Numeric Problems Involving First-Order Processes

Type 1

Assuming a drug is eliminated from plasma through a first order linear process and given the rate constant or half-life and the initial concentration of a drug in plasma, calculate the concentration at some time in the future.

Example 1:  A penicillin solution containing 300 units/ml has a half-life of 8 days in plasma.  What will the concentration be in 7 days?

Solution


Type 2

Assuming a drug is eliminated from plasma through a first order linear process and given the half-life or rate constant and the initial concentration of a drug in plasma, calculate the time required to reach a specified lower concentration.

Example 2:  A penicillin solution has a half-life of 6 days.  How long will it take for the concentration to drop to 70% of the initial concentration?

Solution


Type 3

Assuming a drug is eliminated from plasma through a first order process and given an initial concentration and the concentration of a drug in plasma after a specified elapsed time, calculate the rate constant or half-life.

Example 3:  A penicillin solution has an initial potency of 90mg/6ml.  After 1 month in a cold room, the concentration is found to be 80mg/6ml.  What is the half-life of the penicillin solution under the storage conditions?

Solution


B.6