Question

The therapeutic concentration—the concentration needed to be effective—of acetaminophen (C₈H₉NO₂, molar mass 151.2 g/mol) is 10-20 μg/mL. Assume that the density of blood is 1.0 g/mL.

If the concentration of acetaminophen in the blood was measured at 17 ppm, is this concentration in the therapeutic range?

Answer 1

A concentration of 17 ppm of acetaminophen in blood is within the therapeutic range of 10–20 µg/mL. To find the number of active molecules in a 325 mg Tylenol pill, one needs to use Avogadro's number and the molar mass of acetaminophen.

Step-by-step explanation:

The student is asking whether a concentration of acetaminophen of 17 parts per million (ppm) in the blood falls within the therapeutic range of 10-20 µg/mL. To answer this, it's important to understand that 1 ppm is equivalent to 1 µg/mL assuming a blood density of 1.0 g/mL. Therefore, a concentration of 17 ppm is the same as 17 µg/mL. Given that the therapeutic range is 10-20 µg/mL, a concentration of 17 µg/mL is indeed within the therapeutic range.

To calculate the number of active molecules of acetaminophen in a 325 mg pill, we use Avogadro's number (6.022 × 1023 molecules/mol) and the molar mass of acetaminophen, which is 151.2 g/mol. We convert 325 mg to grams, getting 0.325 g, and then use the following calculation:

Number of molecules = (0.325 g / 151.2 g/mol) × (6.022 × 1023 molecules/mol)

This calculation would yield the number of acetaminophen molecules in one Tylenol pill. The same principle of stoichiometry applies to calculations involving any drug's dosage and its molecular content. Keeping within therapeutic ranges is crucial for safety and effectiveness when using medications like acetaminophen. It's particularly important to avoid overdosing, as this can lead to liver damage and other severe health complications.

Answer 2

A blood acetaminophen concentration of 17 ppm is equivalent to 17 µg/mL, which is within the therapeutic range of 10-20 µg/mL. The molecular mass of acetaminophen is 151.2 g/mol, which helps calculate the quantity in pills.

Step-by-step explanation:

To determine if the concentration of acetaminophen in the blood at 17 parts per million (ppm) is within the therapeutic range of 10-20 µg/mL, we must first understand the units and how to convert between them. Since 1 ppm is equivalent to 1 µg/mL, given that the density of blood is 1.0 g/mL, then a concentration of 17 ppm is the same as 17 µg/mL. This is within the therapeutic range of acetaminophen concentration in the blood, which confirms that the measured concentration is effective and safe.

The molecular mass of acetaminophen (C8H9NO2) is important for dosing calculations. The molecular mass, which is 151.2 g/mol, allows us to understand the amount of the substance in terms of its atoms and molecules. For instance, if a Tylenol pill contains 325 mg of acetaminophen, to find the number of active molecules in a single pill, you would have to convert the mass (mg) to moles using the molar mass and then use Avogadro's number to convert moles to molecules. It is crucial to administer the right amount and not exceed the recommended dosage as overdose can lead to liver damage and other severe health implications.