King Saud University College of Pharmacy Department of Pharmaceutics LAB 6 Kinetics: order of reactions Rates and orders of reactions Rate: the rate of a chemical reaction of a process is the velocity with which the reaction occurs. Consider the following chemical reaction: drug A → drug B Rate constant: the order of a reaction refers to the way in which the concentration of drug influences the rate of a chemical reaction or process. Zero-Order Reactions When the reaction rate is independent of the concentration of the reacting substance. A = A₀ - k₀t Where: A₀: amount of drug at t=0. A: amount of drug at time t. k₀: zero-order rate constant, (mass/time). Zero-Order Reactions A A₀ slope = -k₀ Slope = ∆Y = y₂-y₁ ∆X x₂ - x₁ Time Graph of zero-order equation A = A₀ - k₀t First-Order Reactions When the reaction rate depends on the concentration of the reactant. -kt A = A₀ e Or log A = -kt/2.303 + log A₀ Where: A₀: amount of drug at t=0. A: amount of drug at time t. k: first-order rate constant, (time⁻¹). First-Order Reactions log A log A ₀ slope = -k/2.303 Time Graph of first-order equation log A = -kt/2.303 + log A₀ Half-Life Half-Life (t½): is the time required for the amount or concentration of a drug to decrease by one half. Zero-order half-life: t½ = 0.5 A₀/ k₀ First-order half-life: t½ = 0.693/ k Shelf life Shelf life (t½): is the time required for the amount or concentration of a drug to decrease to 90% of the initial concentration. Zero-order shelf life: t90 = 0.1 A₀/ k₀ First-order shelf life : t90 = 0.105/ k Practice Problems 1. Find the log of 35. 1.5441 2. Find the log of 0.028. - 1.553 3. Evaluate e – 1.3 0.2725 4. Find the value of k in the following expression: 25 = 50e –4k K= 0.173 Practice Problems 5. Plot the following data on both semilog graph paper and standard rectangular coordinates. a. b. c. d. e. Time (min) Drug A (mg) 10 96.0 20 89.0 40 73.0 60 57.0 90 34.0 120 10.0 130 2.5 Does the decrease in the amount of drug A appear to be a zeroorder or a first-order process? Does the amount of drug A extrapolate to zero on the x axis? What is the equation for the line produced on the graph? What is the rate constant k? What is the half-life t 1/2 t90? Home Work 6. Plot the following data on both semilog graph paper and standard rectangular coordinates. Time (min) Drug A (mg) 4 70.0 10 58.0 20 42.0 30 31.0 60 12.0 90 4.5 120 1.7 Answer questions a, b, c, d, and e as stated in Q5.