CHAPTER-7
KINETICS AND DRUG STABILITY
Syllabus:
General considerations and concepts, half life
determination. Influence of temperature, light, solvent, catalytic species and
other factors. Accelerated stability study, calculation of expiry date.
Rate
The
rate of a chemical reaction of process is the velocity with which the reaction
occurs.
Let us consider the following
reaction:
drug
A ®
drug B
If the amount of the drug A is
decreasing with respect to time (i.e. the reaction is going in a forward direction),
then the rate of this reaction can be expressed as follows:
The
negative sign appears because concentration of drug A decreases with time.
Since the amount of drug B is
increasing with respect to time, the rate of the reaction can also be expressed
as:
The
positive sign appears because the concentration of the product B increases with
time.
Usually, in pharmacokinetics,
only the parent (or pharmacologically active) drug is measured experimentally.
The metabolites of the drug or the products of the decomposition of the drug
may not be known or may be very difficult to quantitate. Hence, The rate of a reaction is determined
experimentally by measuring the disappearance of drug A at given time
intervals.
Order of a reaction
If
C is the concentration of drug A, the rate of decrease in C (of drug A) can be
expressed by a general expression as function of time, t as: ........................eqn. 1
Where k = rate constant and n = order of the reaction.
If n = 0 then the reaction is
called a zero-order reaction,
if n = 1 then the reaction is
called a first-order reaction.
if n = 2 then the reaction is
called a second order reaction.
If a reaction is: aA +
bB ® Product
and if the reaction rate = - k
[A] a [B]b then
the reaction is said to be (a + b) order.
Example: In the reaction of ethyl acetate
and sodium hydroxide in aqueous solution, for example,
CH3COOC2H5 + NaOHsoln
® CH3COONa
+ C2H5OH
the rate expression is
The reaction is
first-order (a = 1) with respect to ethyl acetate and first-order (b = 1) with
respect to sodium hydroxide solution; overall the reaction is second-order (a +
b = 2).
Suppose
that in this reaction sodium hydroxide and water was in great excess and ethyl
acetate was in a relatively low concentration. In this case the concentration
of sodium hydroxide may be taken as constant and the rate equation can then be
written as:
in which k’ = k [NaOH]. The reaction is then said to be pseudo-first order, because it only
depends on the first power (a = 1) of the concentration of ethyl acetate.
* The overall order of a reaction is
determined by experiments.
Molecularity
of a reaction
The over all reaction may take place
by several steps. Each step is called an elementary step. The order of each
elementary step is the number of reactant molecules taking part in that
reaction, hence, the order of an elementary step is called the molecularity of
the reaction.
|
Reaction
|
Order
|
Molecularity
|
Elementary reaction -I
|
2 NO
®
N2O2.
|
Second
Rate
= k [NO]2.
|
Bimolecular
|
Elementary reaction – II
|
N2O2
+ O2 ®
2NO2.
|
Second
Rate
= k [N2O2][O2]
|
Bimolecular
|
Overall reaction
|
2NO
+ O2 ®
2NO2.
|
Second
Found
from experiment
|
|
Specific
rate constant
The constant k associated with a
single step (elementary) reaction is called a specific rate constant for that
reaction. If the specific rate constant of an elementary reaction is changed by
some factors (like temperature, light, catalyst, solvents etc.) then the
overall reaction rate will also change.
Zero-Order Reactions
If
the concentration of drug A is decreasing at a constant time interval t. then
the rate of disappearance of drug A is expressed as:
.............................eqn.
2
The term k0 is the
zero-order rate constant and is expressed in units of concentration / time
[e.g. (mg/ml)/ min).]
or dC = - k0 dt
Integrating both sides:
or, C
= - k0 t + C0. ..............................
eqn.3
where C0 is the
concentration of drug at t= 0.
Half life of the reaction:
At t = t1/ 2 C = C0.
Replacing t and C in eqn. 3 C0. = - k0
t1/ 2 + C0.
or, k0 t1/ 2 = C0.
or, t1/ 2
Unit of k
Graphical representation
Fig: Plot of Conc vs. time Fig. Rate vs. time
Example
A
drug in suspension follows apparent zero-order kinetics in which the
concentration of the drug in the solution remains constant with time. When the
drug in the solution degrades or lost by any means new drug molecules from the
suspended solid particles dissolve in the solution to keep the concentration
constant at the equilibrium solubility.
That is the solid suspended particles acts as reservoir of drug.
1st Order Reactions
In first order reaction the rate of reaction is proportional
to the concentration of the drug remaining and can be expressed as:
or simply
........................ eqn 4
Integrating eqn 4 we get,
ln
C =
-kt +
A where is a constant
Initially when t = 0, C = C0.
Hence, the equation will be
ln
C = -kt + ln C0. ............................. eqn. 5
or, or, or, C
= C0 e -k t . ....................... eqn. 6
Another form of eqn. 5 is the expression in log10
format:
log C = + log C0 . ...........................................
eqn. 7
Half life of the reaction
At
t = t1/ 2 C = C0.
Replacing t and C in eqn. 7
log C0 = + log C0
.
or, = log C0
. - log C0.
or, t1/2 = = = =
or,
t1/2 =
Graphical representation
Fig : Plot of eqn. 7 Fig:
Plot of eqn.6
Unit of k : min-1.
Example
All the passive transport of drug molecules through the
biological membranes follows first order kinetics.
Degradation of hydrogen peroxide into water and oxygen: 2H2O2 ® 2H2O
+ O2.
INFLUENCE OF TEMPERATURE AND OTHER
FACTORS ON REACTION RATE
Influence
of temperature
The speed of many reaction
increases about two to three times with each 100 C rise in
temperature. The effect of temperature on a rate constant of a reaction is
given by the equation, first suggested by Arrhenius,
A plot of log k vs 1/T yields a slope equal to - Ea /
2.303 R from which the value for the
energy of activation ( Ea) and Arrhenius
factor (A) can be calculated.
So Ea = Slope x 2.303 R
and A = 10 intercept
Influence
of light (Photoreaction)
Light energy, like heat, may provide
the activation energy necessary for a reaction to occur.
The energy unit of light radiation is
photon and it is equivalent of 1 quantum of energy.
The photochemical reaction rate
depends on the wavelength of light, intensity of light and the number of photons actually absorbed by
the material.
Examples:
1. Ergosterol,
under UV light, transforms into Vitamin D.
2. Oxidation
of benzaldehyde by light.
3. Adriamycin,
furosemide, menadione, nifedipine, sulfacetamide, theophylline etc. undergoes
photodegradation.
Study of photo reactions are required
to prepare suitable packaging material for the product e.g. color-glass bottles
or paper box or aluminium foil etc.
Influence
of solvent
Solvent
Reactant Product
The following facts are found:
If polarity of product > polarity of reactant then reaction
rate increases if the solvent is more polar.
If polarity of product < polarity of reactant then reaction
rate increases if the solvent is less polar.
Example:
In this reaction the product
(ethylacetate) is less polar than the reactants (ethanol, acetaic anhydride)
hence the reaction will be faster in non-polar solvent like hexane, and slower
in polar solvent like nitrobenzene.
Influence
of catalytic species
The rate of a reaction is influenced
by the presence of a catalyst.
The equilibrium constant
of the reaction
·
A catalyst increases both forward and backward
reaction rate, hence a catalyst cannot change the equilibrium constant K of the
reaction.
·
It does not affect the yield of the product
also.
·
Only it
makes the reaction faster.
Catalyst:
It is defined as a substance that influences the rate of a reaction but itself
remain unchanged chemically.
Negative
catalyst: A catalyst that reduces the rate of reaction.
e.g. Phosphoric acid reduces the
reaction rate of H2O2
®
H2O + O2.
Inhibitor:
A substance that reduces the rate of reaction and itself gets changed
chemically.
Homogeneous
catalysis: If the catalyst and the reactants remain in the same phase the
process is called homogeneous catalysis.
e.g. Hydrochloric acid catalyses the
hydrolysis of sugar.
Heterogeneous
catalysis: If the catalyst and the reactants are in separate phases the
process is called a heterogeneous catalysis.
e.g. Platinum powder is suspended in
reaction medium of hydrogenation reaction.
Catalyst
poison: Substances those reduces the action of catalyst are called catalyst
poison.
e.g. Copper acts as catalyst in
hydrogenation of ethylene. Carbon monoxide acts as poison of copper.
Promoters:
Substances those increases the activity of a catalyst are called promoters.
e.g. Ferric ion (Fe3+)
acts as catalyst in decomposition of hydrogen peroxide. Cupric ion (Cu++)
act as promoter to ferric ion.
ACCELERATED STABILITY STUDY
Accelerated stability testing
Instabilities in modern
formulations are often detectable only after considerable storage periods under
normal conditions. To reduce the time required to obtain information, various
tests that involve storage of the products under conditions that accelerate
decomposition have been introduced.
Objectives of accelerated stability tests:
(i)
the rapid detection
of deterioration in different initial formulations of the same product - this
is used in selecting the best formulation
from a series of possible choices;
(ii)
the prediction of
shelf life, which is the time a product will remain satisfactory when
stored under expected or directed storage condition; and
(iii) the
provision of rapid means of quality
control, which ensures that no unexpected change has occurred in the stored
product.
All these objectives are based on obtaining a more rapid
rate of decomposition by applying to the product a storage condition that
places a higher stress or challenge to it when compared with normal storage
conditions.
Common high stresses or challenges:
(a) Temperature
An increase in temperature causes
an increase in the rate of chemical reactions. The products are therefore
stored at room temperatures greater than room temperature. The nature of the
product often determines the range covered in the accelerated test.
Samples are removed at various
time intervals and the extent of decomposition is determined by analysis.
(b) Humidity
Storage of the product in
atmospheres of high humidity will accelerate decomposition that result from
hydrolysis. Marked acceleration will be obtained if a “naked” product (i.e. not
enclosed in a container) is subjected to these tests. This type of stability
tests are useful in determining the degree of protection that should be
afforded by the container.
(c) Light
A source of artificial light is
used to accelerated the effect of sunlight or sky light. the source should emit
a similar distribution of radiant energy to that in sunlight because
photochemical reactions involve the absorption of light of definite
wavelengths.
“Day light” fluorescent lamps
provide a satisfactory source.
The prediction of shelf-life:
Say, the room temperature = 250C
Method 1: Prediction from Arrhenius plot:
Concentration of undecomposed
drug is plotted against time (hr) at various temperature above room temperature
(250C)
The stability constants at
various temperatures are plotted in Arrhenius plot (i.e. log k vs 1/T).
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|
From the Arrhenius plot the
stability constant at room temperature i.e. (k 25) is determined by
extrapolation.
Let us assume that when the drug
is 10% decomposed it is to be said that the product has expired.
i.e. at time t = 0 hour drug
concentration remaining = 100%
at
time = t hour drug
concentration remaining = 90%
Now we have to calculate the time
‘t’.
If the product is kept at room
temperature (250C)then the following equation from 1st order
kinetics may be used:
log C = log Co - (k25
/2.303) x t
or, t = (2.303 / k25)
= (2.303/k25) log (Co / C)
=
(2.303/k25) log (100/90)
Since k25 value is
known, therefore t can be
calculated.
Method -II: Simplified techniques for stability prediction:
Free and Blythe describe such
technique for liquid products where the decomposition behaves according to the
general kinetic laws.
In this case log(% of drug
remaining) is plotted against time (in days).
From the graph the time for the
potency (concentration) to fall to 90% of the original value (i.e t90%
) are read at different temperature.
Then the log (t90%) is
plotted against (1/T) and the time at 250C gives the shelf life of
the product (in days).
Expiry time = Time required for
90% degradation at room temperature (i.e. 250C) = t25.