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1. Rate and orders of reactions 6/7/2018 1 The rate of reaction is the velocity with which a reactant or reactants undergo chemical change. The rate, velocity or speed of a reaction is given by the expression dc / dt . where dc is increase or decrease of concentration over a time interval dt Rate:  dc/ dt This expression gives the increase (+) or decrease (-) in concentration (C ) within a given time intervals ( dt ) The reaction rate is a description of the drug concentration with respect to time. Most commonly, zero-order and first-order reactions are encountered in pharmacy.

2. 6/7/2018 2 Formation of ethyl acetate from ethyl alcohol and acetic acid. CH 3 COOH + C 2 H 5 OH = CH 3 COOC 2 H 5 + H 2 O In this reaction the rate of forward reaction ( Rf ) may be calculated by measuring the concentration of acetic acid or ethanol as the reaction progresses. The rate of reverse reaction ( Rr ) may calculated by measuring the concentration of ethyl acetate or water

3. 6/7/2018 3 The law of mass action relates these experimentally determined rates to the concentration of all of the reacting species. This law states that, at a given temperature, the rate of the reaction is at each instant proportional to the product of the concentration of each of the reacting species raised to a power equal to the number of molecules of each of these species participating in the process Rate = k[A] x [B] y reaction order = x + y The order of a reaction is simply the sum of the exponents on the concentration terms for a rate law Example 1: Rate = k [A] 1 [B] = k [A] is 1st order in [A] and 0th order in [B] and 1st order for the reaction.

4. 6/7/2018 4 It is important to note that for a net chemical reaction, which is the sum of all of the elementary processes, there is no requirement that the order of the reaction with respect to a chemical species be identical to its stoichiometric coefficient indicated in the net chemical equation. because chemical species that appeared as both reactants and products in the various elementary processes have been removed to create a balanced net equation

5. 6/7/2018 5 it may be necessary for some elementary processes to occur more than once in order to arrive at net balanced equation Additionally, some elementary processes may be reversible (i.e., products revert to reactants) during an overall chemical reaction

6. 6/7/2018 6 zero-order process - dY / dt = K0Y where K0 is the zero-order rate constant and the minus sign shows negative change over time Since Y =1, - dY / dt = K0 This equation clearly indicates that Y changes at a constant rate, since K0 is a constant. This means that the change in Y must be a function of factors other than the amount of Y present at a given time. The integration of the Eqn. yields the following: Y = Y0 -K0t where Y is amount present at time t and Y0 is amount at time zero

7. 6/7/2018 7 As a molecule of drug becomes product, the reservoir of drug contributes to the concentration of drug in solution, and so the concentration of drug in solution does not change. This is the kinetic situation that we have in suspensions Because the concentration of drug in solution is constant, the rate of degradation in suspensions is constant.

8. A plot of the amount decomposed (as ordinate) against time (as abscissa) is linear with a slope of k0 The units of k0 are concentration time-1. eg . Many decomposition reactions in the solid phase or in suspensions apparently follow zero-order kinetics. 6/7/2018 8

9. 6/7/2018 9 First-order process - dY / dt = KY 1 where K is the first-order rate constant. Since Y 1 =Y, - dY / dt = KY Upon integration of the above Eqn., we obtain: Y = Y0e -Kt ln Y = ln Y0 - Kt or log Y = log Y0 – Kt/2.303 The rate of the reaction is not constant as it decreases as the concentration of drug decreases.

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11. 6/7/2018 11 The units of k1 are time–1. If there are two reactants and one is in large excess, then reaction may still follow first-order kinetics because the change in concentration of the excess reactant is negligible. This type of reaction is a pseudo first-order reaction.

12. 6/7/2018 12 Second order Rate depends on the product of two concentration terms. In the simplest case they refer to the same species. For example: 2HI -> H 2 + I 2 Here the reaction is relies on the collision of two HI molecules. The rate of reaction from the law of mass action is given by: Rate = k[Hl] [HI] = k[HI] 2

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14. 6/7/2018 14 Half-life This is the time taken for the concentration (of, say, a drug in solution) to reduce by a half. Rearrangement of the integrated equations for t

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16. 6/7/2018 16 First-Order Half-Life A solution of a drug contained 500 units/ mL when prepared. It was analyzed after 40 days and was found to contain 300 units/ mL. Assuming the decomposition is first order, at what time will the drug have decomposed to one-half of its original concentration? Answer = 54.3 days Zero-Order Half-Life A drug suspension (125 mg/ mL ) decays by zero-order kinetics with a reaction rate constant of 0.5 mg/ mL /h. What is the concentration of intact drug remaining after 3 days (72 hours), and what is its t1/2? Answer 89mg/ mL , 125 hours

17. 6/7/2018 17 Determination of Order The order of a reaction can be determined by several methods. 1. Substitution Method The data accumulated in a kinetic study can be substituted in the integrated form of the equations that describe the various orders. When the equation is found in which the calculated k values remain constant within the limits of experimental variation, the reaction is considered to be of that order

18. 6/7/2018 18 2. Graphic Method A plot of the data in the form of a graph can also be used to ascertain the order. If a straight line results when concentration is plotted against t, the reaction is zero order. The reaction is first order if log c versus t yields a straight line, It is second order if 1/c versus t gives a straight line 3. Half-Life Method In a zero-order reaction, the half-life is proportional to the initial concentration, C , The half-life of a first-order reaction is independent of C ; t1/2 for a second-order reaction, in which a = b, is proportional to 1/ C ;

19. Shelf life 6/7/2018 19 Shelf life is the time period at which there will be 90% of the original concentration in the formulation. After this time period, the formulation is considered expired

20. 6/7/2018 20 Aspirin is a nonsteroidal anti-inflammatory drug that hydrolyzes in solution. The k1 of this reaction at pH 2.5 is 5 × 10 −7 sec- 1 (0.0018/hour). What is the shelf life? As one can see, aspirin is very unstable in aqueous solution. Would making a suspension increase the shelf life of aspirin?

21. 6/7/2018 21 If we suspend aspirin rather than formulating it in solution, what is the shelf life if[Drug]0 = 0.65 g/5 mL and the solubility of aspirin is 1g/300mL? We can calculate k0 from k1 and the drug solubility: The increase in the shelf life of suspensions as compared to solutions is a result of the interplay between the solubility and the stability of the drug

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23. 6/7/2018 23 Shelf Life of an Aspirin Suspension A prescription for a liquid aspirin preparation is called for. It is to contain 325 mg/5 mL or 6.5g/100 mL. The solubility of aspirin at 25°C is 0.33 g/100 mL ; therefore, the preparation will definitely be a suspension. The other ingredients in the prescription cause the product to have a pH of 6.0. The first-order rate constant for aspirin degradation in this solution is 4.5 × 10 -6 sec -1 . Calculate the zero-order rate constant. Determine the shelf life, t 90 , for the liquid prescription, assuming that the product is satisfactory until the time at which it has decomposed to 90% of its original concentration (i.e., 10% decomposition) at 25°C. Answer: k0 = k × [Aspirin in solution], from equation

24. Effect of Temperature on Reaction Rate 6/7/2018 24 A number of factors other than concentration may affect the reaction velocity. Among these are temperature, solvents, catalysts, and light The application of heat to increase the rate of a chemical reaction is a common laboratory procedure The rate of most solvolytic reactions of pharmaceuticals is increased roughly 2- to 3-fold by a 10°C increase near room temperature Collision Theory Reaction rates are expected to be proportional to the number of collisions per unit time. Because the number of collisions increases as the temperature increases, the reaction rate is expected to increase with increasing temperature

25. 6/7/2018 25 The Arrhenius plot: The relationship of reaction rate to temperature was described by Arrhenius as follows where k is the rate constant of any order A is a constant for the reaction (actually the hypothetical rate at infinite temperature) Ea is activation energy in calories per mole R is the gas constant (1.987 cal/K per mole) and T is temperature in kelvins

26. 6/7/2018 26 The pharmaceutical industry uses the Arrhenius plot, a graph of log k versus the reciprocal of temperature to determine the shelf life for drugs that are relatively stable at room temperature. The drug is tested at higher temperatures, a plot constructed and the room temperature rate constant extrapolated from the plot Room temperature shelf life can be calculated from the extrapolated rate constant, k. Ea, the energy barrier that the reactants have to climb to become products, ranges between 12.2 and 24.5 kcal/mol for drug degradations.

27. 6/7/2018 27 Practical applications: If we have information about the stability of a drug at one temperature, given the linear relationship between log rate constant and reciprocal temperature, we can calculate a ratio of rate constants that can be used to estimate shelf life. Here is the Arrhenius equation rearranged to facilitate these calculations:

28. 6/7/2018 28 Eg . If we were interested in determining how much faster a drug degradation would proceed at autoclave temperature (120°C) than room temperature (20°C), assuming an energy of activation of 12.2 kcal/mol, our equation would be antilog (2.315) = 210 times faster

29. 6/7/2018 29 Decomposition of 5-HMF The rate constant k1 for the decomposition of 5 hydroxymethylfurfural at 120°C (393 K) is 1.173 hr-1 or 3.258 × 10-4 sec-1 and k2 at 140°C (413 K) is 4.860 hr-1. What is the activation energy, Ea, in kcal/mole and the frequency factor, A, in sec-1 for the breakdown of 5-HMF within this temperature range? We have At 120°C, using Arrhenius equation we obtain

30. 6/7/2018 30 The results of Arrhenius calculations for pharmaceutically important temperature spreads for energies of activation between the limits of 12.2 and 24.5 kcal/mol

31. 6/7/2018 31 Q10 method Using this method, one can estimate the effect of a 10° rise in temperature on the stability of pharmaceuticals Q10 is the ratio of two rate constants for a drug measured at two temperatures that are 10°C apart. This relationship can be used to estimate the change in the rate and therefore a new shelf life at any new temperature using the equations below. The ratio of the rate constants for any temperature spread, ΔT, is:

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33. 6/7/2018 33 Eg 1. Let's say a newly reconstituted product that is susceptible to hydrolysis is labeled to be stable for 24 hours in a refrigerator(5 o C) . Ea =19.4 What is the estimated shelf life at room temperature?

34. 6/7/2018 34 You are a community pharmacist and have just reconstituted a cefaclor suspension for a patient with otitis media . The product has a shelf life of 14 days at refrigerator temperature (5°C). The patient's mother wants to know if it would hurt the drug to keep it in the car for an hour while she does some shopping. You estimate the temperature inside of the car on this particular day to be 35°C . Estimate how much time will be lost from the shelf life if the suspension is stored inside the car for 1 hour if a product has been stored at a different temperature for a portion of its shelf life, a shelf life adjustment can be calculated from

35. 6/7/2018 35 If we use Ea of 19, what is the ratio of rate constants for this change in temperature? The product will not sit for all of its shelf life at 35°C. It will be at that temperature for 1 hour. We know that the rate at 35°C is 27 times the rate at 5°C. This means that sitting for 1 hour at 35°C is equivalent to sitting for (1 hourX27) 27 hours at 5°C.

36. 6/7/2018 36 Ex 1. Asparaginase is an antineoplastic drug that has a shelf life of 8 hours at refrigerator temperature (5°C) after reconstitution. The patient will use only half of the vial and will require another dose the following day. Estimate the shelf life of the reconstituted drug when stored in the freezer (−20°C). Because asparaginase is a large protein with many functional groups, and data on its routes of degradation are not readily available, we will assume an activation energy of 19 kJ/mol.

37. 6/7/2018 37 Ex 2. Reconstituted ampicillin suspension is stable for 14 days when stored in the refrigerator (5°C). If the product is left at room temperature for 12 hr, what is the reduction in the expiration dating? Ex 3. Calculate the factors by which rate constants may change for ( a) a 25°C to 50°C temperature change and ( b) a 25°C to 0°C temperature change.

38. 6/7/2018 38 Stability study The purpose of stability study is to provide evidence on how the quality of an active substance or pharmaceutical product varies with time under the influence of a variety of environmental factors such as temperature, humidity, and light Required if significant change occurs during 6-month storage under conditions of accelerated testing.

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41. 6/7/2018 41 Stability tests for dosage forms: 1. Tablets-Dissolution (or disintegration, if justified), water content and hardness/friability. For coated and colour tablets additional tests may require for texture and colour stability. 2.Capsules-Hard gelatin capsules: brittleness, dissolution (or disintegration, if justified), water content, and level of microbial contamination 3. Emulsions: Phase separation, pH, viscosity, level of microbial contamination, and mean size and distribution of dispersed globules

42. 6/7/2018 42 Oral solutions and suspensions: Formation of precipitate, clarity for solutions, pH, viscosity, level of microbial contamination. Additionally for suspensions, redispersibility , rheological properties, mean size and distribution of particles should be considered. Also, polymorphic conversion may be examined, if applicable Powders and granules for oral solution or suspension Water content, and reconstitution time. Reconstituted products (solutions and suspensions) should be evaluated as described in“Oral solutions and suspensions” above, after preparation according to the recommended labeling, through the maximum intended use period

43. 6/7/2018 43 Nasal sprays: solutions and suspensions Clarity (for solution), level of microbial contamination, pH, particulate matter, unit spray medication content uniformity, number of actuations meeting unit spray content uniformity per container, droplet and/or particle size distribution, weight loss, pump delivery, microscopic evaluation (for suspensions), foreign particulate matter and extractable/leachable from plastic and elastomeric components of the container, closure and pump Suppositories Softening range, dissolution (at 37°C). Large volume parenterals (LVPs) Colour , clarity, particulate matter, pH, sterility, pyrogen / endotoxin , and volume

44. 6/7/2018 44 Topical, ophthalmic and otic preparations Included in this broad category are ointments, creams, lotions, paste, gel, solutions, eyedrops , and cutaneous sprays. Topical preparations should be evaluated for clarity, homogeneity, pH, resuspendability (for lotions), consistency, viscosity, particle size distribution (for suspensions, when feasible), level of microbial contamination/sterility and weight loss (when appropriate). Evaluation of ophthalmic or otic products (e.g. ointments, solutions and suspensions) should include the following additional attributes: sterility, particulate matter and extractable. Evaluation of cutaneous sprays should include: pressure, weight loss, net weight dispensed, delivery rate, level of microbial contamination, spray pattern, water content, and particle size distribution (for suspensions)

45. 6/7/2018 45 Small volume parenterals (SVPs) Colour , clarity (for solutions), particulate matter, pH, sterility, endotoxins . powders for injection solution should include monitoring for colour , reconstitution time and water content. Specific parameters to be examined at appropriate intervals throughout the maximum intended use period of the reconstituted drug product, stored under condition(s) recommended in labeling, should include clarity, colour , pH, sterility, pyrogen and particulate matter. Suspension for injection should include, in addition, particle size, distribution, redispersibility and rheological properties. Emulsion for injection should include, in addition, phase separation, viscosity, mean size and distribution of dispersed phase globules

46. 6/7/2018 46 ACCELERATED STABILITY TESTING To assess the stability of a formulated product it is usual to expose it to 'high stress‘ i.e. conditions of temperature, humidity and light intensity that are known from experience to be likely causes of breakdown High stress conditions enhance the deterioration of the product and therefore reduce the time required for testing extrapolations to 'normal' storage conditions must be made with care, and that the formulator must be sure that such extrapolations are valid.

47. 6/7/2018 47 The objectives of accelerated tests may be defined as: 1. The rapid detection of deterioration in different initial formulations of the same product. This is of use in selecting the best formulation from a series of possible choices; 2. The prediction of shelf-life, which is the time a product will remain satisfactory when stored under expected or directed storage conditions; 3. The provision of a rapid means of quality control, which ensures that no unexpected change has occurred in the stored product

48. 6/7/2018 48 Common high stresses or challenges Temperature challenge Humidity challenge Light challenge Applied to pharmaceutics, chemical kinetic information permits a rational approach to the stabilization of drug products, and prediction of shelf life and optimum storage conditions.