L11/12 - Chemical Kinetics and Stability of Dosage Forms

• Importance of Drug Stability

  - instability can result in reduced solubility/bioavailability- affects storage requirements
• Degradation by hydrolysis(susceptible drugs/functional groups?)

  - eg ester, amide, imide, carbamate, lactam, lactone- can be acid/base catalysed- we can optimise using buffers or modify drug structure to prevent hydrolysis

  
• Degradation by oxidation


  - via radical mechanisms eg peroxy ROO*- catalysed by UV, heat- initiation, propagation, termination stepRH -> R* + HR + O2 -> ROO- add antioxidant (if drug susceptible to oxidation)- susceptible drugs/groups = steroids, sterols, C=C, Sulfur, ethers
• Other Degradation pathwaysRoutes of degradation

  Isomerisation - racemisationPhotochemical - need to use amber glass to block UV. (eg nitroglycerin)Polymerisation - occurs at high conc.Direct, Competitive, Sequential
• Zero order reaction


  Rate is independent of the concentration of the reactants.Conc changes have NO effect on rate
• First order reaction


  Rate is directly proportional to the concentration of one reactantconc. changes have a PROPORTIONAL effect on rate
• Second order reaction


  Rate is directly proportional to the product of the concentrations of two reactantsconc. changes have a SQUARED PROPORTIONAL effect on rate
• Shelf life (t95)


  The time period that a specific drug characteristic remains within a particular specification.Where drug remains at/above 95% of the label dose. Time at which 95% of API remains.Based on accumulation of degradation product/ % drug remaining
• Molecularity and rate equation

  The number of reactant molecules or ions involved in the rate-determining step of a reactionUnimolecular: rate = k [A]Bimolecular: rate = [A] [B] OR rate = [A]^2(etc)
• Law of Mass Action


  The rate of a chemical reaction is proportional to the product of the molar concentrations of the reactants equal to no. of molecules
• Order of reaction

  The sum of the powers to which the concentrations of the reactants are raised in the rate equationIndividual order of each reaction must be determined experimentally
• Rate constant (k)(what does it describe/predict? What are units?)

  - describes reaction profile for specific conditions- predicts reactivity- units dependent on order of reaction- always +ve
• Half-life (t½)


  The time required for the concentration of a reactant to decrease by half
• Zero order kinetics(t1/2 eqn, t95 eqn, what values do you plot? What does the graph look like? What's the integrated rate eqn? What's the gradient? What happens to rate over time?)


  - Rate is independent of the concentration of the reactants- Rate remains constant over time- Plot [A] over t gives straight line (gradient = -k)- shelf life is dependent on initial conc- increasing initial conc increases shelf lifet(1/2) = [A]0 / 2Kt95 = [A]0 / 20Kkinetic plot: [A] by timegradient = -kIntegrated rate equation: [A]t = [A]0 - kt

  
• First Order Kinetics(t1/2 eqn, t95 eqn, what values do you plot? What does the graph look like? What's the integrated rate eqn? What's the gradient? What happens to rate over time?)

  - Reaction rate decreases over time- plot ln[A] over t gives straight line (gradient = -k)- shelf life is independent of initial conc- increasing initial conc. has no effect on shelf lifet(1/2) = 0.693/kt95 = 0.0513/kkinetic plot: ln[A] by timegradient = -kIntegrated rate eqn: ln[A]t = ln[A]0 - kt

  
• Second Order Kinetics(t1/2 eqn, t95 eqn, what values do you plot? What does the graph look like? What's the integrated rate eqn? What's the gradient? What happens to rate over time?)


  - Reaction rate decreases over time- shelf life (t95) is dependent on initial conc.- plot 1/[A] over t gives straight line (gradient = k)- increasing initial conc decreases shelf lifet(1/2) = 1/ [A]0 kt(1/2) = 19 t95t95 = 1/ 19[A]0 kkinetic plot: 1/[A] by tgradient = kIntegrated rate eqn: 1/[A]t = 1/[A]0 + kt

  
• Factors affecting reaction rate

  concentrationpHtempcatalystsionic strength (eg electrolytes added to drug solution)excipients
• Solubility


  The ability of a substance to dissolve in a solvent
• Bioavailability


  The rate and extent to which a drug reaches circulation and is available to produce an effect
• Determining Reaction Order

  Graphical Method:plot all as first order. Should obtain plots as shown in imageShelf life method:- based on relationship between [A]0, t95 and reaction order0 order: as [A]0 increases, t95 increases1st order: [A]0 and t95 are independent2nd order: as [A]0 increases, t95 decreasesSubstitution Method- substitute degradation data into integrated rate equations to see which they fit with

  
• Effect of ionic strength on rate

  - electrolytes often added to drug solutions- inert species can affect rate of drug degradation
• Effect of pH on reaction rate(how can we protect drugs from acid/base catalysis? What's the eqn for specific acid/base catalysis?)(How can we optimise formulation? What do we plot to obtain this?)

  - hydrolysis is often caltalysed by H+/OH- ions- hydrolysis rate increases at high/low pH- add buffer to protect drugs from acid/base catalysisΔ[A] / Vt = (K + Kh[H+] + Koh[OH-]) x [A]where k = rate constant in waterKh/Koh = catalytic coefficients for specific acid/base catalysis- determine degradation rate constant over a range of pH values to optimise formulation- plot k vs [buffer]- plot pH vs k (at [buffer]=0) to determine when drug is most stable - at which pH the drug should be buffered.
• Effect of temp on reaction rate(free energy equation - The Van't Hoff isochore - what does it describe? What are its rearrangements?)

  - molecules must collide with correct Ea to react- Van't Hoff isochore describes the variation of equilibrium with temperatureΔG = ΔH - TΔSΔG = -RT lnKlnK = -ΔH/RT + ΔS/R OR lnK = ΔH-TΔS / -RT
• Arrhenius equation(What does it do? What are the rearrangments?)

  - Relates the rate constant of a reaction to the temperature and activation energy- related to fraction of molecules with sufficient Ea combined with steric effectsk = Ae ^-Ea/RTwhere k = rate constant (frequency of reactions) A = arrhenius factor/constant (frequency of collisions that could yield a reaction)e = exponential (inverse = ln)(e^-Ea/RT - probability of collision resulting in reaction) lnK = lnA - Ea/RTEa = (lnA-lnK) RTT = Ea / R (lnA-lnK)
• Arrhenius plots(what do you plot? What's the gradient? What's the y intercept?)

  - plot lnK against 1/T- y intercept = lnA- gradient = -Ea/RT

  
• Stress Testing

  - identifies degradation products/pathways- carried out on a single batch- tests for temp, humidity, oxidation, photolysisEg by determining rate constant (k) at various temps, rate of decomposition can be determines at 25degrees or lower using Arrhenius eqn
• Drug stability testing protocols(What do they determine? What do we need to define?)

  - determine how and how long a drug should be stored- temp and humidity for storage- storage time- suitable light conditions for storage- no. of batches to be sampled- no. of replicates within each batch
• Accelerated stability testing

  - exaggerated conditions of temperature, humidity, light and other factors- can estimate use by dates in a few weeks- assumes reaction mechanism is constant over experimental range and extrapolation