Drug Stability and Chemical Kinetics PDF

11/23/2024 Drug Stability and Chemical Kinetics Salma Essam, PhD Department of Pharmaceutics Faculty of Pharmacy Alexandria University 1 Temperature 2 1 ...

11/23/2024 Drug Stability and Chemical Kinetics Salma Essam, PhD Department of Pharmaceutics Faculty of Pharmacy Alexandria University 1 Temperature 2 1  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Collision theory It postulates that: A collision must occur between molecules for a reaction to occur A reaction between molecules doesn’t take place unless the molecules are of a certain energy (Ea, activation energy: this energy is needed first to break the bonds in the reactants and then to form new bonds in the products). 3 Chemical kinetics: Factors affecting reaction rate Temperature Collison theory Reaction rates are proportional to the number of collisions per unit time. As temperature increases, the number of collisions increases. So, the reaction rate increases with increasing temperature. Typically, a 10°C increase in temperature can produce a 2-5-fold increase in decay/degradation. However, better descriptions are given by the Arrhenius theory. 4 2  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Arrhenius straight-line equation: 𝐸𝑎ൗ log 𝑘 = log 𝐴 − 2.303𝑅 ∗ 𝑇 or 𝑘 𝐸𝑎 𝑇2 − 𝑇1 log( 2ൗ𝑘 ) = 1 2.303𝑅 ∗ 𝑇1 𝑇2 5 Chemical kinetics: Factors affecting reaction rate Temperature Arrhenius straight-line equation: 𝐸𝑎ൗ log 𝑘 = log 𝐴 − 2.303𝑅 ∗ 𝑇 Symbol & designation Value &/or unit Arrhenius factor/frequency factor A Same unit as rate constant (k) (Varies with different reactions) Energy of activation cal / mol Ea (Varies with different reactions) or joule / mol 6 3  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Arrhenius straight-line equation: 𝐸𝑎ൗ log 𝑘 = log 𝐴 − 2.303𝑅 ∗ 𝑇 Symbol & designation Value &/or unit 1.98 cal. mol-1. K-1 R Gas constant or 8.314 joule. mol-1. K-1 Kelvin (K = °C + 273) T Absolute temperature Ex. 25°C = 298 K 7 Chemical kinetics: Factors affecting reaction rate Temperature Arrhenius plot 𝐸𝑎ൗ 𝒍𝒐𝒈 𝒌 = log 𝐴 − 2.303𝑅 ∗ 𝑻 8 4  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Practice problems (1) The degradation of a certain drug follows first-order kinetics and has first-order degradation rate constants of 0.0001 per hour at 60°C and 0.0009 per hour at 80°C. Calculate Ea for this degradation reaction. 9 Chemical kinetics: Factors affecting reaction rate Temperature Practice problems (1) 𝒌 𝑬𝒂 𝑻𝟐 − 𝑻𝟏 𝒍𝒐𝒈( 𝟐ൗ𝒌 ) = 𝟏 𝟐. 𝟑𝟎𝟑𝑹 ∗ 𝑻𝟏 𝑻𝟐 𝑬𝒂 𝟑𝟓𝟑 − 𝟑𝟑𝟑 𝒍𝒐𝒈(𝟎. 𝟎𝟎𝟎𝟗ൗ𝟎. 𝟎𝟎𝟎𝟏) = (𝟐. 𝟑𝟎𝟑 ∗ 𝟏. 𝟗𝟖) ∗ (𝟑𝟓𝟑 ∗ 𝟑𝟑𝟑) Ea = 25,574 cal / mol = 25.574 kcal / mol 10 5  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Practice problems (2) An oral antibiotic solution (10 mg/ml) degrades with rate constants of 1.173 h-1 at 120°C and 4.86 h-1 at 140°C. Calculate its frequency factor at this temperature range. 11 Chemical kinetics: Factors affecting reaction rate Temperature Applications The effect of temperature on reaction (degradation) rates can be pharmaceutically applied in: Accelerated stability studies Q10 method for shelf-life estimation 12 6  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Applications: Q10 Method 𝑘 𝑇+10 𝑄10 = 𝑘𝑇 Q10 (temperature coefficient) is the factor by which the rate constant increases for a 10°C temperature increase. Q10 is calculated based on Ea of reactions. 13 Chemical kinetics: Factors affecting reaction rate Temperature Applications: Q10 Method 14 7  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Applications: Q10 Method To generalize the Q10 approach to estimate the effect of increasing or decreasing temperature by variable amounts, the following equation can be used: Δ𝑇ൗ 𝑘 𝑇2 𝑡90(𝑇1 ) 𝑄Δ𝑇 = 𝑄10 10 = = 𝑘 𝑇1 𝑡90(𝑇2 ) ΔT = T2 – T1 15 Chemical kinetics: Factors affecting reaction rate Temperature Applications: Q10 Method The Q10 method can be applied to estimate shelf life for a certain product that has been stored or is going to be stored under a different set of conditions (e.g., room temperature (25°C), cold room (15°C), and refrigerator (5°C)). 16 8  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Practice problems (3) An antibiotic solution has a shelf life of 48 hours in the refrigerator (5°C). What is its estimated shelf life at room temperature (25°C)? Given that Q10 value is 3. 17 Chemical kinetics: Factors affecting reaction rate Temperature Practice problems (3) 𝚫𝑻ൗ 𝒌𝑻𝟐 𝒕𝟗𝟎(𝑻𝟏 ) 𝑸𝚫𝑻 = 𝑸𝟏𝟎 𝟏𝟎 = = 𝒌𝑻𝟏 𝒕𝟗𝟎(𝑻𝟐 ) 𝟐𝟓−𝟓ൗ 𝟒𝟖 𝟑 𝟏𝟎 = 𝒕𝟗𝟎(𝑻𝟐 ) 𝟒𝟖 𝒕𝟗𝟎(𝑻𝟐 ) = 𝟐𝟓−𝟓ൗ = 𝟓. 𝟑𝟑 𝒉 𝟑 𝟏𝟎 18 9  11/23/2024 Chemical kinetics: Factors affecting reaction rate Temperature Practice problems (4) An ophthalmic solution has a shelf life of 6 hours at room temperature (25°C). What is the estimated shelf life in a refrigerator at 5°C? Given that Q10 value is 3. 19 pH 20 10  11/23/2024 Chemical kinetics: Factors affecting reaction rate pH Chemical degradation of some drugs is affected by the presence of acids or bases. Two types of pH-catalysis mechanisms: General acid/base catalysis (Buffer system) Specific acid/base catalysis 21 Chemical kinetics: Factors affecting reaction rate pH Specific acid/base catalysis Specific acid-catalysis/ Specific base-catalysis/ Specific hydrogen ion catalysis Specific hydroxyl ion catalysis (low pH) (high pH) It refers to a process in which the It refers to a process in which the reaction rate depends upon the reaction rate depends upon the specific acid. specific base. 22 11  11/23/2024 Chemical kinetics: Factors affecting reaction rate pH Specific acid/base catalysis Specific acid-catalysis/ Specific base-catalysis/ Specific hydrogen ion catalysis Specific hydroxyl ion catalysis (low pH) (high pH) The specific acid is defined as The specific base is defined as the protonated form of the solvent the deprotonated form of the (e.g., H3O+). solvent (e.g., OH-). Solvent catalysis may occur simultaneously with specific acid or base catalysis. 23 Chemical kinetics: Factors affecting reaction rate pH Specific acid/base catalysis The pH dependence of specific acid-base-catalyzed reactions can be expressed as: + − 𝑘𝑜𝑏𝑠 = 𝑘0 + 𝑘𝐻 𝐻 + 𝑘𝑂𝐻 𝑂𝐻 kobs (Time-1) is the observed reaction rate constant (experimentally determined) k0 (Time-1) Uncatalyzed/solvent-catalyzed rate constant kH (Conc-1. time-1) Specific acid-catalysis rate constant kOH (Conc-1. time-1) Specific base-catalysis rate constant 24 12  11/23/2024 Chemical kinetics: Factors affecting reaction rate pH Specific acid/base catalysis 𝑘𝑜𝑏𝑠 = 𝑘0 + 𝑘𝐻 𝐻 + + 𝑘𝑂𝐻 𝑂𝐻 − Slightly acidic pH Low pH 𝑘𝑜𝑏𝑠 = 𝑘0 + 𝑘𝐻 𝐻+ 𝑘𝑜𝑏𝑠 = 𝑘𝐻 𝐻+ Slightly alkaline pH High pH 𝑘𝑜𝑏𝑠 = 𝑘0 + 𝑘𝑂𝐻 𝑂𝐻− 𝑘𝑜𝑏𝑠 = 𝑘𝑂𝐻 𝑂𝐻− Low H+ or OH- concentration 𝑘𝑜𝑏𝑠 = 𝑘0 25 Chemical kinetics: Factors affecting reaction rate pH Determination of k0, kH and kOH 𝑘𝑜𝑏𝑠 = 𝑘0 + 𝑘𝐻 𝐻 + 𝑘𝑜𝑏𝑠 = 𝑘0 + 𝑘𝑂𝐻 𝑂𝐻 − 26 13  11/23/2024 Chemical kinetics: Factors affecting reaction rate pH Determination of pH of maximum stability: Rate-pH profile Acid-catalyzed hydrolysis Base-catalyzed hydrolysis 𝒌𝒐𝒃𝒔 = 𝒌𝑯 [𝑯+ ] 𝒌𝒐𝒃𝒔 = 𝒌𝑶𝑯 [𝑶𝑯− ] 𝑙𝑜𝑔𝑘𝑜𝑏𝑠 = 𝑙𝑜𝑔𝑘𝐻 + 𝑙𝑜𝑔[𝐻+ ] 𝑘𝑤 = [𝐻+ ][𝑂𝐻− ] 𝑙𝑜𝑔𝑘𝑜𝑏𝑠 = 𝑙𝑜𝑔𝑘𝐻 − (−𝑙𝑜𝑔 𝐻 + ) 𝑘𝑂𝐻 𝑘𝑤 𝑘𝑜𝑏𝑠 = ൘[𝐻]+ 𝒍𝒐𝒈𝒌𝒐𝒃𝒔 = 𝒍𝒐𝒈𝒌𝑯 − 𝒑[𝑯+ ] 𝑙𝑜𝑔𝑘𝑜𝑏𝑠 = 𝑙𝑜𝑔𝑘𝑂𝐻 𝑘𝑤 − 𝑙𝑜𝑔 𝐻+ 𝒍𝒐𝒈𝒌𝒐𝒃𝒔 = 𝒍𝒐𝒈𝒌𝑶𝑯 𝒌𝒘 + 𝒑𝑯 27 Chemical kinetics: Factors affecting reaction rate pH Determination of pH of maximum stability: Rate-pH profile pH of maximum stability: A: > 4.5 B: 4–8 C: 4.5 D: < 8.5 28 14  11/23/2024 Medium effect: ionic strength/ primary salt effect 29 Chemical kinetics: Factors affecting reaction rate Medium effect: ionic strength Ionic strength is the cumulative measure of both charge on the ion as well as its concentration in the solution. Electrolytes are often added to solution formulations, for example, as buffers to adjust solution pH or as salts to adjust tonicity. In addition to these additives, ionizable drugs can contribute to the ionic strength of the formulation. 30 15  11/23/2024 Chemical kinetics: Factors affecting reaction rate Medium effect: ionic strength Ionic strength (μ) can be calculated from: μ = ½ ∑(mz2) = ½ (mAzA2 + mBzB2 + …) where: m: molar concentration of ion z: charge number/valence of ion 31 Chemical kinetics: Factors affecting reaction rate Medium effect: ionic strength Example: For a monovalent drug (0.01 M) solution containing a 0.001 M of Ca2+ ion buffer, calculate the ionic strength of the solution. μ = ½ (mAzA2 + mBzB2 ) = ½ ((0.01)*(1)2) + ((0.001)*(2)2) = 0.007 M 32 16  11/23/2024 Chemical kinetics: Factors affecting reaction rate Medium effect: ionic strength The equation which describes the influence of electrolyte on the rate constant of interacting ionic species (primary salt effect) is the Brønsted–Bjerrum equation: log kobs = log k0 + 2A zA zB √μ where, k0 is the rate constant of zero ionic strength A is a constant for a given solvent and temperature zA and zB are the charge numbers of the two interacting ions μ is the ionic strength 33 Chemical kinetics: Factors affecting reaction rate Medium effect: ionic strength log kobs = log k0 + 2A zA zB √μ Examples: Similarly-charged ions: acid-catalyzed hydrolysis of a cationic drug. Oppositely-charged ions: base-catalyzed hydrolysis of a cationic drug. 34 17  11/23/2024 Chemical kinetics: Factors affecting reaction rate Medium effect: ionic strength Excess OH- Excess H+ 35 Oxygen and light 36 18  11/23/2024 Chemical kinetics: Factors affecting reaction rate Oxygen and light For drugs susceptible to oxidation, availability of oxygen from the atmosphere can be detrimental to stability. In addition, oxygen dissolved either in liquid formulations or in the adsorbed water layers in solid formulations can promote oxidative degradation. 37 Chemical kinetics: Factors affecting reaction rate Oxygen and light The susceptibility of a drug to the presence of oxygen can be tested by comparing its stability in ampoules purged with oxygen to that when it is stored under nitrogen. The susceptibility of a drug to light can readily be tested by comparing its stability when exposed to light to that when stored in the dark. 38 19  11/23/2024 Answers to practice problems 2) A= 7.9 * 1012 h-1 4) t90 (T2) = 54 h 4 39 20