The mole and molar mass

Example 1: molar mass of glucose

Problem Find the molar mass of glucose, $\mathrm{C_6H_{12}O_6}$.

1. List each element and how many atoms of it are in one molecule: 6 C, 12 H, 6 O.
2. Multiply each count by its atomic mass.
   $$6(12.01) = 72.06 \qquad 12(1.008) = 12.096 \qquad 6(16.00) = 96.00$$
3. Add them up.
   $$M = 72.06 + 12.096 + 96.00 = 180.16\ \text{g/mol}$$

Answer 180.16 g/mol

Example 2: grams to moles

Problem How many moles of water are in 25.0 g of water?

1. Molar mass of water.
   $$M = 2(1.008) + 16.00 = 18.02\ \text{g/mol}$$
2. Divide the mass by the molar mass. Grams cancel, leaving moles.
   $$n = \frac{25.0\ \text{g}}{18.02\ \text{g/mol}} = 1.387\ \text{mol}$$
3. 25.0 g has 3 significant figures, so round to 3.

Answer 1.39 mol of water

Example 3: moles to molecules and atoms

Problem How many molecules are in 0.250 mol of $\mathrm{CO_2}$? How many oxygen atoms is that?

1. Multiply moles by Avogadro's number.
   $$N = 0.250\ \text{mol} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 1.5055 \times 10^{23}$$
2. Round to 3 significant figures: $1.51 \times 10^{23}$ molecules.
3. Each $\mathrm{CO_2}$ molecule has 2 oxygen atoms.
   $$2 \times 1.5055 \times 10^{23} = 3.011 \times 10^{23}$$

Answer $1.51 \times 10^{23}$ molecules of $\mathrm{CO_2}$, containing $3.01 \times 10^{23}$ oxygen atoms

Example 4: grams to atoms in two steps

Problem How many copper atoms are in a 10.0 g copper wire?

1. Grams to moles, using Cu = 63.55 g/mol.
   $$n = \frac{10.0\ \text{g}}{63.55\ \text{g/mol}} = 0.15736\ \text{mol}$$
2. Moles to atoms. Keep the unrounded moles so the last digit stays right.
   $$N = 0.15736\ \text{mol} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 9.476 \times 10^{22}$$
3. Round to 3 significant figures.

Answer $9.48 \times 10^{22}$ copper atoms