Drug Stability - Part 1 PDF

Kinetic Principles in Drug Degradation Part 1 Colette Gouveia Lecture 5  Introduction Basic requirements of pharmaceutical products 1. Efficacy: Optimum therapeutic level for specified period of time. 2. Safety: Minimum or no side effect...

Kinetic Principles in Drug Degradation Part 1 Colette Gouveia Lecture 5  Introduction Basic requirements of pharmaceutical products 1. Efficacy: Optimum therapeutic level for specified period of time. 2. Safety: Minimum or no side effects. 3. Stability: The products should retain their properties during storage. This should guarantee the efficacy and safety  Stability “Stability of a pharmaceutical preparation is the capability of a formulation in a specific container-closure system to remain within specified limits at certain temperature throughout its shelf life.”. The properties of a drug substance or drug product may be physical, chemical, microbiological, toxicological or performance properties such as disintegration and dissolution. The period between the date of manufacture and expiry date is known as the label shelf-life. The process in which the shelf-life is determined is called a stability analysis.  The USP defines the stability of pharmaceutical product as “extent to which a product retains within specified limits” and throughout its period of storage and use (i.e its shelf life) the same properties and characteristics that it possessed at the time of its manufacturer A drug substance is studied under three (3) categories of stabilities - 1. Solid state stability of drug only 2. Compatibility studies ( drug+ excipients ) 3. Solution phase stability  Importance of Stability Studies Development of optimum formulation (preformulation studies) Determines the optimum storage conditions (temperature, light, humidity) Selecting the proper container for dispensing (glass or plastic, clear or opaque, cap liners) Predicting the shelf life of the drug Anticipating drug excipient interactions. Stabilization of the drugs against degradation Determines container closure system suitability. Safety point of view of patient. Prevention of economical repercussion Essential quality attribute.  Factors Affecting Drug Stability 1. Temperature: high temperature accelerate oxidation, reduction and hydrolysis reaction which lead to drug degradation 2. pH: - Acidic and alkaline pH influence the rate of decomposition of most drugs 3. Moisture 4. Light: affects drug stability through its energy or thermal effect which lead to oxidation 5. Pharmaceutical dosage forms: Solid dosage forms are more stable than liquid dosage forms for presence of water. 6. Concentration: Rate of drug degradation is constant for the solutions of the same drug with different concentration. So, ratio of degraded part to total amount of drug in diluted solution is bigger than of concentrated solution. 7. Drug incompatibility: Reactions between components of pharmaceutical dosage forms itself or between these components and cover of the container. 8. Oxygen: Exposure of drug formulations to oxygen affects their stabilit  Degradation Studies Most drugs are susceptible to chemical decomposition in their dosage forms. Degradation can lead to loss of the drug’s potency and generation of impurities in drug products. Such impurities are controlled in drug products by understanding of the rates and mechanisms of drug degradation reactions and implementing stabilization strategies. Kinetic studies helps us to determine the speed or rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered.  Chemical Kinetics The branch of Physical chemistry which deals with the rate of reactions is called Chemical Kinetics The study of Chemical Kinetics includes : 1. The rate of the reactions and rate laws. 2. The factors as temperature, pressure, concentration and catalyst, that influence the rate of a reaction. 3. The mechanism or the sequence of steps by which a reaction occurs.  Applications 1. Drug stability 2. Dissolution 3. Drug release 4. Pharmacokinetics 5. Drug actions The knowledge of the rate of reactions is very valuable to understand the chemistry of reactions. It is also of great importance in selecting optimum conditions for an industrial process so that it proceeds at a rate to give maximum yield. Rate of a Chemical Reaction  Speed or Rate of Reaction Definition: It is the change in the concentration of a reactant or a product with time. Represented as molarity per second (M/s) Consider a reaction : A→ B The concentration of the reactant A decreases with time while that of the product B increases with time  Reactant Rate = - Δ [A] = change in concentration of A Δt over a time period Δt Product Rate = Δ [B] = change in concentration of B over Δt over a time period Δt - Δ [A] is a negative value because A decreases with time, and represents the rate of disappearance of the reactant A Δ [B] is a positive value because B increases with time, and the rate Δ [B] is a positive value and Δt represents the the rate of appearance of product B  Types of Rates Initial Rates - Rates measured at the beginning of the reaction, which is dependent on the initial concentrations of reactants. Average Rates -Average rate depends upon the change in concentration of reactants or products and the time taken for that change to occur. Instantaneous Rates - The rate of a reaction, measured at a particular moment of time is known as the instantaneous rate. - It is obtained when we consider the average rate at the smallest time interval say dt (i.e when Δ t approaches 0)  Average Reaction Rates From the table of the preceding slide, the conversion of reactants to products can be calculated. At the beginning of the reaction, the concentration of A represented as [A]is 0.1000 mol/L or 0.1000 M M. After 50 seconds, it falls to 0.0905 M For this example, we could determine the average rate as being - Δ [A] = 0.0905 M – 0.1000 M Δt 50 s – 0 s = 1.9 X 10 -4 M/s The above equation is known as average rate of reaction The Rate Law or Rate Expression and Rate Constant The Rate Law or Rate Expression and Rate Constant The expression which relates of rate of reaction to concentration of the reactants is known as rate law. It is also called as rate equation or rate expression. Consider a general reaction : aA + bB → cC+ dD Capital letters (A&B) denote reactants and the (C&D) denote products, while small letters (a,b,c,d) denote Stoichiometric i.e. ,molecular coefficients. The rate expression for this reaction is: Rate of reaction ∝ to [A]m [B]n or Rate of reaction = k [A]m [B]n Where m = rate order of the reaction with respect to A n = rate order of the reaction with respect to B m+n = overall order of the reaction k = the rate constant for the reaction, its value does not change with change in concentration but with change in temperature Where the [ ] represents the concentration in moles per liter The Rate Law or Rate Expression and Rate Constant k [A]m [B]n can also be written as: - d[R] = k [A]m [B]n dt This form is known as differential rate equation, where k is a proportionality constant called rate constant or velocity constant or specific reaction rate.  Rate Law or Rate Expression and Rate Constant At a fixed temperature the rate of a given reaction depends on concentration of reactants. The exact relation between concentration and rate is determined by measuring the reaction rate with different initial reactant concentrations. By a study of numerous reactions, it is shown that : “the rate of a reaction is directly proportional to the reactant concentrations, each concentration being raised to some power.” NOTE The concentration of the products do not appear in the rate law because the reaction rate is being studied under conditions where the reverse reaction does not contribute to the overall rate. The value of the exponent (n) must be determined by experiment only. It cannot be written from the balanced equation. Order of reaction In the previous slide, the reaction rate = k [A]m [B]n The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. Where m+n = overall order of the reaction Such that if m=2 and n=1, the reaction rate = K [A]2[B]1 HENCE The reaction is second order with respect to A and first order with respect to B. The overall order is the sum of the exponents of concentration terms that afford a linear plot, i.e., third order Units of rate mole / liter second (mole l ]s) mole / liter min (mole l min)  Order of a reaction Order of a reaction can be 0, 1, 2, 3 and even a fraction. Depending upon order of reaction, reactions are termed as zero, first or second order reactions. A zero-order reaction means that the rate of reaction is independent of the concentration of reactants. Reactions may be classified according to the order. If in the rate law; 𝑹𝒂𝒕𝒆 = 𝒌[𝑨]𝒎 [𝑩]𝒏 m + n = 1, it is First order reaction m + n = 2, it is Second order reaction m + n = 3, it is Third order reaction Order of reaction cannot be predicted by merely looking at the balanced chemical equation, i.e., theoretically but must be determined experimentally  Order of a reaction and Units of Rate Constant For a nth order reaction, A products Where Rate = k [A]n k= Rate = concentration X 1 [A ]n time (concentration)n k = ( concentration)1-n time -1 For example NH4 (aq) + NO2 (aq) → N2 (g)+ H2O (l) We express the way in which the concentration affects the reaction rate by using the following equation Where the rate law is Rate = k [NH4+ ][NO2 -] The exponents above for NH4+ and NO2 - are both 1. We say then that the reaction is first order in NH4+ and first order in NO2 -. These numbers are called individual reaction orders for each reactant. The overall reaction rate is obtained by adding these together (1+1=2). This reaction then is second order overall.  Types of Reactions Chemical reactions may be classed into two types : (a)Elementary reactions An elementary reaction is a simple reaction which occurs in a single step. b) Complex reactions A complex reaction is that which occurs in two or more steps i.e, products are obtained after completion of a sequence of elementary reactions. Molecularity of a Reaction  Molecularity of an Elementary Reaction The molecularity of an elementary reaction is defined as the number of reactant/s involved in an elementary reaction. Unimolecular reactions : (molecularity = 1) i.e., A → Product Example: Br2 → 2Br Bimolecular reactions : (molecularity = 2) i.e., A + B → Example: CH3 COOC2H5 + H2𝑶 → CH3 COOH +C2H5 OH Products or A + A → Products Termolecular reactions : (molecularity = 3) i.e., A + B + C → Products Example: 2NO + O2 → 2NO2 Reactions that involves more than one steps( complex reactions ) may have different molecularity and order of reaction. Differences between Order and Molecularity Order of the reaction Molecularity of the reaction 1. It is the number of reacting 1. It is the sum of the species taking part in a simple powers of the reaction. concentration terms in 2. It is the theoretical value the rate law equation. determined from the balanced single step reaction. 2. It is the experimentally determined value. 3. It is always a whole number i.e. 1, 2, 3 etc. 3. Order of the reaction can 4. Molecularity of the reaction be fractional values also. cannot be zero. 4. It can be zero 5. Molecularity of a complex reaction has no meaning. It is 5. Order is same for the expressed for each elementary whole reaction, no step. Methods of determining order of reaction Reaction order and rate equation are experimentally determined, while molecularity of a reaction is often evident from the reaction mechanism. Reaction order can be experimentally determined by one of several methods: 1. Initial rate method – is governed by changing the concentrations of one reactant while keeping the others constant. Expression of the relationship between the rate of reaction and concentration. 2. Integrated rate law - Expression of the relationship between the concentration of reactants and time. The equation which gives a constant value of k decides the order of reaction. 3. Substitution 4. Half-life method – this technique is utilized only when the rate law is involved by only a single concentration term 5. Graph method-this technique is utilized in the presence of a single reactant, where the data are plotted according to different integrated rate equations so as to yield a straight line.Slope gives the value of rate constant Determining Reaction Order (Method of Initial Rates)  Determining Reaction Order (Method of Initial Rates) The three commonly encountered rate process: Zero order reaction First order reaction Second order reaction However, Pseudo order reactions also exist  Zero Order Reaction It is also called as constant rate process. The reaction is said to be zero- order reaction , if the rate of reaction is independent of the concentration i.e., the rate of reaction can not be increased further by increasing the concentration of reactants. This set of data shows no effect on rate with increasing [A]. 1. Rate is independent of [A]. 2. Zero order 3. Rate = k[A]0 = k  Zero Order reactions Rate = k[A]0 = k Independent of reactant concentration Rate is the same at any [reactant] Constant reaction rate Reaction does not slow down as reaction progresses  First Order Reaction Measure the (initial) rate of reaction at several different [reactant]. Look for the effect of [reactant] on rate. In this set of data when [A] doubles ,the rate also doubles Rate is directly proportional to [A] First order Rate = k [A]  First Order Reaction Rate = k[A]1 = k Directly proportional to [reactant] Therefore, greater the concentration , faster the reaction. First-order process is said to follow linear kinetics  Second Order reactions In this set of data when [A] doubles the rate quadruples. Rate is directly proportional to [A]2 Second order Rate = k [A]2  Second Order reactions Rate = k[A]2 Proportional to square of [reactant] [Reactant] decreases with time Not linear – slope becomes less steep Reaction slows down as reaction progresses Rate decreases  Pseudo-order reaction The reactions which appear to be higher order but follow lower order kinetics are called pseudo-order reactions. In case of elementary reactions (which complete in one step), the order and molecularity are identical. Consider a general reaction. A + B → Products in which the reactant B is present in a large excess. Since it is elementary, its rate law can be written as Rate = K[A][B] As B is present in large excess, its concentration remains practically constant during the course of the reaction. Thus, the rate law can be written as Rate = K’[A] Where the new rate constant K’=K[B]. Thus, the actual order of the reaction is second order but in practice it is of first order. Therefore, the reaction is said to be pseudo-first order.  Pseudo-order reaction Example: a. Hydrolysis of an ester: CH3COOC2H5 + H2O(Large excess) → CH3COOH + C2H5 OH The rate law for the reaction can be written as Rate =K[CH3COOC2H5][H2O] Since water is present in large excess, its concentration remains practically constant during the course of the reaction. Thus, the above rate law can be written as Rate = K’[CH3COOC2H5] The reaction is actually second order but in practice it follows first- order kinetics. Thus, it is a pseudo-first order reaction Determining Reaction Order (The Integrated Rate Law)  Zero-Order Integrated Rate Law A → products Rate = k (differential rate law) i.e – D[A]/Dt = k [A]t = – kt + [A]0 (integrated rate law) Using y = mx + b Slope = – k Y intercept = [A]0 [Reactant] decreases linearly with time  First-Order Integrated Rate Law A → products Rate = k[A] (differential rate law) i.e – D[A]/Dt = k[A] ln [A] = – kt + ln [A] t 0 [A] t (integrated rate ln  kt law) [A] 0 y = mx + b Slope = – k Y intercept = ln [A] 0 [Reactant] decreases with time Not linear – slope becomes less steep Reaction slows down as reaction progresses Rate decreases  Second-Order Integrated Rate Law A → products Rate = k[A]2 (differential rate law) i.e – D[A]/Dt = k[A]2 1 1  kt  (integrated rate law)[A] t [A] 0 y = mx + b Slope = k Y intercept = 1/[A]0 Determination of Reaction Order Other Methods  The Half-Life of a Reaction The half-life (t1/2)of a reaction is the time required for the concentration of a reactant to fall to one-half of its initial value. If initial concentration = 1.0 M and the half-life is 100 seconds, then the concentration will fall to 0.50 M in 100s. The half-life expression defines the dependence of half life on rate constant and initial concentration Is different for different reaction orders  Zero-Order Reaction Half-Life [A] t – kt  [A] 0 at t t1/2 [A]t 1/2 [A] 0 1/2[A] 0 – kt1/2  [A] 0 [A] 0 t1/2  2k Zero-order half-life varies and depends (directly) on initial concentration  First-Order Reaction Half-Life [A] t ln  kt [A] 0 at t t 1/2 [A] t 1/2 [A] 0 1/2[A] 0 ln ln 1/2  kt 1/2 [A] 0  0.693  kt 1/2 0.693 t1/2  k First-order half-life is constant and independent of concentration Second -Order Reaction Half-Life 1 1  kt  [A] t [A] 0 at t t1/2 [A] t 1/2 [A] 0 1 1  kt1/2  1/2[A] 0 [A] 0 1 1 kt1/2   1/2[A] 0 [A] 0 2 1 kt1/2   [A] 0 [A] 0 1 t1/2  k[A] 0 Second -order half-life varies and depends (inversely) on initial concentration. Summarizing Basic Kinetic Relationships Reaction order and rate law determined by experiment Rate law (differential) relates rate of reaction to concentration Integrated rate law relates concentration to time Half-life of first order reaction is independent of initial concentration Complex Reactions  Molecularity of a Complex Reaction Most chemical reactions are complex reactions. These occur in a series of steps. Each step is an elementary reaction. The stepwise sequence of elementary reactions that convert reactants to products is called the mechanism of the reaction. In any mechanism, some of the steps will be fast, others will be slow. Thus, the slowest step is the rate determining step of the reaction.  Complex Reactions A single reaction pathway is not always involved, the overall order, being the result of several reactions. There are three basic types of complex behaviour: Many reactions cannot be expressed by simple zero-, first-, and second or third- order equations. These are reactions involving simultaneous breakdown by more than one route or by a sequence of reaction steps They involve more than one-step or elementary reactions and accordingly are known as complex reactions. There are three basic types of complex behaviour: parallel consecutive (series) reversible  Complex Reactions -Parallel Consider the reaction Here reactant A form a mixture of products, it undergoes one of two irreversible first order reactions to form either product B or C Usually only one of the products is desirable, the others being byproducts. (Yield of B/Yield of C) = k1 / k2 Parallel reactions involve two or more simultaneous drug degradation pathways. Values of the rate constants k1 and k2 for each route may be evaluated separately by determining experimentally the overall rate constant, kexp, and also the ratio R of the concentration of products formed by each reaction from R =[A]/ [B] = k 1/k2. The rate constants can then be calculated from k1 = kexp (R/(R + 1)) and k2 = k1 /R Parallel reactions are common in drug systems General acid–base catalysis belongs to this class of reactions. At 35 ° C, The decomposition of prednisolone was found to involve parallel pseudo–first-order reactions with the appearance of acidic and neutral steroidal products:  An important parallel reaction in industry occurs in the production of ethylene oxide, a reagent in many chemical processes and also a major component in explosives. Ethylene oxide is formed through the partial oxidation of ethylene k1 2C H + O 2C2H4O 2 4 2 However, ethylene can also undergo a combustion reaction k2 C H +3O 2CO2 +2H2O 2 4 2 To select for the first reaction ,the oxidation of ethylene takes place in the presence of a silver catalyst which increases k1 compared to k2. The graph displays the concentration profiles for species A,B and C in parallel reaction in which k1 is > k2 A – solid line B –dashed line C-dotted line  Complex Reactions - Consecutive Consecutive (series)reactions in which a drug decomposes to an intermediate, which is transformed into the final product. This is also a first order irreversible reaction Consecutive reactions are common in radioactive series in which a parent isotope decays by a first order process into a daughter isotope and so on through a chain of disintegrations. Oftentimes ,the intermediate product B is the desired product  In the oxidation of ethylene into ethylene oxide ,another reaction can occur in which ethylene oxide ethylene oxide can decompose into carbon dioxide and water. k3 2C2H4 O + 5/2 O2 2CO2 + 2H2O Thus ,in the limiting case when k2 ˃ k1, the reaction can approximated as A C and the apparent rate follows 1st order kinetics A – solid line B –dashed line C- dotted line  Complex Reactions - Reversible A B+C The simplest reversible reaction is one in which both the forward and the reverse steps are first-order processes. Here the product reforms as the reactants: there are two reactions occurring simultaneously: first-order decomposition of A, rate constant k1 and second-order formation of A from B and C. The rate constant is often written as k -1.