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KINETICS AND DRUG STABILITY

Dereje K.

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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

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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

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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.

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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

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WHY DO WE STUDY ABOUT DRUG STABILITY?

Safety of the patient [toxic products or less potent product]Legal requirements with identity, strength, purity and qualityTo prevent economic repercussions.

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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.

kcn

Ratedt

dc

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ORDERS OF REACTIONSthe 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

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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

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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:

1111

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

kdtdct

00

C – C0 = -kt

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Units of the rate constant Kc = co – KtK = co – c /t

K = Concentration / time = mole / liter . second = M. sec-1

C

t

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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 t13

t1/2 = co / 2K

t90% = t0.9 = 0.1 co / k

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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?

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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

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FIRST ORDER REACTION

The most common pharmaceutical reactions e.g; drug absorption & drug degradation

The reaction rate of change is proportional to drug concentration.

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- dc/dt = kc1 = kc - dc/c = kdt

t

t

t

c

dtkc

dc

00

ktcc o lnln

303.2loglog 0

ktcc

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C = co e –kt

Difficult to determine slope lnc = lnco – ktSlope = c1 – c2 / t1 – t2

Slope = -k

lnco

Log coLog c = log co – kt / 2.303Slope = c1 – c2 / t1 – t2

Slope = -k / 2.303

Or use semi log paper

C Lnc

Logc

t t

t

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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/ t0.919

t1/2 = 0.693 / K

t0.9 = 0.105 / K

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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?

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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.

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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

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SECOND ORDER REACTIONRate 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

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dc/dt = -kc2

dc/c2 = -kdt

t

t

c

c

dtkc

dc

02

0

ktcc

0

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2nd Order reaction

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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

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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].

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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