Transcript order of reaction

CONTENTS
INTRODUCTION
RATE OF REACTION
MOLECULARITY OF REACTION
METHODS TO DETERMINE THE ORDER OF REACTION
FACTORS INFLUENCING REACTION RATES
REFERENCES
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INTRODUCTION
Chemical kinetics concerned with the study of rates of
chemical reaction. A number of principles and related rate
process involved in the study of chemical kinetics are of
immense help in the proper formulation and stabilization of
pharmaceutical products.
Instability in formulations is mainly due to
decomposition. The speed of decomposition follows the rate
process. Dissolution as well as diffusion from solid dosage forms
follows rate processes. The rate processes are also applicable to
the study of absorption, distributions and elimination of drugs.
The principles studied under chemical kinetics provide a
considerable advantage in the development of stable dosage2
forms.
RATE OF REACTION:
•The rate of chemical reaction is defined as the change in
concentration of a reactant in the particular period of time.
•The unit of reaction is the unit of concentration divided by the
unit of time.
•Concentration is normally expressed in moles per; the rate of
reaction is specified as mole liter -1 sec-1.
•The rate of reaction is given by +dc/dt
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Where + or - indicates the increase or decrease respectively in
Concentration dc with in a time interval of dt.
Thus the rate of reaction is given by the change in concentration
divided by the time needed for the change.
To specify the rate ,any of the reactants or any of the products can
be utilized .
For example consider the reaction:
CH3COOH+C2H5OH --------- > CH3COOC2H5+H20
In the case the rate of forward reaction is given as:
Rf
=
d(CH3COOH)
dt
= -d(C2H5OH )
dt
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In the above example the different expressions for the rate is made
equivalent since the concentration of each decreases by an
equivalent amount.
The rate expression + dc/dt indicates an instantaneous rate.
The rate of reaction, when two or more molecules are undergoing a
reaction, is given as per example:
aA+Bb=products
The rate of reaction is -1 . d(A) = -1 . d(B)
a
dt
=
b
dt
Ka+b(A)a (B)b
Where k is rate constant.
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RATE CONSTANT:
Consider the reaction
A--------> products
The rate law is
-d(A) = k(A)
dt
Where d(A)/dt = rate of chemical reaction
K = reaction rate constant
A = active concentration of the reactant
This means that the rate doubles when concentration is doubled.
The value of k is independent of concentration, but it is dependent
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on the temperature.
MOLECULARITY OF REACTION
Molecularity is defined in terms of a number which is equal to the
number of molecules or atoms that must collide simultaneously to
give the products
The
stoichiometric
equation
is
essential
to
decide
molecularity of a reaction.
Unimolecuar reaction :
In these reaction , molecularity is one that is one type
of molecule stoichiometrically partcipates in reaction .
Example : Isomerism of transstilbene to cisstilbene.
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H
Ar
H
C = C -------------
H
Ar
H
C =
C
Ar
Ar
trasstillibene
cisstilbene
Bimolecular reaction:
In these reactions, molecularity is two types of
molecules are stoichiometrically involved in the reaction. Bi molecular
reactions are of two categories, depending on whether the two
molecules undergoing a change are of same type or different.
Example :1 same type of reactants.
Oxidation of hydrogen peroxide
2H202 ------------- 2H20+ 02
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Example: 2 Different types of reactants.
Alkaline hydrolysis of ethyl acetate.
CH3C00C2H5 + NaOH ------ CH3C00Na + C2H0H
Ter molecular reaction :
Reactions of termolecular and other higher molecularity are
seldom observed. This is because three or more molecules having
sufficient kinetic energy must meet simultaneously in the same
region of space to yield a product.
ORDER OF REACTION
Order of reaction is defined as the number of concentration
terms on which the rate of a reaction depends when determined
experimentally.
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The order of reaction is established with respect to each
reactant. This can be verified by plotting log concentration of a
reactant on y axis and time on x axis.
If a straight line is obtained, then the order will be ‘one’ with
respect to that reactant. The overall order of a reaction is equal to the
powers of the concentration terms affecting the experimentally
determined rate.
The order that the common in pharmacy are zero, first, pseudo
first, and second orders.
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ZERO ORDER REACTION :
It is defined as a reaction in which the rate does not
depend on the concentration terms of the reactants.
This is mathematically expressed as:
-dc/dt=ko
• Where minus indicates the absorbance decreasing.
• Ko specific rate constant.
Examples:
 Oxidation of vitamin-A in an oily solution.
 Photo chemical degradation of chlorpromazine in aqueous
solution.
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Mechanism:
In zero order reaction, the rate must depend on some factor
other than the concentration term. The rate limiting factors are
solubility as in suspensions or absorption of light as in photo
chemical reactions.
The rate equation for zero order can be written as
-dA = ko
dt
Where A is the absorbance of the preparation. In this
reaction, the concentration is measured in terms of optical density .
The negative sign indicates colour fading. If equation is integrated.
Integrate equation between initial absorbance, Ao at t=o time, and
absorbance, At at t = t .
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Ao
ʃAt dA = -ko 0 ʃ t dt
At - Ao = -k o t
or
ko =
A O - At
t
This equation is the integral equation for zero order reaction. In general, integral
equation helps in estimating the reaction rate constant of any order. It also permits
us to calculate the concentration of drug remain undecomposed after any time, t.
Normally, the initial concentration is epressed as ‘ a’ and the concentration at any
time t, is’c’. Then, equation becomes
Ko = (a-c)
t
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Equation may be written as
C=a – kot
Equation represents a linear expression, when c is plotted on y
axis against t on x axis. The line gives a negative slope and the
magnitude is equal to ko. A representative zero order plot is
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Absorbance
Slope is negative
Slope =ko
Times (hours)
Units for ko are con/time . If concentration is expressed as moles/liter
then k0 will be moles /liter.sec. If a straight line is obtained then the
reaction follows a zero order rate.
The colour development during storage is also a sign
of chemical reaction i.e. instability . Still the order remains zero order
.Then slope is positive.
Optical density
Slope is
positive
slope=ko
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Time(hours)
HALF LIFE :
It is time required for the concentration of the reactant to half of its
initial concentration.
The half life equation can be derived as follows:
c = a/2
t = t1/2
Substitute these values in the equation
ko
= (a-c)/t
(a-c) = a-(a/2) = (1/2)a
Then equation will be t1/2
=
ko
=
ko
ko
a/2ko
Units is time scale i.e.sec/conc, min/conc, hrs/conc
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Shelf life :
It is defined as the time required for the concentration of the
reactant to reduce to 90% of its initial concentration .
Shelf life is represented as t90 and has the units of time/conc.
As per defination the terms in equation c =a – kot is change to
c =
90a
100
t =
t90
Substituting these values in the equation c = a-kot then equation will
be
(a – 0.9a) = 0.1a
t90 =
k0
ko
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First order reaction :
It is defined as a reaction in which rate of reaction depends up on the
concentration of one reactant.
First order reaction is can be written as
-dc α c
dt
-dc = k1c
dt
% un react
Slope is negative
Slope = k1/2.303
Time(hrs)
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First order half life:
t1/2= 0.693/k
here half life depends on the concentration of the drug
undergoing the reaction
E.g.: Absorption, Distribution and Elimination
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Shelf life: (T90%)
It is defined as the time required for the concentration of
the reactants to reduce to 90% of its initial
concentration.
T90% = 2.303/K1 log Co/0.9Co
T90% = 0.152 t1/2
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Pseudo first order reaction :
It is defined as a reaction which is originally second order, but it is made to behave
like a first reaction.
In second order reaction the rate depends up on concentration terms of two
reactants . The rate will be
-dc/dt = k2(A)(B)
A and B are the reactants in the reaction k2 is second order reaction.
The reaction conditions are maintained in such a way that one reactant (B) is
present in large excess compared to concentration of other reactant(A).
The concentration of ‘B’ does not change during the reaction. Then equation
Changes to
-dc/dt = k2 (A)(constant) =k1(A)
This type of reaction also termed as apparent first order
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Examples :
 Acid catalyzed hydrolysis of erythromycin.
 Acid catalyzed hydrolysis of digoxin
Pseudo first order kinetics provide linear relationship between log
concentration vs. time.
Pseudo first order kinetics proceeds at slow rate than compare to
second order .
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Second order reaction
It is defined as a reaction in which the rate depends on the
concentration terms of two reactants each raised to the power one.
Consider the following reaction
A+B Products
Products
The rate equation can be written as
- dA /dt = - dB/dt
= K2[A]I[B]I
Where [A] and [B] are the concentration of A and B,
respectively, and k2 is the specific rate constant for second order.
In other words, the rate of reaction is first order with respect to A,
and again first order with respect to B . So the overall order of this
reaction is second order.
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Second order reaction can be verified by plotting log
concentration of A vs. time. A straight line indicates that it is a first
order with respect to A. Similarly, we can establish a linear
relationship by plotting an appropriate graph with respect to B. This is
the proof for a second order reaction.
Examples:- (a) Alkaline hydrolysis of esters such as
methyl acetate or ethyl acetate.
(b) Hydrolysis of chlorobutanol in presence of
sodium hydroxide.
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x/a(a-x)
A linear plot for second order reaction where a=b
Slope =k2
Time(min)
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Methods to determine order of reaction:

Substitution method

Graphical method

Half life method
Substitution method : This pictorial method may be more reliable
because deviations from the best fit line can be easily observed.
Graphical method : Substituting the values in the respective
equations of the order of reaction , the values are used to plot a
graph . If a straight line is obtained by plotting concentration (a)
against time (t) indicates a zero order reaction.
If a log(a-x) vs. t yields a straight line indicates a first order
reaction.
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For a second order reaction a plot of 1/(a-x) vs. t yields a straight line
provide the initial concentration of the two reactants involved in the
reactions of the same .
The reaction of third order when a plot of 1/(a-x)2 vs. t results a straight
line with all the reactants at the same initial concentrations.
Half life method : In zero order half life is proportional to the initial
concentrations of the reactants .
In first order half life is independent of the initial concentration of
reactants.
In second order half life is inversely proportional to initial concentrations
of reactants (a = b).
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Factors influencing reaction process:
Many factors affect the reaction except concentration
Temperature :In general the rate of degradation increases with rise
in temperature It is given by Arrhenius equation
K
= Ae-EA/rt
Ionic strength: Ionic strength of a solution may influence the rate of
degradation .
Solvent effect : The replacement of water with non aqueous solvents
such as alcohol propylene glycol take place to reduce
decomposition by hydrolysis .
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Di electric constant :
Di electric constant has an influence on reaction rates . It is a
property liquids and therefore the di electric constant of the
solvents affect the rate of hydrolytic reactions.
Catalyst :
A catalyst is the substance which alters the speed of the
reactions with out being it self alter chemically. It does not alter the
equilibrium of the reaction but speed up the reaction .
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References :
 Drug
stability , cartensen .J.I. Third edition 2000
 Chemical kinetics and drug stability .
Modern pharmaceutics, volume 121.
Gilbert.S. Banker, Christopher, T.Rodes chapter-6
 Kinetics and drug stability, Physical pharmacy Alfred
Martin4th edition
 Kinetics and catalysis ,Physical Pharmacy
R.Manavalan C. Ramaswamy 2nd edition
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