Theophylline is a pharmaceutical drug that is sometimes used to help with lung function. You observe a case where the initial lab results indicate that the concentration of theophylline in a patient's body decreased from 2.0×10^-3 M to 1.0×10^-3 M in 24 hours. In another 12 hours the drug concentration was found to be 5.0×10^-4 M. What is the value of the rate constant for the metabolism of this drug in the body?

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goldserval389Lv1

2 Jun 2021

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You are interested in studying the kinetics of decomposition of a new pharmaceutical drug you just synthesized in the lab. You conduct an experiment at 25âC that allows you to measure the concentration of the drug as a function of time. A plot of the natural logarithm of the concentration of the drug (expressed in M) vs. time in minutes is given in the figure. An analysis of these data using linear regression gives the equation written in the plot.

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4.2 what is the rate constant of the reaction? answer: 0.270 min-1

4.3 what is the half-life of the drug? answer: 2.57 min

4.4 what is the initial concentration of drug used in the experiment? answer: 6.07 Ã 10-3 M

4.5 what will the concentration of drug be if you continue your experiment and measure a point at t = 24 min? answer: 9.30 Ã 10-6 M

4.6 In an independent experiment you found that the activation energy of the reaction is 150 kJ/mol. What is the half-life of the drug at 10âC? answer: 63.6 min

âPolymer beads 800 micrometer in diameter are used for timed released drug delivery. Initial uniform concentration of the drug in the beads is 5 micrograms/cm^3 and the diffusion coefficient for the drug through the polymer is 1x10^-8 cm^2/s. The beads are ingested and pass through the GI tract in your body in a period of 12 hours. Assume the concentration of the drug is zero in the GI tract.

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b. What are the initial and boundary conditions for the equation in part a?

c. What is the drug concentration at the center of the bead after 4 hours?

d. How long does it take to release 50% of the drug?

e. What fraction of the drug is released during the 12-hour ingestion period?