Molar Mass

A dozen eggs has a different mass than a dozen oranges. Similarly, a mole of carbon has a different mass than a mole of sulfur, as shown in Figure 6. The mass of one mole of a substance is called a molar mass. For an element, the molar mass is the same as its atomic mass expressed in grams. For example, the atomic mass of carbon is 12.0 amu, so the molar mass of carbon is 12.0 grams.

For a compound, you can calculate the molar mass by adding up the atomic masses of its component atoms, and then expressing this sum in grams. A carbon dioxide molecule is composed of one carbon atom (12.0 amu) and two oxygen atoms $(2 \times 16.0 \mathrm{amu} = 32.0 \mathrm{amu})$. So carbon dioxide has a molar mass of 44.0 grams.

Mole-Mass Conversions

Once you know the molar mass of a substance, you can convert moles of that substance into mass, or a mass of that substance into moles. For either calculation, you need to express the molar mass as a conversion factor. For example, the molar mass of CO₂ is 44.0 grams, which means that one mole of CO₂ has a mass of 44.0 grams. This relationship yields the following conversion factors.

$\frac{44.0 \mathrm{g} {\mathrm{CO}}_2}{1 \mathrm{mol} {\mathrm{CO}}_2} \frac{1 \mathrm{mol} {\mathrm{CO}}_2}{44.0 \mathrm{g} {\mathrm{CO}}_2}$

Suppose you have 55.0 grams of CO₂. To calculate how many moles of CO₂ you have, multiply the mass by the conversion factor on the right.

$55.0 \mathrm{g} {\mathrm{CO}}_{2 }\times \frac{1 \mathrm{mol} {\mathrm{CO}}_2}{44.0 \mathrm{g} {\mathrm{CO}}_2} = 1.25 \mathrm{mol} {\mathrm{CO}}_2$

You can check your answer by using the conversion factor on the left.

$1.25 \mathrm{mol} {\mathrm{CO}}_{2 }\times \frac{44.0 \mathrm{g} {\mathrm{CO}}_2}{1 \mathrm{mol} {\mathrm{CO}}_2} = 55.0 \mathrm{g} {\mathrm{CO}}_2$