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- 1. KINETICS AND DRUG STABILITY Dereje K. 1
- 2. 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 2
- 3. 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 3
- 4. 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. 4
- 5. 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 5
- 6. WHY DO WE STUDY ABOUT DRUG STABILITY? Safety of the patient [toxic products or less potent product] Legal requirements with identity, strength, purity and quality To prevent economic repercussions. 6
- 7. 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. kc n Rate dt dc 7
- 8. ORDERS OF REACTIONS the 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 8
- 9. 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 9
- 10. 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: 10
- 11. 11 11 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 kdtdc t 00 C – C0 = -kt
- 12. 12 12 Units of the rate constant K c = co – Kt K = co – c /t K = Concentration / time = mole / liter . second = M. sec-1 C t
- 13. 13 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 t 13 t1/2 = co / 2K t90% = t0.9 = 0.1 co / k
- 14. 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? 14
- 15. 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 15
- 16. FIRST ORDER REACTION The most common pharmaceutical reactions e.g; drug absorption & drug degradation The reaction rate of change is proportional to drug concentration. 16
- 17. - dc/dt = kc1 = kc - dc/c = kdt 17 t t t c dtk c dc 00 ktcc o lnln 303.2 loglog 0 kt cc
- 18. 18 18 C = co e –kt Difficult to determine slope lnc = lnco – kt Slope = c1 – c2 / t1 – t2 Slope = -k lnco Log co Log c = log co – kt / 2.303 Slope = c1 – c2 / t1 – t2 Slope = -k / 2.303 Or use semi log paper C Lnc Logc t t t
- 19. 19 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/ t0.9 19 t1/2 = 0.693 / K t0.9 = 0.105 / K
- 20. 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? 20
- 21. 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. 21
- 22. 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 22
- 23. SECOND ORDER REACTION Rate 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 23
- 24. dc/dt = -kc2 dc/c2 = -kdt 24 t t c c dtk c dc 0 2 0 kt cc 0 11 2nd Order reaction
- 25. 25 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
- 26. 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]. 26
- 27. 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 27

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