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Reaction kinetics
By
A. S. Adebayo, Ph. D.
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KINETICS
 Applications
 Chemical
reactions such as
decomposition of medicinal
compounds
 Processes of drug absorption,
distribution and elimination from the
body
 Shelf life determination.
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Shelf life determination
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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.
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Rate of Reaction
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
n
C
dt

where n=0,1 or 2 for zero, first & second order
reactions respectively
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Order of Reaction
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 MichaelisMenten kinetic process

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First Order Kinetics

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.

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First Order Kinetics (cont.)

On integration, the equation above gives:

On rearrangement and conversion to log
in base 10:
ln C  ln Co  k t  0
kt
log C  log Co 
2.303
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Log concentration versus time
Log
Conc
.
Slope = -k/2.303
Time
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Exercises??
Determine the expression for rate
constant, k
 Determine the expression for process
half-life, t1/2
 Write the exponential forms of the
equation in natural log and log in base
10.
 What is the significance of process halflife?

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Zero order reaction
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).

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Zero order reaction (cont.)

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.

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Zero order reaction (cont.)

Zero order Equation:
 dCo
k
dt

Co= original concentration of reacting
material, k=reaction rate constant, dt=
change in time.
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Zero order processes

Expression of zero order equation:

Ct  Co  kt
Ct=conc. at time t, Co=conc. at time o.
 Plot of C against t gives a straight line
with slope of -ko

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Concentration versus time (Zeroorder plot)
Conc
Slope = -k0
Time
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Reaction half-life (Zero-order)

For a zero order reaction, the time for
50% reaction, t½, is given as:
Co Co


ko
2ko
1
t1 / 2
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2
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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
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Apparent Zero Order Reaction
Kinetics (Cont.)

Ordinarily, the equation for
decomposition is first order:
 d C 
 k C 
dt
C=the conc. of drug remaining undecomposed at time t
 k=the known first order rate constant.

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Apparent Zero Order Reaction
Kinetics (Cont.)

When concentration is rendered constant
by suspended particles offering
replacement, then
k C   ko
thereby turning the first order rate law
into;
 d C 
 ko

dt

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Chemical instability

Can present as;
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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.
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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.

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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.
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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 (CoCt) vs. t is linear.

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Factors Affecting Rate of Reactions
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The rate of reaction (degradation of
pharmaceutical products) can be influenced
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temperature,
moisture,
solvent (pH, dielectric constant, etc),
light (radiation),
catalysts,
oxygen and
concentration of reactant (s).
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Temperature
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:
E

 RTa
k  Ae
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Arrhenius equation

Log transformation gives:
Ea 1
log k  log A 
2.303 RT


k is the rate of reaction
A is a constant known as the frequency factor
Ea is the activation energy,
 R is the gas constant (1.987 calories deg1mole-1 OR 8.314 J mole-1)
 T is the absolute temperature.
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Arrhenius equation….
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:

Ea T2  T1 
k2
log

k1 2.303R T2T1
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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?
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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:
k 2 Ea (T2  T1 )
log
k1

2.303RT1T2
k = reaction rate, T = temperature,
 R = gas constant, Ea = activation
energy

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Concept of Q10
Q10 
k (T 10)
KT
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.

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Concept of Q10…..
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Q10 estimates can be
made with the equation:
where t90T2 is the
estimated shelf life
t90T1 is the shelf life at a
given temperature
∆T is the difference in
temperature between T1
and T2 (i.e. T2 – T1)
Increase in ∆T will
decrease shelf life while
a decrease in ∆T will
increase shelf life
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t 90 (T2 ) 
t 90 (T1 )
T 

Q10 10
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Shelf-life Prediction

Shelf-life at different storage temperature can
be estimated as:
t 90 (T2 ) 
t 90 (T1 )
T 

Q10 10
 t90T2 is the estimated shelf life
 t90T1 is the shelf life at a given temperature
 ∆T is the difference in temperature between
T1
and T2
 Increase in ∆T will decrease shelf life while a
decrease in ∆T will increase shelf life
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TUTORIAL QUESTIONS
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.
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TUTORIAL QUESTIONS
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?
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TUTORIAL QUESTIONS
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?
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TUTORIAL QUESTIONS
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
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ºC
K
40
0.00011
50
0.00028
60
0.00082
70
0.00196
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THANK YOU FOR YOUR
ATTENTION
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