Question 3.7: (a) Determine the number of water molecules and the numbers ...
(a) Determine the number of water molecules and the numbers of H and O atoms in 3.26 g of water.
(b) Determine the mass of 7.92 × 1019 carbon dioxide molecules.
Strategy Use molar mass and Avogadro’s number to convert from mass to molecules, and vice versa. Use the molecular formula of water to determine the numbers of H and O atoms.
Setup (a) Starting with mass (3.26 g of water), we use molar mass (18.02 g/mol) to convert to moles of water. From moles, we use Avogadro’s number to convert to number of water molecules. In part (b), we reverse the process in part (a) to go from number of molecules to mass of carbon dioxide.
(a) 3.26 \cancel{g H_{2}O} × \frac{1 \cancel{mol H_{2}O}}{18.02 \cancel{g H_{2}O}} × \frac{6.022 × 10^{23} H_{2}O molecules}{1 \cancel{mol H_{2}O}} = 1.09 × 10^{23} H_{2}O molecules
Using the molecular formula, we can determine the number of H and O atoms in 3.26 g of H2O as follows:
1.09 × 10^{23} \cancel{H_{2}O molecules} × \frac{2 H atoms}{1 \cancel{H_{2}O molecules}} = 2.18 × 10^{23} H atoms
1.09 × 10^{23} \cancel{H_{2}O molecules} × \frac{1 O atoms}{1 \cancel{H_{2}O molecules}} = 1.09 × 10^{23} O atoms
(b) 7.92 × 10^{19} \cancel{CO_{2} molecules} × \frac{1 \cancel{mol CO_{2}}}{6.022 × 10^{23} \cancel{CO_{2} molecules}} × \frac{44.01 g CO_{2}}{1 \cancel{mol CO_{2}}} = 5.79 × 10^{-3} g CO_{2}