Chemical Kinetics and Stability - Physical Pharmacy II PDF

Physical Pharmacy II Lec 1 Chemical kinetics and stability The purpose of stability testing is to provide evidence on how the quality of a drug substance or drug product varies with time under the influence of a variety...

Physical Pharmacy II Lec 1 Chemical kinetics and stability The purpose of stability testing is to provide evidence on how the quality of a drug substance or drug product varies with time under the influence of a variety of environmental factors, such as temperature, humidity, and light, and to establish a retest period for the drug substance or a shelf life for the drug product and recommended storage conditions.. Chemical kinetics: - It is a part of theoretical mechanics in which the laws of the movement of the material bodies under the influence of furze are studied.. What are the benefits of studying chemical kinetics? Kinetics analyzes the speed (rate) of the process. ) (. Kinetics is usable in transitioning systems. Kinetics shows how to overcome the energy barrier in order the complete transformation to be performed. In physics the change in the location of a body in time is called speed. In chemistry, the change in the concentration of a reactant or product time unit is called rate, and is denoted by the symbol (R) or (r).. Factors that affect reaction rate are: 1. The physical state of the reactants, 2. The concentrations of the reactants, 3. The temperature at which the reaction occurs, 4. The presence of a catalyst, 5. Dielectric constant, pH, ionic strength, P a g e 1 | 13 Physical Pharmacy II Lec 1 6. Electric field of surface in adsorption. Reaction rate = Delta capital stands for change in Rates, Order, and Molecularity of Reactions where dc is the increase or decrease of concentration over an infinitesimal time interval dt. c / t) dc / dt dc dt. Here, below we show to you the both type of expressions (i.e. in the term of decrease in concentration of reactants over time interval at concentration vs time diagram. C initial rate = Conc. Mostly in instantaneous rate = / for A B M + (time), mostly in seconds P a g e 2 | 13 Physical Pharmacy II Lec 1 Below the other expression of rate (i.e. the increase in the concentration of products over time interval) at concentration time diagram. c rate =+ for A B + According to the law of mass action, the rate of a chemical reaction is proportional to the product of the molar concentration of the reactants each raised to a power usually equal to the number of molecules, a and b, of the substances A and B, respectively, undergoing reaction. In the reaction. A B aA+bB products the rate of the reaction will be Rate = 1 [ ] Rate law: (or rate equation) for chemical reaction is an equation that links the reaction rate with the concentration or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders.) For the hypothetic reaction; P a g e 3 | 13 Physical Pharmacy II Lec 1 A+B C+D Rate = so Rate = K [A] [B] this is the rate law Note: the concentrations of the reactants only is written k = (small) is the rate constant the power of each of [A] × [B], here is one (1) means the order of each reactant The order of the whole reaction is the summation of the both orders (i.e. 1+1 = 2) What is the rate constant (k)? The rate constant is a proportionality factor in the rate law of chemical kinetics that relates the molar concentration of reactants to reaction rate. It is also known as the reaction rate constant or reaction rate coefficient and is indicated in an equation by the letter K (small), for the elementary r×n A B K Rate = k [ A ] Is k being really constant? For an elementary reaction (single step reaction) it is constant, but it is affected by Temperature, or solvent, or a slight change in one of the reacting species, Rate constants derived from reactions consisting of a number of steps of different molecularity (complex reactions) are functions of the specific rate constants for the various steps. Any change in the nature of a step due to a modification in the reaction conditions or in the properties of the molecules taking part in this step could lead to a change in the value of the overall rate constant. P a g e 4 | 13 Physical Pharmacy II Lec 1 Units of the Basic Rate Constants The units of rate constant depend on the overall order of reaction. To arrive at units for the rate constants appearing in zero-, first-, and second-, and third- order rate laws, the equation expressing the law is rearranged to have the constant expressed in terms of the variables of the equation. Thus, for a zero- Order r×n: r× n: R=kk=R R = M s-1 ( M = mole / liter) so k=M s-1 s = seconds For first order reaction; R=k[A] k= For second order reaction; R=k[ ]2 K= For third order reaction R=k[A]3 k= There is other may be calculate the unites of k is applying a simple formula: P a g e 5 | 13 Physical Pharmacy II Lec 1 k= For example, for zero order; K= For 1- order; K= For 2- order; K= For 3- order; K= Order of reaction It is a number that relates the rate of a chemical reaction with the concentration of the reacting substances: the sum of all the exponents of the term expressing concentration of the molecule or atoms determining the rate reaction. For example, for the hypothetical reaction: A+B C+D Rate = k [ A ]n [ B ]m n is the order of reaction relating the reactant A m is the order of reaction relating the reactant B (n + m) is the overall order of the reaction. n or m may be a negative or positive value. It may be integer or a fraction number. P a g e 6 | 13 Physical Pharmacy II Lec 1 k [A] n [B] m n Am B (n + m) n m Experimentally it was found that the order of reaction could be varying between (-3 +3) or zero. what is meant by zero, +ve, or ve values for reactions for order by reactions? ve vv Because of order of a reaction is a measure how rate of a reaction depends on varying the concentrating of the reactants, so: +Ve order value means increasing the concentration of the reactants causes increase in the rate of the reaction. V -ve order value means increasing the concentration of the reactants causes decrease in the rate of the reaction. Zero order Value means increasing the concentration of the reactants does not cause in any change in the rate of the reaction. Molecularity Molecularity is the total number of molecules, atoms, or ions reacting in an elementary process. Note: molecularity cannot give complete detail about order of reaction especially those of several steps while kinetic study gives details. Elementary reactions (single step reactions) are classified according to their molecularity into: 1- Unimolecular reactions; (reactions with a single reactant molecule), like; 1- A C+D : P a g e 7 | 13 Physical Pharmacy II Lec 1 Br2 2Br : unimolecular r×ns O3(g) O2 (g) + O(g ) 2- Bimolecular reaction (reaction with two reactant molecules), like; A+B C+D O3 (g) + O(g) 2O2 (g) Bimolecular r×n H2 + I2 2HI 3- Termolecular reaction (reaction with three reactant molecules) 2 xy + Z Y2 Z + x2 Termolecular r×n 2CO2 + O2 2CO2 Molecularity may be equal to the under of the reaction or not. Examples are listed below for the bath cases: 1) N2O5(G) 2NO2(g) + O2(g) unimolecular n=1, 1st order 2) H2 + I2 catalyst 2HI Bimolecular n=2, 2nd order acid 3) CH3COOCH3 H+ CH3COOH + CH3OH Bimolecular st n=1, 1 order 4) H2 + D2 2HD Bimolecular n=1.5 Pseudo- order reaction (or Apparent- order reaction) when one of the reactants is present in large excess or does not affect the overall reaction and can be held constant, the reaction is called Pseudo or apparent order. The overall order of the reaction does not depend on the order of that substance. Pseudo Example: P a g e 8 | 13 Physical Pharmacy II Lec 1 A+B+C E+F Rate = k [ A ]n [ B ]n [ C ]l Reaction order = n + m + l If [ A ] is not changed during the reaction time intervals, so = Apparent rate constant The hydrolysis of esters by water in acidic media obeys pseudo- first order instead of 2nd- order. CH3COOCH3 + H2O H+ CH3COOH + CH3OH R = k [ CH3COOCH3 ] [ H2O ] 3COOCH3 2O ] present in large extent so it is held constant Many hydrolysis decomposition reactions of drug molecules are second-order, usually the amount of water present is in excess of what is needed for the reaction to proceed. In other words, the concentration of water is essentially constant throughout the reaction. In this case, the second-order reaction behaves like a firstorder reaction and is called an apparent or pseudo- first order. Half-Life: The half-life is the time required for half of the material to disappear; It is the time at which A has decreased to ½ A. A A. Shelf-Life: The shelf-life is the time required for 10% of the material to disappear, "it is the time at which A has decreased to 90% of its original concentration (i.e. 0.9 A). A Zero- order reactions The rate of reaction is apparently independent of the reactant concentration (rate does not vary with increasing or decreasing of reactant concentration. P a g e 9 | 13 Physical Pharmacy II Lec 1 Will on what depends the rate of reaction? It depends on: 1. Quantity of the light absorbed, 2. Amount of catalyst 3. surface area of the reactant. Zero-order reactions are not popular. It occurs in heterogeneous reactions, for example; 2NH3(G) Mo N2 + 3H2 2HI(g) Mo or A4 H2 + I2 CH3COCH3 HI CH3COCH2I + HCl K = M s-1 In pharmacy; Garret and Carper found that the loss in color of a multisulfa product (as measured by the decrease of spectrophotometric absorbance at wavelength of 500nm) followed a zero- order rate. Garret Carper Derivation y the Integrated form of Zero-order rate reaction For the r×n A B Rate = k [ A ]n Rate = n So - - =k -k dt [A] [A] =- [ A ] = -kt + [ A ] P a g e 10 | 13 Physical Pharmacy II Lec 1 Derivation of half-life equation [ A ] = -kt + [ A ] - P a g e 11 | 13 Physical Pharmacy II Lec 1 It is apparent from the above equation that half-life time in zero- order reaction is proportionally to the concentration of the starting the starting material ting +ve diagram given. [A] From the diagram we conclude; 1- The straight line of decrease means rate does not depends on [ A ] 1 1 1 2- (+2)1 > (+2)2 > (+2)3 1st half-life 2nd 3rd + 1 (+2)1 half -life half life Sample Exercise a) c) ½ decrease, ½ ½ Solution [ A ] = 1.5 M , [ A ] = 0.75 M a) [ A ] [ A ] = -kt -[ A ] + [ A ] = -kt [ A ] - [ A ] = kt 1.5M 0.75 M = K × 120 sec K= K = 0.00625 Ms-1 12 | 13 Physical Pharmacy II Lec 1 b) + ½ = +½= + ½ = 96 seconds Page 13 | 13