Kinetics and drug stability ed

KINETICS AND DRUG STABILITY
Dereje K.
1

Kinetics
Kinetics Motion or
movement
Velocity, rate or
rate of change
Kinetics deals with the study of the rate at which processes
occur and mechanism of chemical reactions
2

It involves the study of rate of change and the way in which
this rate is influenced by the concentration of reactants,
products, and other chemical species that may be present,
and by factors such as solvents, pressure, and temperature.
Kinetics applies to:
Stability
Incompatibility,
Dissolution,
Absorption,
Distribution
Drug action at molecular level
Elimination processes
3

WHY DO WE STUDY ABOUT KINETICS?
It gives an in light into the mechanism of changes involved
Allows a prediction of the degree of change that will occur
after a given time has elapsed.
4

DRUG STABILITY
• The resistance of the drug to the various chemical, physical, and
microbiological reactions that may change the original properties of
the preparations during transport, storage and use.
• Quantitatively it is expressed as shelf life.
Shelf life
 is the time during which the medicinal product is predicted to
remain fit for its intended use under specified conditions of storage.
 It is the time from manufacture or preparation until the original
potency or content of the active ingredient has been reduced by
10% [t10 or t90] which is the limit of chemical degradation
5

WHY DO WE STUDY ABOUT DRUG STABILITY?
Safety of the patient [toxic products or less potent product]
Legal requirements with identity, strength, purity and quality
To prevent economic repercussions.
6

RATES AND ORDERS OF REACTIONS
RATES
• the speed or velocity of a reaction with which a reactant or
reactants undergoes a change.
• It is determined by the change in the concentration of the
reactants or products as a function of time.
• The rate may be determined by the slowest or rate
determining step.
kc
n
Rate
dt
dc

7

ORDERS OF REACTIONS
the number of concentrations that determine rate.
the way in which the concentration of the reactant influences
the rate.
Law of mass action
 The rate of a reaction is proportional to the molar concentrations of the
reactants each raised to power equal to the number of molecules
undergoing reaction.
a A + b B Product
Rate α [A]a .[B]b
Rate = K [A]a .[B]b
Order of reaction = sum of exponents
Order of A = a and B = b
Then Overall order = a + b
8

Example:
The reaction of acetic anhydride with ethyl
alcohol to form ethyl acetate and water
(CH3 CO)2 + 2 C2H5OH 2 CH3 CO2 C2H5 + H2O
Rate = K [(CH3 CO)2 O] . [C2H5OH]2
Order for (CH3 CO)2 O is 1st order
Order for [C2H5OH]2 is 2nd order
Overall order of reaction is 3rd Order
9

ZERO ORDER REACTIONS
rate is constant and is independent of the concentration of
any of the reactants.
A constant rate of drug release from a dosage form is highly
desirable.
Equation for zero order:
10

11
11
Equation for zero order:
a [A] k Product (P)
Rate = - dc/dt = K [c]0
- dc/dt = k dc = - k dt
co = Initial concentration
ct = Concentration at time t
 
t
t
c
c
kdtdc
t
00
C – C0 = -kt

12
12
Units of the rate constant K
c = co – Kt
K = co – c /t
K = Concentration / time
= mole / liter . second
= M. sec-1
C
t

13
Determination of t1/2
Let c = co /2 and t1/2 = t
substitute in equation;
c = co – k t
Note: Rate constant (k) and t1/2 depend on co
Determination of t0.9
Let c = 0.9 co and t= t0.9
substitute in equation;
c = co –k t
13
t1/2 = co / 2K
t90% = t0.9 = 0.1 co / k

Examples
• Drug X degrades by a zero-order process with a rate constant
of 0.05 mg ml1 year−1 at room temperature. If a 1%
weight/volume (w/v) solution is prepared and stored at room
temperature:
1. What concentration will remain after 18 months?
2. What is the half-life of the drug?
14

Answer
1. C0 = 1% w/v = 10 mg/ml; t =18 months = 1.5 year; k0 = 0.05
mg ml−1 year−1
C = C0 – k0t = 10 – (0.05 × 1.5) = 9.93 mg/ml
2. t1/2 = 0.5C0/k0 = (0.5 × 10)/0.05 = 100 years
15

FIRST ORDER REACTION
The most common pharmaceutical reactions
e.g; drug absorption & drug degradation
The reaction rate of change is proportional to drug
concentration.
16

- dc/dt = kc1 = kc
- dc/c = kdt
17
 

t
t
t
c
dtk
c
dc
00
ktcc o lnln
303.2
loglog 0
kt
cc 

18
18
C = co e –kt
Difficult to determine slope
lnc = lnco – kt
Slope = c1 – c2 / t1 – t2
Slope = -k
lnco
Log co
Log c = log co – kt / 2.303
Slope = c1 – c2 / t1 – t2
Slope = -k / 2.303
Or use semi log paper
C Lnc
Logc
t t
t

19
Determination of t1/2
Let t = t1/2 and C = C0 /2
substitute in ln C = ln C0 – Kt
t1/2 = ln 2/ K = 0.693 / K
K units = 0.693 / t1/2 = time-1
Determination of t0.9
Let t = t0.9 c = 0.9 Co
substitute in ln c = ln co – Kt
t0.9 = 0.105 / K and K = 0.105/ t0.9
19
t1/2 = 0.693 / K
t0.9 = 0.105 / K

Examples
1 Ten (10) ml aqueous solutions of drug A (10% w/v) and drug B
(25% w/v) are stored in two identical test tubes under
identical storage conditions at 37°C for 3 months. If both
drugs degrade by first-order, which drug will retain the highest
percentage of initial concentration?
(a) Drug A
(b) Drug B
(c) They will be the same.
2. The concentration of drug X in aqueous solution drops by 10%
per month when stored at room temperature. If the
degradation occurs by first order, what concentration will
remain if a 5 mg/ml solution of the drug is stored under the
same conditions for 3 months? 20

3. A 5 gm/100 ml solution of drug X is stored in a closed test tube
at 25°C. If the rate of degradation of the drug is 0.05 day−1,
calculate the time required for the initial concentration to
drop to (a) 50% (half-life) and (b) 90% (shelf-life) of its initial
value.
4. A 5 gm/100 ml solution of drug X is stored in a closed test tube
at 25°C. If the rate of degradation of the drug is 0.05 day−1,
calculate the time for the drug concentration to degrade to
2.5 mg/ml.
21

PSEUDO ORDER REACTIONS
• For some reactions, the rate of the reaction may be
independent of the concentration of one or more of the
reacting species over a wide range of reactions.
• These may occur under the following conditions:
One or more of the reactants enters into the rate equation
in great excess compared to others;
One of the reactant is catalyst;
One or more of the reactants is constantly replenished
during the course of reaction
22

SECOND ORDER REACTION
Rate depends on the product of two concentration terms.
When you have two components reacting with each other or
one component reacting with itself.
Example: 2HI = H2 + I2 , here the reaction is not simply a
matter of an HI molecule falling apart, but relies on the
collision of two HI molecules.
The rate of reaction from the law of mass action is given by:
Rate = dc/dt = k[HI][HI] = k[HI]2
23

dc/dt = -kc2
dc/c2 = -kdt
24
 

t
t
c
c
dtk
c
dc
0
2
0
kt
cc

0
11
2nd Order reaction

25
2nd order graph
Units of K:
1/C = 1/Co + Kt
K = (1/C - 1/Co) / t
K = M-1. sec -1
i.e, K is dependent on initial drug concentration.
Derive equation for t1/2 and shelf life
Half life: t1/2 = 1 / KCo
Shelf life: t0.9 = 0.11 / KCo

DETERMINATION OF ORDER AND RATE CONSTANTS
1. Substitution method [data plotting method]
• Data accumulated in experimental kinetic study may be
substituted in the integrated form of the equation that
describes the various reaction orders and observing which
plot is a straight line.
• Accordingly, plot of:
Concentration against time …….. zero order reaction [if
straight line]
ln concentration against time ……. First order reaction [if
straight line]
1/concentration against time …….. second order reaction
[if straight line].
26

2.Half-life method
• This method is based on the relationship between the initial
concentration of the reactant, the halflife, and the reaction
order.
• For zero-order reactions, t1/2 increases with increasing
concentration, whereas for first-order reactions, t1/2 does not
change with change in concentration
27

Kinetics and drug stability ed

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