Reaction kinetics

Reaction kinetics By A. S. Adebayo, Ph. D.

KINETICS • Applications • Chemical reactions such as decomposition of medicinal compounds • Processes of drug absorption, distribution and elimination from the body • Shelf life determination.

Shelf life determination • 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.

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: • where n=0,1 or 2 for zero, first & second order reactions respectively

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 Michaelis-Menten kinetic process

First Order Kinetics • n=1 and the reaction rate is dependent on the concentration of one of the reactants in the formulation. • C is the concentration remaining un-decomposed, unabsorbed, yet to be distributed, metabolized or excreted at time t as the case may be • k is the first order rate constant.

First Order Kinetics (cont.) • On integration, the equation above gives: • On rearrangement and conversion to log in base 10:

Log Conc. Slope = -k/2.303 Time Log concentration versus time

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 half-life?

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).

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.

Zero order reaction (cont.) • Zero order Equation: • Co= original concentration of reacting material, k=reaction rate constant, dt= change in time.

Zero order processes • Expression of zero order equation: • Ct=conc. at time t, Co=conc. at time o. • Plot of C against t gives a straight line with slope of -ko

Conc Slope = -k0 Time Concentration versus time (Zero-order plot)

Reaction half-life (Zero-order) • For a zero order reaction, the time for 50% reaction, t½, is given as:

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

Apparent Zero Order Reaction Kinetics (Cont.) • Ordinarily, the equation for decomposition is first order: • C=the conc. of drug remaining un-decomposed at time t • k=the known first order rate constant.

Apparent Zero Order Reaction Kinetics (Cont.) • When concentration is rendered constant by suspended particles offering replacement, then • thereby turning the first order rate law into;

Chemical instability • Can present as; • 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.

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.

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.

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 (Co-Ct) vs. t is linear.

Factors Affecting Rate of Reactions • The rate of reaction (degradation of pharmaceutical products) can be influenced • temperature, • moisture, • solvent (pH, dielectric constant, etc), • light (radiation), • catalysts, • oxygen and • concentration of reactant (s).

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:

Arrhenius equation • Log transformation gives: • 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 deg-1mole-1 OR 8.314 J mole-1) • T is the absolute temperature.

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:

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?

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 = reaction rate, T = temperature, • R = gas constant, Ea = activation energy

Concept of Q10 • 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.

Concept of Q10….. • 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

Shelf-life Prediction • Shelf-life at different storage temperature can be estimated as: • 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

TUTORIAL QUESTIONS • 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.

TUTORIAL QUESTIONS • 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?

TUTORIAL QUESTIONS 7. The rate constant for decomposition of 5-hydroxymethylfurfural 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?

TUTORIAL QUESTIONS 8. Analysis of the rate of degradation of a colourant in a multi-sulfa drug preparation shows the following results: • Assuming a first-order process, compute the activation energy and the value of K at 25 ºC

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Reaction kinetics