Pharmaceutical Dosage Forms III - PPC 301 Lecture Notes (Fall 2024-2025)

# Pharmaceutical Dosage Forms III - PPC 301 ## Fall 2024-2025 ### Lecture (8) ## Introduction to Kinetics - 1st order Prepared by: **D. Basant A. Abou-Taleb, M.sc., PHD** Lecturer of Pharmaceutics & Ph. Technology Department Pharos University of Alexandria (PUA) ## Introduction - We are preparing a...

# Pharmaceutical Dosage Forms III - PPC 301 ## Fall 2024-2025 ### Lecture (8) ## Introduction to Kinetics - 1st order Prepared by: **D. Basant A. Abou-Taleb, M.sc., PHD** Lecturer of Pharmaceutics & Ph. Technology Department Pharos University of Alexandria (PUA) ## Introduction - We are preparing a pharmaceutical formulation. - **What are the most important aspects in any formulation?** 1. System 2. Efficacy 3. Stability ## Introduction - Some drugs in pharmaceutical products are susceptible to chemical degradation. - **Why do we care about drug degradation?** 1. Loss of drug efficacy 2. Changes in physical appearance (eg. Discoloration, malodour) 3. Toxicity ## Introduction 1. What are the classes of drugs that are susceptible to degradation? 2. For how long will the drug be stable? ... Expiry date/Shelf-life 3. How would you know the shelf-life? 1. 1st, you need to understand the degradation reaction. 2. 2nd, you need to know the "order of the reaction". How? 3. 3rd, you need to calculate a few parameters (constants). 4. Finally, you can calculate the half-life and shelf-life. 4. What are the factors affecting the degradation reaction? Why should you know them? ## Introduction - 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 manufacture. - **Stability of pharmaceutical product** may be also defined as the capability of a particular formulation in a specific container/closure system to remain within its **physical, chemical, microbiological therapeutic and toxicological specification.** ## Introduction cont. - Assurance that the packed product will be stable for its anticipated shelf life must come from an accumulation of valid data on the drug in its commercial package (**Stability testing**). - Pharmaceutical products are expected to meet their specifications for identifying purity, quality and strength throughout their defined **storage period** at specific storage condition. ## Introduction: Importance of stability studies - **Development of optimum formulation** through (pre-formulation studies) - Finding 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**. ## Types of stability | Type of Stability | Conditions Maintained Throughout the Shelf-Life of the Drug Product | |:---|:---| | Chemical | Each active ingredient retains its chemical integrity and labeled potency, within the specified limits. | | Physical | The original physical properties, including appearance, palatability, uniformity, dissolution, and suspendability are retained. | | Microbiological | Sterility or resistance to microbial growth is retained according to the specified requirements. Antimicrobial agents that are present retain effectiveness within the specified limits. | | Therapeutic | The therapeutic effect remains unchanged. | | Toxicological | No significant increase in toxicity occurs. | ## Half life (t1/2) - It is the time for drug to decompose to 50% of its original concentration. (to decrease by half) ## Shelf life (t0) - It is the time required for drug to lose 10% of its original concentration. - **OR** - It is the time at which the material decreased to 90% of its initial concentration. ## Expiry date - It is the date until which the drug product is valid to be used. (Fully potent and safe to patient) ## Reaction kinetics: - **Kinetics:** It is the study of how a system changes as function of time. - **Reaction kinetics:** It is the study of rate of chemical change and the way in which this rate is influenced by conditions of concentration of reactants and products, solvent, ionic strength and temperature. ## Chemical degradation (Reactions) - Hydrolysis - Oxidation - Isomerisation - Photochemical decomposition - Polymerization ## Reaction kinetics: Rate & order of reactions ### Fields of rate process: - **Stability & Incompatibility:** Here the rate process can lead to inactivation of the drug through decomposition or conversion into inactive or toxic form. - **Dissolution:** Here the main concern is the rapidity with which a solid dosage form is changed to molecular solution. - **Pharmacokinetics:** Concerns with the rate of drug absorption, distribution, metabolism and elimination. ## Reaction kinetics: Rate & order of reactions ### Importance of the rate process: - For **drug manufacturer** as he must demonstrate that his product is **stable** and can be stored for reasonable time **without** changing to **inactive** or **toxic** form. - The **pharmacist** must be aware of potential **instability** of the **drug** that he handles. - The **physician** and the **patient** must be assured that the prescribed **drug** will reach the site of action in **sufficient concentration**. ## Drug Reaction kinetics: II. Order of Reactions - **We have a new drug.** All we know is: the drug chemically degrades by ..... How long does it stay chemically stable on the shelf? - **Do an experiment.** Prepare a drug solution (of known concentration) Take samples at certain time & analyze the drug concentration at each time point (= remaining concentration) - **What is the reaction order?** Plot a graph: Remaining drug concentration versus Time Did you get a straight line or a curve? Slope? - **Calculate the shelf-life.** Which equation to use? We have three ## A memory refreshment - **The straight-line equation:** - Y=aX+ b - A(slope) = ΔΥ = Constant - ΔΧ - **Why is the straight line important for us?** Because her the slope is constant - (Slope is the constant that I can use to calculate shelf-life) ## Drug Reaction Kinetics - **What is the Reaction rate?** COOH OCOCH3 1 +1H2O COOH OH 1 +1CH3COOH acetylsalicylic acid salicylic acid acetic acid - Rate= - dc/dt - Rate a [ Acetylsalicylic acid]n - Rate = K[acetylsalicylic acid]n - Rate constant Order of reaction(0,1,2,..) ## Drug Reaction Kinetics - **Rate law:** - It is the mathematical expression showing how the rate of the reaction depends on the concentration of the reactants. - **Reaction order(n)** 1. It is determined experimentally 2. Showing how the reactants affect the reaction rate 3. Not depend on the number of molecules in the balanced equation ## Reaction kinetics: Rate & order of reactions ### I. Rate of the reaction: (Velocity or speed of reaction): - It the change in concentration of reactants over time and is given by: - + dc - dt - **This expression gives the increase (+) or decrease (-) in concentration (C) within a given time intervals (dt)** ## Reaction kinetics: Rate & order of reactions - **Notes:** 1. Rate of any reaction **depends on concentration**. 2. **By time** during decomposition reaction **concentration of reactants** (initial concentration) **decreases**. ## Reaction kinetics: I. Rate - **Example:** Formation of ethyl acetate from ethyl alcohol and acetic acid. - CH3COOH + C2H5OH = CH3COOC2H5 + H2O - **In this reaction the rate of forward reaction (Rf) may be calculated by measuring the concentration of acetic acid or ethanol as the reaction progresses.** - (RF) = - d(CH3COOH) = - d(C2H5OH) - dt dt ## Reaction kinetics: I. Rate - CH3COOH + C2H5OH = CH3COOC2H5 + H2O - **The rate of reverse reaction (Rr) may calculated by measuring the concentration of ethyl acetate or water as the reaction takes place.** - (R₁) = - d(CH3COOC2H5) = - d(H₂O) dt dt ## Reaction kinetics: I. Rate & Order of Reactions - **Example:** - 1 CH3COOC2H5 + 1 H2O = 1 CH3COOH + 1 C2H5OH - **Rate × (ethyl acetate)n** - **Rate = K(ethyl acetate)n** - **where;** - Rate = + dc - dt - K: Rate constant - n : Order of the reaction (0,1,2,...) ## Finally - ........... - ........... - ........... ## Reaction kinetics: II. Order of Reactions - **Classification of reactions according to the reaction order:** 1. Zero order reaction 2. Frist order reaction 3. Second order reactions 4. Pseudo Frist order reactions ## Zero-order Reaction (n=0) - **Definition:** The decomposition reaction proceeds at a constant rate & is independent of the concentration of the reactant. - **Reaction equation:** - Rate = dc = k[C]n - dt - **The straight-line equation is:** - Ct = C。- kt - **Where** - Ct → remaining concentration of the reactant at time t (unit?) - C. → initial concentration of the reactant (unit?) - k → reaction rate constant (unit?) - **Graphs:** For zero order reaction: - - dA = Ko - dt - Ko = Moles liter-1| second-1 - Ko = Moles/liter - second ## Zero-order Reaction (n=0) - **Half-life(to.5)** - t0.5 = 0.5℃。 - k - **Shelf-life (10.9)** - t0.9 = 0.1℃。 - k - **Example:** Photodegradation of cefotaxime under UV light (solution yellowing) ## Zero order reaction example 1 - Drug (X) decomposes following zero-order kinetics, with a rate constant 0.16mg/ml/year at Room Temperature. - If you prepared 1% W/V solution of Drug (X): 1. What is the remaining concentration after 18 months? 2. What is the drug shelf-life? ## Answer - ............ ## Frist-order Reaction (n=1) - **Definition:** The decomposition reaction proceeds at a rate directly proportional to the concentration of one reactant. (If conc. Is doubled, the rate will also double) - **Reaction equation:** - Rate = dc = k[C]n - dt - **The straight-line equation is:** - log Ct = log C。 – kt - 2.303 - **Where** - Ct → remaining concentration of the reactant at time t (unit?) - Co → initial concentration of the reactant (unit?) - k → reaction rate constant (unit?) ## Frist-order Reaction (n=1) - **Graphs:** ## Frist order reaction - **First Order Reactions** - Rate of the reaction depends on one of the reactants. - If the concentration is doubled the rate will also double. ## Frist order reaction - **First Order Reactions** - Rate of the reaction depends on one of the reactants. - Kt - Log Ct = Log Co 2.303 - 2.303 - K - t - Log Co - Ct - **where;** - Co: Initial concentration - Ct: Remaining concentration - K: Rate constant ## Frist order reaction - **Graphical representation** - t1/2 = 0.693/k - t90 = 0.105/k - **Example:** Polymerization of Ampicillin - At the beginning, ampicillin polymerizes at a faster rate. As the remaining concentration decreases, the rate of polymerization also decreases. ## Frist order reaction - **At t1/2:** - The remaining concentration is equal half the initial concentration. - 2.303 - Co - K = - t - LogCt , - K = - 2.303 - t - Log 1 - 2 - Co - K = - 2.303 - t - Log2 , - t1/2 - = - 2.303 - k - Log2 - **Therefore t1/2 = 0.693/ k** ## Frist order reaction - **At t90 :** - The remaining drug concentration is 90% of the initial concentration. - 2.303 - Co - K = - t - LogCt , - K = - 2.303 - t - Log 0.9Co - 2.303 - 1 - K = - t - L090.9 , - t90 - = - 2.303 - k - Log 1 - 0.9 - **Therefore t90 = 0.105/k** - **Unit of t1/2, t 90 are time** - **So, K unite= Time -1** ## Frist order reaction example 1 - **Decomposition of Hydrogen Peroxide** - The catalytic decomposition of hydrogen peroxide can be followed by measuring the volume of oxygen liberated in a gas burette. From such an experiment, it was found that the concentration of hydrogen peroxide remaining after 65 min, expressed as the volume in milliliters of gas evolved, was 9.60 from an initial concentration of 57.90. - (a) Calculate k - (b) How much hydrogen peroxide remained undecomposed after 25 min? ## Frist order reaction example 1 - **Answer** - ............ ## - “ - Let's Interact - " ## - **Thank you**