Problem 111 - Chemistry: The Central Science in SI Units, Global Edition

Question

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 (a) Is Ritalin an acid or a base? An electrolyte or a nonelectrolyte? (b) A tablet contains a \(10.0-\mathrm{mg}\) dose of Ritalin. Assuming all the drug ends up in the bloodstream, and the average man has a total blood volume of \(5.0 \mathrm{~L}\), calculate the initial molarity of Ritalin in a man's bloodstream. (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?

Step-by-Step Solution

Answer

(a) Ritalin is a weak base and an electrolyte. (b) The initial molarity of Ritalin in the bloodstream is \(\frac{10.0 \times(1/1000) \times (1/233)}{5.0}\) M. (c) The concentration of Ritalin in the blood after 6 hours is \(\frac{1}{4} \times \frac{10.0 \times(1/1000) \times (1/233)}{5.0}\) M.

Step 1: (a) Acid or base? Electrolyte or nonelectrolyte?

The structure of methylphenidate (Ritalin) is not given in the exercise, but it contains an amine group in its molecular structure. Amines can act as weak bases, so Ritalin is likely a weak base. It can form ions in solution by accepting a proton from water molecules, which means it is an electrolyte.

Step 2: (b) Calculate the initial molarity of Ritalin in the bloodstream

To compute the initial molarity, we first need to convert the mass of Ritalin in a tablet (10.0 mg) to moles. Then, we'll divide the number of moles by the blood volume (5.0 L) to obtain the molarity. The molecular weight of Ritalin (methylphenidate) is approximately 233 g/mol. Converting the mass of Ritalin in a tablet to moles: \[10.0\ \text{mg} \times \frac{1\ \text{g}}{1000\ \text{mg}} \times \frac{1\ \text{mol}}{233\ \text{g}}\] Now we divide the moles of Ritalin by the blood volume to obtain the initial molarity: \[Initial\ Molarity = \frac{10.0 \times(1/1000) \times (1/233)}{5.0}\]

Step 3: (c) Concentration of Ritalin in the blood after 6 hours

To find the concentration of Ritalin after six hours, we'll consider its half-life of three hours. This means that after three hours, the concentration is halved, and after another three hours, it's halved once again. So, after six hours, the concentration will be one-fourth (1/4) of its initial value. From part (b), we have the initial molarity: \[Initial\ Molarity = \frac{10.0 \times(1/1000) \times (1/233)}{5.0}\] After 6 hours, the concentration will be one-fourth of its initial value: \[Concentration\ after\ 6\ hours = \frac{1}{4} \times \frac{10.0 \times(1/1000) \times (1/233)}{5.0}\] Now we just need to perform the calculation to find the concentration of Ritalin in the blood after six hours.

Key Concepts

Methylphenidate

Methylphenidate, commonly known by its brand name Ritalin, is a medication widely used for treating attention-deficit/hyperactivity disorder (ADHD) in both children and adults. It works by increasing the levels of certain neurotransmitters in the brain, which can help improve focus and reduce impulsivity.
Methylphenidate's chemical structure includes an amine group, which plays a role in its behavior in the body. This amine group makes methylphenidate a weak base, as it can accept protons from water molecules in solution.
Understanding whether a substance is an acid or a base is important in chemistry because it affects how it interacts with other compounds.

• Acids donate protons (H+) in a solution, while bases accept protons.
• Methylphenidate, being a weak base, doesn't completely ionize in solution.

This weak ionization property mildly influences how it functions in the bloodstream, contributing to its classification as a weak base.

Half-life

Half-life is a concept that refers to the time it takes for the concentration of a substance to decrease to half of its initial value in a given environment. This concept is significant in pharmacology because it helps determine how long a drug stays active in the body and how frequently it needs to be administered.
For methylphenidate, the half-life is approximately 3 hours in the bloodstream.

• After 3 hours, only half of the initial concentration will remain.
• After another 3 hours or 6 hours in total, the concentration will be reduced to one-quarter of its original concentration.

By understanding the half-life, physicians can better manage dosing schedules to maintain appropriate therapeutic levels of the drug, ensuring its effectiveness while minimizing potential side effects.

Electrolytes

Electrolytes are substances that dissociate into ions when dissolved in water, thus conducting electricity. They play critical roles in numerous physiological processes, including nerve signal transmission and muscle function.
Methylphenidate acts as an electrolyte because it forms ions in solution, even though it is classified as a weak base. It does not dissociate completely, resulting in fewer free ions compared to strong electrolytes. However, it still contributes to the electrolyte balance in the bloodstream.

• Being a weak electrolyte, the extent to which methylphenidate dissociates is limited.
• The balance of electrolytes in the body is crucial for maintaining proper electrical function in tissues.

The drug's classification as an electrolyte is essential in understanding how it interacts within the body and how it impacts overall bodily functions.

Weak bases

Weak bases are a type of base that do not completely ionize in solution. As a result, they only partially accept protons, forming fewer ions compared to strong bases. This characteristic makes them less effective at changing the pH of a solution significantly.
Methylphenidate is considered a weak base due to the presence of an amine group in its structure.

• It partially ionizes, forming only a small number of charged particles.
• Its weak base nature affects its solubility and the way it interacts with other substances in the body.

Understanding weak bases helps explain why methylphenidate has a specific pharmacokinetic profile, influencing how quickly it can be absorbed into the bloodstream, its mode of action, and how it is ultimately eliminated from the body.