Ritalin is the trade name of a drug, methylphenidate, used to treat attention-deficit/hyperactivity disorder in young adults. The chemical structure of methylphenidate is (c) Ritalin has a half-life of 3 hours in the blood, which means that after 3 hours the concentration in the blood has decreased by half of its initial value. For the man in part (b), what is the concentration of Ritalin in his blood after 6 hours?

Verified step by step guidance

1. Identify that the problem involves the concept of half-life, which is the time required for a quantity to reduce to half its initial value.
2. Recognize that the half-life of Ritalin is given as 3 hours, meaning every 3 hours, the concentration of Ritalin in the blood is halved.
3. Determine that after 6 hours, which is two half-lives (since 6 hours / 3 hours per half-life = 2), the concentration will be halved twice.
4. Calculate the concentration after the first half-life (3 hours) by dividing the initial concentration by 2.
5. Calculate the concentration after the second half-life (6 hours) by dividing the concentration after the first half-life by 2 again.

Key Concepts

Half-life

Half-life is the time required for the concentration of a substance in the body to reduce to half its initial value. In pharmacology, understanding half-life is crucial for determining dosing schedules and predicting how long a drug will remain effective in the bloodstream. For Ritalin, with a half-life of 3 hours, the concentration decreases significantly over time, impacting therapeutic effects.

Exponential Decay

Exponential decay describes the process by which a quantity decreases at a rate proportional to its current value. In the context of drug concentration, this means that after each half-life, the remaining amount of the drug is halved. This concept is essential for calculating the concentration of Ritalin in the blood after multiple half-lives, as it follows a predictable pattern.

Concentration Calculation

Concentration calculation involves determining the amount of a substance in a given volume of solution, often expressed in units like mg/L or μg/mL. For Ritalin, knowing the initial concentration and applying the half-life allows for the calculation of remaining concentration after a specified time, which is vital for assessing drug levels in patients and ensuring effective treatment.