Final answer:
A Tylenol #3 pill contains 325 mg of acetaminophen, and when calculating the number of active molecules in such a pill, the molecular mass of acetaminophen is required. By using Avogadro's number and the conversion of mass from milligrams to grams, one can find there are approximately 1.29 × 1021 molecules of acetaminophen per pill.
Step-by-step explanation:
The Tylenol #3 being prescribed to the patient contains acetaminophen as an active ingredient, often combined with hydrocodone for more severe pain. When calculating the number of active molecules in a 325 mg Tylenol pill, it's essential first to find the molecular mass of acetaminophen (C8H9NO2), which needs to be calculated using atomic masses: carbon (C) = 12.01, hydrogen (H) = 1.01, nitrogen (N) = 14.01, and oxygen (O) = 16.00.
To obtain the molecular mass, sum the atomic masses based on the molecular formula: (8 × 12.01) + (9 × 1.01) + 14.01 + (2 × 16.00) = 151.17 amu for acetaminophen. We then convert the mass of the pill from milligrams to grams (325 mg = 0.325 g) and use Avogadro's number (6.022 × 1023 molecules/mol) to find the number of molecules: (0.325 g / 151.17 g/mol) × (6.022 × 1023 molecules/mol) yielding approximately 1.29 × 1021 active molecules of acetaminophen per pill.