Chemical Kinetics Lecture Notes PDF

TOPIC 10: Chemical Kinetics Learning Objectives Apply reaction rate and reaction order calculations to drug stability Discuss the concept of pseudo reaction order Calculate the half life and shelf life of pharmaceutical products Discuss stability testing protocols and regulatory requirem...

TOPIC 10: Chemical Kinetics Learning Objectives Apply reaction rate and reaction order calculations to drug stability Discuss the concept of pseudo reaction order Calculate the half life and shelf life of pharmaceutical products Discuss stability testing protocols and regulatory requirements 2 Outline 1. Common Drug Degradation Reactions 1. Hydrolysis 2. Oxidation 2. Order of Reaction 1. Zero-Order Reactions 2. First-Order Reactions 3. Pseudo Reaction Order 3. Stability and Shelf Life of Drugs 1. Factors 2. Accelerated Stability Testing 3. Enzyme Catalysis Reactions 4. Pharmacokinetics 1. Zero-Order Absorption 2. Frist-Order Absorption 5. Radioactivity 3 Common Drug Degradation Reactions Most common mechanism of drug degradation (for small molecular pharmaceuticals): 1. Solvolysis (Hydrolysis) 2. Oxidation 3. Photolysis Focus on solvolysis and oxidation Since water is the most common solvent encountered by pharmaceuticals, hydrolysis is the primary solvolysis reaction 4 Relevant Terms CHEMICAL KINETICS Deals with the stability of drugs and the mode of action of their degradation through the examination of rates of reaction and reaction mechanisms STABILITY The ability of a drug to retain its chemical, physical, microbiological and biopharmaceutical properties within specified limits throughout its shelf-life STABILITY TESTS Series of tests designed to obtain information on the stability of a pharmaceutical product in order to define its shelf-life and utilization period under specified packaging and storage conditions 5 Relevant Terms SHELF LIFE Expiration Dating Period or Validity Period The period of time during which a drug product is expected, if stored correctly, to remain within specification as determined by stability studies on a number of batches of the product Shelf-life is used to establish the expiry date of each batch of drug product Time required for 10% of the material to disappear, time at which A has decreased to 90% of its original concentration EXPIRATION DATE Date placed on the container label of a drug product designating the time prior to which a batch of the product is expected to remain within the approved shelf-life specification if stored under defined conditions and after which is must not be used HALF LIFE Time required for one-half of the material to disappear, time at which A has decreased to 1/2A 6 Stability Testing To provide evidence on how the quality of drug substance or drug product varies with time under the influence of a variety of environmental factors, such as temperature, humidity and light To establish a retest period for the drug substance or a shelf life for the drug product and recommend storage conditions 7 Common Drug Degradation Reactions Most common mechanism of drug degradation (for small molecular pharmaceuticals): 1. Solvolysis (Hydrolysis) 2. Oxidation 3. Photolysis Focus on solvolysis and oxidation Since water is the most common solvent encountered by pharmaceuticals, hydrolysis is the primary solvolysis reaction 8 Hydrolysis Occurs when a water molecule, with the hydroxyl ion (OH-) acting as a nucleophile, interacts with a functional group to degrade the rug Major target: carbonyl functional groups (C=O), ex. carboxylic acids, esters, amides Responsible for the distinctive, vinegary odor of acetic acid in bottles of aspirin stored for long periods of time under nonideal conditions (high temperature, high humidity) Can be accelerated by either acids or basis: pH of the aqueous environment is a critical factor in stability 9 Oxidation While oxygen is not required for an oxidation reaction, oxygen is the primary oxidizing agent of concern for most pharmaceutical degradation reactions limiting oxygen by packing product in an inert atmosphere sealing the bottle with foil to exclude atmospheric exposure prior to dispensing oxidation reactions may be dependent to pH, the control of pH via buffering may aid in the inhibition of such degradation reactions use of chelating agents and antioxidants 10 Review of Concepts Reaction Rates 11 Review of Concepts Reaction Rates 12 Review of Concepts Reaction Rates Consider the decomposition of N2O5 to give NO2 and O2: 2N2O5 (g) 🡪 4NO2 (g) + O2 (g) Time (s) [N2O5] [NO2] [O2] 0 0.0200 0 0 100 0.0169 0.0063 0.0016 200 0.0142 0.0115 0.0029 300 0.0120 0.0160 0.0040 400 0.0101 0.0197 0.0049 500 0.0086 0.0229 0.0057 600 0.0072 0.0256 0.0064 700 0.0061 0.0278 0.0070 13 Review of Concepts Reaction Rates 2N2O5 (g) 🡪 4NO2 (g) + O2 (g) Time (s) [N2O5] [NO2] [O2] 300 0.0120 0.0160 0.0040 400 0.0101 0.0197 0.0049 15 Review of Concepts Reaction Rate and Stoichiometry 16 Review of Concepts Rate Law and Reaction Order 17 Review of Concepts Rate Law, Reaction Order and Rate Constant Rate Law Order Units of k Rate = k Zero concentration/time Rate = k[A] First order with respect to A 1/time First order overall Rate = k[A]2 Second order with respect to A 1/concentration x time Second order overall Rate = k[A][B] First order with respect to A 1/concentration x time First order with respect to B Second order overall 18 Order of Reactions Understanding the rate of reaction, reaction order, and how rate constants are determined will assist the pharmacist in determining beyond use dates, maintaining proper storage conditions, and developing stable products. An effective approach to achieving this understanding is via the mathematical analysis of the degradation process. Mass degradation reaction can be illustrated as follows 19 Order of Reactions D drug molecule undergoing degradation W reacting molecule of water* d[D] is a very small change in the drug concentration, [D], over a very small change in time, dt (-): drug concentration is decreasing with respect to time 20 Order of Reactions k2 : rate constant, represent the speed of the degradation process What is the reaction order of this equation? 21 Order of Reactions In this generic example, the reaction order is determined to be second order. Rate constants, k, from different drug degradation reactions of the same reaction order can be compared to assess the relative stability of drug. 22 Order of Reactions Zero Order Reactions Rate is independent of the concentrations of the reactants Rate is determined by a decrease in the drug concentration [D] Velocity of the decrease in concentration is constant [D]0 initial drug concentration [D]t drug concentration after a specified time, t 23 Order of Reactions Zero Order Reactions Slope is equal to –k0 k0 [D] concentration [t] time 24 Order of Reactions Zero Order Reactions HALF - LIFE 25 Order of Reactions Zero Order Reactions HALF - LIFE In a zero-order reaction, at ambient temperature, k0 was determined to be 0.380 (mg/mL∙days-1). If the initial drug concentration, [D]0 was 200 mg/mL, how long will it take for the initial concentration to decrease by 50%? 26 Order of Reactions First Order Reactions Rate is directly proportional to the concentration of one of the reactants [D]0 initial drug concentration [D]t drug concentration after a specified time, t k first-order degradation constant 27 Order of Reactions First Order Reactions k0 [D] Concentration [t] Time 28 Order of Reactions First Order Reactions HALF - LIFE [D]t = ½[D]0 t = t1/2 29 Order of Reactions ZERO ORDER FIRST ORDER Equation for k Units for k Equation of t1/2 Equation for t90 30 Order of Reactions Pseudo Reaction Order 31 Order of Reactions Pseudo Reaction Order 32 Order of Reactions Pseudo Reaction Order 33 Order of Reactions Pseudo Reaction Order 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? 34 Stability and Shelf-life of Drugs SHELF LIFE Expiration Dating Period or Validity Period The period of time during which a drug product is expected, if stored correctly, to remain within specification as determined by stability studies on a number of batches of the product Shelf-life is used to establish the expiry date of each batch of drug product Time required for 10% of the material to disappear, time at which A has decreased to 90% of its original concentration 35 Stability and Shelf-life of Drugs Suppose that for a first order reaction, one had to start with 1.2 mg/mL of drug. To obtain 90% of 1.2, multiply with 0.9 36 Stability and Shelf-life of Drugs Suppose that for a first order reaction, one had to start with 1.2 mg/mL of drug. To obtain 90% of 1.2, multiply with 0.9 37 Stability and Shelf-life of Drugs Suppose that for a first order reaction, one had to start with 1.2 mg/mL of drug. To obtain 90% of 1.2, multiply with 0.9 If k = 0.03 mg/mL/h. Solve for t90. 38 Effects of Temperature Collision Theory of Reaction Rates The mechanism of a reaction depends on two factors: 1. Frequency factor 2. Activation The larger the frequency factor, the faster a reaction will procced. However, not all molecules collide with sufficient energy to contribute to a reaction. “molecules must have a certain energy to react” 39 Effects of Temperature 40 Effects of pH The magnitude of the rate of a reactions catalyzed by H+ and OH- ions can vary considerably with pH. The pH of optimum stability can be determined by plotting log k against pH. When log k increases with a decreasing pH 🡪 acid catalysis When log k increases with a increasing pH 🡪 basic catalysis These plots also known as pH-rate profiles, are very useful in guiding the formulation of stable dosage forms. 41 Accelerated Stability Testing 42 Accelerated Stability Testing 43 Accelerated Stability Testing It is not practical to wait for years to observe how long it takes for a drug to decompose. Various types of stress are applied to drug compounds to speed the process. 1. Temperature: accelerate rate of reaction 1. Humidity: increases decomposition by hydrolysis 1. Light: used to increase the effect of daylight or sunlight on a drug product 44 Expiration Date Equation For a first-order reaction, the initial concentration of a drug is 200 mg/mL. The specific rate constant k is obtained from an Arrhenius plot and is equal to 3 x 10-5 h-1 at 25°C (77°F). The limit of viability of the drug is 150 mg/mL, at which stage its shelf life has expired. 45 Expiration Date Equation Drug accelerated stability testing, a medicine was analyzed to have 3.2 mg/mL of active drug, and its stability constant k was found to be 0.05 mg/mL/h. How long will it take before the drug decomposes by 10%? [A]t = [A]0 – kt90 END