1. CONTENTS I NTRODUCTION R ATE OF REACTION M OLECULARITY OF REACTION M ETHODS TO DETERMINE THE ORDER OF REACTION F ACTORS INFLUENCING REACTION RATES R EFERENCES 1

2. 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 dosage forms. 2

3. 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 3

4. 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: CH 3 COOH+C 2 H 5 OH --------- > CH 3 COOC 2 H 5 +H 2 0 In the case the rate of forward reaction is given as: R f = d(CH 3 COOH) = -d(C 2 H 5 OH ) dt dt 4

5. 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. 5

6. 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 on the temperature. 6

7. 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. 7

8. C = C -------------  C = C H H Ar H H trasstillibene cisstilbene Ar 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 2H 2 0 2 -------------  2H 2 0+ 0 2 8

9. Example: 2 Different types of reactants. Alkaline hydrolysis of ethyl acetate. CH 3 C00C 2 H 5 + NaOH ------  CH 3 C00Na + C 2 H0H 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. 9

10. 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. 10

11. 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=k o Where minus indicates the absorbance decreasing. K o specific rate constant. Examples: Oxidation of vitamin-A in an oily solution. Photo chemical degradation of chlorpromazine in aqueous solution. 11

12. 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, A o at t=o time, and absorbance, A t at t = t. 12

13. Ao ʃ At dA = -k o 0 ʃ t dt A t - A o = -k o t or k o = A O - A t 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 13

14. Equation may be written as C=a – k o t 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 k o. A representative zero order plot is Absorbance Times (hours) Slope is negative Slope =k o 14

15. Units for k o 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. slope=k o Optical density Time(hours) Slope is positive 15

16. 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 = t 1/2 Substitute these values in the equation k o = (a-c)/t (a-c) = a-(a/2) = (1/2)a Then equation will be t1/2 = k o k o k o = a/2k o Units is time scale i.e.sec/conc, min/conc, hrs/conc 16

17. 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 t 90 and has the units of time/conc. As per defination the terms in equation c =a – k o t is change to c = 90a 100 t = t 90 Substituting these values in the equation c = a-k o t then equation will be (a – 0.9a) = 0.1a t 90 = k 0 k o 17

18. 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 = k 1 c dt Slope = k 1 /2.303 Slope is negative Time(hrs) % un react 18

19. First order half life: t 1/2 = 0.693/k here half life depends on the concentration of the drug undergoing the reaction E.g.: Absorption, Distribution and Elimination 19

20. Shelf life: (T 90% ) It is defined as the time required for the concentration of the reactants to reduce to 90% of its initial concentration. T 90% = 2.303/K 1 log C o /0.9C o T 90% = 0.152 t 1/2 20

21. 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 = k 2 (A)(B) A and B are the reactants in the reaction k 2 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 = k 2 (A)(constant) =k 1 (A) This type of reaction also termed as apparent first order 21

22. 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. 22

23. 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 = K 2 [A] I [B] I Where [A] and [B] are the concentration of A and B, respectively, and k 2 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. 23

24. 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. 24

25. A linear plot for second order reaction where a=b Slope =k 2 x/a(a-x) Time(min) 25

26. 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. 26

27. 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). 27

28. 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. 28

29. 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. 29

30. 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 2 nd edition 30

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