Quick check from College Physics, 13.3 The Ideal Gas Law

The Ideal Gas Law: quick check

The active ingredient in a Tylenol pill is 325 mg of acetaminophen $(C_{8} H_{9} {NO}_{2})$ . Find the number of active molecules of acetaminophen in a single pill.

Answer it in your own words before you look.

Answer
We first need to calculate the molar mass (the mass of one mole) of acetaminophen. To do this, we need to multiply the number of atoms of each element by the element’s atomic mass.

$\begin{array}{l} (8 moles of carbon) (12 grams/mole) + (9 moles hydrogen) (1 gram/mole) \\ + (1 mole nitrogen) (14 grams/mole) + (2 moles oxygen) (16 grams/mole) = 151 g \end{array}$
13.30

Then we need to calculate the number of moles in 325 mg.

$(\frac{325 mg}{151 grams/mole}) (\frac{1 gram}{1000 mg}) = 2.15 \times 10^{- 3} moles$
13.31

Then use Avogadro’s number to calculate the number of molecules.

$N = (2.15 \times 10^{- 3} moles) (6.02 \times 10^{23} molecules/mole) = 1.30 \times 10^{21} molecules$
13.32

How did it go?