Final answer:
The number of active molecules of acetaminophen in a single Tylenol pill, which contains 325 mg of the active ingredient, is calculated to be approximately 1.29×1021 molecules using the molecular mass and Avogadro's number.
Step-by-step explanation:
Finding the Number of Active Molecules in a Tylenol Pill
To find the number of active molecules of acetaminophen in a Tylenol pill, we first need to know the molecular mass of acetaminophen, which is comprised of carbon (C), hydrogen (H), nitrogen (N), and oxygen (O). The molecular formula for acetaminophen is C8H9NO2. We use the atomic masses of these elements to calculate the molecular mass.
The molecular mass of acetaminophen is:
(8 × atomic mass of Carbon) + (9 × atomic mass of Hydrogen) + (1 × atomic mass of Nitrogen) + (2 × atomic mass of Oxygen)
(8 × 12.01 amu) + (9 × 1.01 amu) + (14.01 amu) + (2 × 16.00 amu) = 151.17 amu
Next, using Avogadro's number, which is 6.022×1023 molecules/mol, we can find the number of molecules by first converting milligrams to grams, then using molar mass to find moles, and finally multiplying by Avogadro's number:
Convert 325 mg to grams: 325 mg × (1 g/1000 mg) = 0.325 g
Calculate moles of acetaminophen: 0.325 g / 151.17 g/mol
Moles of acetaminophen = 2.15×10-3 mol
Number of molecules = 2.15×10-3 mol × 6.022×1023 molecules/mol
Number of molecules in one Tylenol pill = 1.29×1021 molecules
It is critical to remember that when using acetaminophen or any medication, following the recommended dosage is necessary due to potential risks such as liver damage. This warning emphasizes the importance of precision in pharmaceutical calculations for safety and efficacy.