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Problem 2. An antibiotic drug is contained in a solid inner core and is surrounded by an outer coating that makes it palatable. The outer coating and the drug are dissolved at different rates in the stomach, owing to their differences in equilibrium solubilities. (a) If D₂ = 4 mm and D₁ = 3 mm, calculate the time necessary for the pill to dissolve completely. (b) Assuming 1st order kinetics (k₂ = 10 h¹) for the absorption of the dissolved drug (i.e. in solution in the stomach) into the bloodstream, plot the concentration in grams of the drug in the blood per gram of body weight as a function of time when the following three pills are taken simultaneously. Pill 1 Pill 2 Pill 3 D₂ (mm) 5 4 3.5 (c) How could you arrange a distribution of pill sizes so that the concentration in the blood was constant over a period (e.g. 3 hours) of time? Additional information: Amount of drug in inner core = 500 mg Solubility of outer layer at stomach conditions = 1.0 mg/cm³ Solubility of inner layer at stomach conditions = 0.4 mg/cm³ Volume of fluid in stomach = 1.2 L Typical body weight = 75 kg Sh = 2, DAB = 6 x 10-4 cm²/min D₁ (mm) 3 3 3

Problem 2. An antibiotic drug is contained in a solid inner core and is surrounded by an outer coating that makes it palatable. The outer coating and the drug are dissolved at different rates in the stomach, owing to their differences in equilibrium solubilities. (a) If D₂ = 4 mm and D₁ = 3 mm, calculate the time necessary for the pill to dissolve completely. (b) Assuming 1st order kinetics (k₂ = 10 h¹) for the absorption of the dissolved drug (i.e. in solution in the stomach) into the bloodstream, plot the concentration in grams of the drug in the blood per gram of body weight as a function of time when the following three pills are taken simultaneously. Pill 1 Pill 2 Pill 3 D₂ (mm) 5 4 3.5 (c) How could you arrange a distribution of pill sizes so that the concentration in the blood was constant over a period (e.g. 3 hours) of time? Additional information: Amount of drug in inner core = 500 mg Solubility of outer layer at stomach conditions = 1.0 mg/cm³ Solubility of inner layer at stomach conditions = 0.4 mg/cm³ Volume of fluid in stomach = 1.2 L Typical body weight = 75 kg Sh = 2, DAB = 6 x 10-4 cm²/min D₁ (mm) 3 3 3

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
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Problem 2. An antibiotic drug is contained in a solid inner core and is surrounded by an outer coating that makes it palatable. The outer coating and the drug are dissolved at different rates in the stomach, owing to their differences in equilibrium solubilities. (a) If D₂ = 4 mm and D₁ = 3 mm, calculate the time necessary for the pill to dissolve completely. (b) Assuming 1st order kinetics (kA = 10 h¹) for the absorption of the dissolved drug (i.e. in solution in the stomach) into the bloodstream, plot the concentration in grams of the drug in the blood per gram of body weight as a function of time when the following three pills are taken simultaneously. Pill 1 Pill 2 Pill 3 D₂ (mm) 5 4 3.5 (c) How could you arrange a distribution of pill sizes so that the concentration in the blood was constant over a period (e.g. 3 hours) of time? Additional information: Amount of drug in inner core = 500 mg Solubility of outer layer at stomach conditions = 1.0 mg/cm³ Solubility of inner layer at stomach conditions = 0.4 mg/cm³ Volume of fluid in stomach = 1.2 L Typical body weight = 75 kg Sh 2, DAB 6 x 10-4 cm²/min = D₁ (mm) 3 3 3
Transcribed Image Text:Problem 2. An antibiotic drug is contained in a solid inner core and is surrounded by an outer coating that makes it palatable. The outer coating and the drug are dissolved at different rates in the stomach, owing to their differences in equilibrium solubilities. (a) If D₂ = 4 mm and D₁ = 3 mm, calculate the time necessary for the pill to dissolve completely. (b) Assuming 1st order kinetics (kA = 10 h¹) for the absorption of the dissolved drug (i.e. in solution in the stomach) into the bloodstream, plot the concentration in grams of the drug in the blood per gram of body weight as a function of time when the following three pills are taken simultaneously. Pill 1 Pill 2 Pill 3 D₂ (mm) 5 4 3.5 (c) How could you arrange a distribution of pill sizes so that the concentration in the blood was constant over a period (e.g. 3 hours) of time? Additional information: Amount of drug in inner core = 500 mg Solubility of outer layer at stomach conditions = 1.0 mg/cm³ Solubility of inner layer at stomach conditions = 0.4 mg/cm³ Volume of fluid in stomach = 1.2 L Typical body weight = 75 kg Sh 2, DAB 6 x 10-4 cm²/min = D₁ (mm) 3 3 3
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