 °C).
Calculate the estimated shelf-life in a refrigerator (5 °C)
An antibiotic has a shelf life of 48 hours in the refrigerator (5 °C). What is its estimated shelf-life at room temperature (25 °C)?
In what ways can chemical instability be manifested on formulated products? List and discuss four main types of reactions involved in chemical degradation.
32
4/11/2020 9:09 PM

4.
5.
6.
A drug suspension (125 mg/ml) decays by zero-order kinetics with a reaction rate constant of 0.5 mg/ml/hr.
What is the concentration of intact drug remaining after 3 days?
How long will it take for the suspension in question 4 above to reach 90 % of its original concentration?
An ophthalmic solution of a mydriatic drug present at
5 mg/ml concentration exhibits first order degradation with a rate of 0.0005/day. How much drug will remain after 120 days? How long will it take for the drug to degrade to 90 % of its original concentration?
33
4/11/2020 9:09 PM

7.The rate constant for decomposition of 5hydroxymethylfurfural was 1.173 H -1 at
120 ºC and 4.860 H -1 at 140 ºC. What is the activation energy and frequency factor, A in sec -1 for the breakdown of
5HMF in this temperature range?
34
4/11/2020 9:09 PM

8. Analysis of the rate of degradation of a colourant in a multi-sulfa drug preparation shows the following results:
 Assuming a firstorder process, compute the activation energy and the value of K at 25
ºC
ºC
40
50
60
70
K
0.00011
0.00028
0.00082
0.00196
4/11/2020 9:09 PM
35

THANK YOU FOR YOUR
ATTENTION
4/11/2020 9:09 PM
36