Final answer:
The number of active molecules of acetaminophen in a single Tylenol pill with a dosage of 325 mg is approximately 1.29 x 10^21, calculated using the molar mass of acetaminophen and Avogadro's number.
Step-by-step explanation:
To find the number of active molecules of acetaminophen in a single Tylenol pill with a dosage of 325 mg, we need to utilize Avogadro's number and the molar mass of acetaminophen, C8H9NO2. First, we calculate the molar mass (molecular weight) of acetaminophen by adding the atomic masses of all the atoms present in the compound. The molecular mass of acetaminophen is 151.16 g/mol.
With the molar mass, you can convert milligrams to moles:
325 mg * (1 g / 1000 mg) * (1 mol / 151.16 g) = 0.00215 moles.
To find the number of molecules, multiply the moles by Avogadro's number (approximately 6.022 x 10^23 molecules/mol):
0.00215 moles * (6.022 x 10^23 molecules/mol) = 1.29473 x 10^21 molecules.
Therefore, there are approximately 1.29 x 10^21 active molecules of acetaminophen in a single Tylenol pill.