Kinetics, Reaction Rates and Drug Stability PDF

Kinetics, Reaction Rates and Drug Stability Introduction Kinetics Introduction comes form the Greek word kinesis meaning movement. Reaction kinetics is the “study of rate of chemical change and in which this rate is influenced the conditions of concentration of the reactants, produc...

Kinetics, Reaction Rates and Drug Stability Introduction Kinetics Introduction comes form the Greek word kinesis meaning movement. Reaction kinetics is the “study of rate of chemical change and in which this rate is influenced the conditions of concentration of the reactants, products, and other by chemical species which may be present, and by factors such as solvent, pressure, and temperature”. Introduction Factors affecting reaction rate: 1. Nature of reactants — major factor 2. Concentration of reactants 3. concentration of catalysts 4. Temperature Introduction One of the most common applications of kinetics in pharmaceutics is the study of the rates of drug degradation in pharmaceutical products and the determination of the proper shelf lives and storage conditions for these products. The stability of the active ingredient of a drug is a major criterion in the rational design and evaluation of drug dosage forms. Problems with stability can determine whether a given formulation is accepted or rejected. 1. Extensive chemical degradation of the active ingredient can cause substantial loss of the active ingredient from the dosage form. 2. Instability of the drug product can cause decreased bioavailability 3. Chemical degradation can produce a toxic product. Rates and Orders of Reactions: The rate of a reaction, or degradation rate, is the velocity with which the reaction occurs. The rate or speed of a reaction can be expressed as the ratio of change in concentration of a reactant (product) to a change in time. Rates and Orders of Reactions: The order of a reaction is the way in which the concentration of a drug or reactant in a chemical reaction affects the rate. The rate of a simple A—> B reaction can be written as Where a is called the order of the reaction Alpha is 1 in first order reactions, second and third order reactions are possible too Alpha could be 0 in case of a zero order reaction. In a more complex reaction A+B —> C the rate becomes: The overall order of the reaction is the sum of exponents (a+b) Rates and Orders of Reactions: The order with respect to one of the reactants is the exponent of that concentration term. The exponents a and b don't have a direct relation with the coefficients in the balanced chemical equation for a reaction. The value of the exponents as well as the overall order can only be determined from experiment (i.e. The order with respect to each reactant cannot be deduced from stoichiometric equation of the reaction). Rates and Orders of Reactions: K is the rate constant of the reaction. The reaction rate constant, k, is a numerical expression of the effect of the nature of reactants and temperature on reaction rate. Units of Rate Constants: Units of Rate Constants: Zero-Order Reactions: The rate law for a zero-order reaction is: The rate in such reactions is constant and independent of the concentrations of the reactants. Other factors, such as absorption of light in certain photochemical reactions, determine the rate. Zero-Order Reactions: In zero order reactions, the drug concentration changes with respect to time at a constant rate. By integrating the rate law between the initial concentration of the reactant (C) and the concentration at time t (C t). Zero-Order Reactions: Zero-Order Reactions: Integrating the rate law between the initial concentration of the product (C) and the concentration at time t (C t). Zero-Order Reactions: Zero-Order Reactions: The half life of a drug in a formulation is the time required for the amount (conc.) of the drug to drop to half its original value. Zero-Order Reactions: Shelf life: The time required for a drug to degrade to 90% of its original concentration (t90%) is also important. This time represents a reasonable limit of degradation for the active ingredient. The t90% can be calculated as: Note that t0.5 and t90 in zero-order reactions are concentration dependent. Zero-Order Reactions: First Order Reactions: Shelf life: The time required for a drug to degrade to 90% of its original concentration (t90%) is also important. This time represents a reasonable limit of degradation for the active ingredient. The t90% can be calculated as: Note that t0.5 and t90 in zero-order reactions are concentration dependent. First Order Reactions: The rate law for the first order reaction is: Integrating the equation between Co (concentration at t=0) and Ct (concentration at time t) gives: First Order Reactions: Converting to common log to the base 10 we get: The previous equations can be converted to exponential forms: The equations express the fact that in a first order reaction, the concentration decreases exponentially with time. In a first-order reaction, rate depends on the first power of a single reactant. First Order Reactions: First Order Reactions: First Order Reactions: First Order Reactions: First Order Reactions: First Order Reactions: Apparent zero-order reactions (suspension): Consider a first order degradation reaction of a drug in solution. The rate of degradation (decline in drug cone.) is proportional to the cone, of the drug: The rate changes with changing cone. Now consider a suspension where the solid drug is in equilibrium with the drug in solution, the concentration wouldn’t change because the solid drug will compensate for the decomposition and so the rate remains constant. As the drug decomposed in solution, more drug is released from the suspended particles so that the concentration is constant. This concentration is the drug’s equilibrium solubility in a particular solvent at a particular temperature (c). Apparent zero-order reactions (suspension): The rate in this case is called apparent zero order rate. The system changes to first-order once all suspended particles have changed to drug in solution. Apparent zero-order reactions (suspension): Apparent zero-order reactions (suspension): Apparent zero-order reactions (suspension): Influence of Temperature on Reaction Rates: Reaction rates are expected to be proportional to the number of collisions per unit time. As temperature increases, the number of collisions increases. Hence, the reaction rate is expected to increase with increasing temperature. Speed or rate of many reactions increase about two to three times with each 10° rise in temperature. An increase in temperature causes an increase in the reaction rate. This effect or relationship is expressed in the equation first suggested by Arrhenius Influence of Temperature on Reaction Rates: The effect of temperature on reaction rate is given by the Arrhenius Equation: By taking the log of both sides, the equation transforms into: In which: Ea is the energy of activation k is the specific reaction rate (cal/mol) A is a constant (Arrhenius or R is the gas constant (1.987 Frequency Factor) cal/deg.mol) T is the absolute temperature Influence of Temperature on Reaction Rates: Arrhenius constant (A) is related to the frequency of molecular collisions in the Collision Theory. The activation energy (Ea ) is the energy barrier that the reactants must surmount to react (energy threshold) or the energy which must be exceeded if the collision of two reactants is to lead to a reaction. As temperature increases, more molecules are activated, and the reaction rate increases; according to the Collision Theory. Influence of Temperature on Reaction Rates: How to determine A and Ea ? Cont. 2. The best estimation of the Arrhenius constant and activation energy is obtained by performing the reaction at three different temperatures at least (log k vs. 1IT). However, two temperatures may be enough to get this estimate. Influence of Temperature on Reaction Rates: Accelerated Stability Testing: Accelerated stability protocols have been developed to reduce the time required to determine the products shelf life at the storage conditions. The accelerated stability protocols depends on calculating the rate constant of the degradation reactions at elevated temperature (by plotting some function of concentration vs. time) and then plotting the log k vs. 1/T(in Kelvin). The rate at room temperature or storage temperature is then obtained by extrapolating the straight line. Accelerated Stability Testing: Accelerated Stability Testing: Limitations of accelerated stability testing based on elevated temperatures: Suitable only if the reaction rate is a thermal phenomenon Not suitable if the degradation depends on diffusion or is a photochemical reaction Not suitable if the degradation is caused by freezing, microbial growth or excessive shaking. Can not be used for products containing suspending or thickening agents that coagulate on heating (Methyl Cellulose). Not suitable for ointments and suppositories that melt at elevated temperature. Some emulsions have higher stability at elevated temperatures. Shelf life vs. expiry date Expiry date is the date after which the medicine should not be used. Example 14-4; Martin’s 6th ed. Co = 94 units/ml; from Arrhenius plot: at 25°C: k= 2.09 x 10'5 hr-1 Experiments showed that when drug falls to 45 units/ml it is not sufficiently potent for use and should be removed from the market. What expiration date should be assigned for this product? Catalysis A catalyst is a substance that influence the rate of the reaction without being altered chemically. A Negative Catalyst decreases the rate of the reaction. An inhibitor decreases the rate of the reaction; however, it is changed permanently during the reaction. Catalysis Catalysts usually act through one of two mechanisms: By combining with the reactant (substrate) to produce a complex, which then decomposes to regenerate the catalyst and yield the product. Through this the catalyst accelerates the rate of the reaction by changing the reaction mechanism and reducing the activation energy. By producing free radicals (CH3* ) which initiates fast chain reactions. Modes of Pharmaceutical Degradation Hydrolysis Hydrolysis of esters and amides is the most common example, these reactions are dependent on H+ and OH- ions as catalysts so to stabilize the formulation, the pH must be adjusted to match the minima in the stability-pH profile if possible. Oxidation Can be prevented by a variety of approaches including the manufacturing and packaging under inert conditions, addition of antioxidants (ascorbic acid, Na sulphite, metabisulphite and bisulphate), the use of chelating agents, reduction in storage temperature and formulation at optimum pH for stability. Modes of Pharmaceutical Degradation Photolysis Light energy can provide the necessary activation energy for the reaction to occur. Radiations of sufficient energy and proper frequency must be absorbed to activate drug molecule to undergo reactions. Photochemical reactions do not depend on temperature to activate the molecules. However, the initial photochemical reactions may be followed by thermal reactions.- Ergosterol conversion to Vit. D is an example of a biological photochemical reaction (photosynthesis). Light effect is not considered a type of catalysis. Furosemide and Nifedipine are examples of drug undergoing photodegradation.