Final Chemistry Notebook

Example: Converting between mass and moles
Knowing a substance’s molar mass is useful, because the molar mass acts as a conversion factor
between the mass of a sample and the number of moles in that sample (Equation 1). For converting
between the number of moles in a sample and the number of molecules in the sample, Avogadro’s
number acts as the conversion factor, as shown in Equation 2 below.
Equation 1
Sample mass (g) = Moles in sample (mol)
Sample's molar mass (g/mol)
Equation 2
Moles in sample (mol) x Avogadro's number (number/mol) = Number of sample molecules
To understand how molar mass and Avogadro’s number act as conversion factors, we can turn to an
example using a popular drink: How many CO2 molecules are in a standard bottle of carbonated
soda?
Thanks to molar mass and Avogadro’s number, figuring this out doesn’t require counting each
individual CO2 molecule! Instead, we can start by determining the mass of CO2 in this sample. In an
experiment, a scientist compared the mass of a standard 16-ounce (454 milliliters) bottle of soda
before it was opened, and then after it had been shaken and left open so that the CO2 fizzed out of
the liquid. The difference between the masses was 2.2 grams—the sample mass of CO2 (for this
example, we’re going to assume that all the CO2 has fizzled out). Before we can calculate the number
of CO2 molecules in 2.2 grams, we first have to calculate the number of moles in 2.2 grams of CO2
using molar mass as the conversion factor (see Equation 1 above):
Equation 3
Now that we’ve figured out that there are 0.050 moles in 2.2 grams of CO2, we can use Avogadro’s
number to calculate the number of CO2 molecules (see Equation 2 above):
Equation 4
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While scientists today commonly use the concept of the mole to interconvert number of particles and
mass of elements and compounds, the concept started with 19th-century chemists who were puzzling
out the nature of atoms, gas particles, and those particles’ relationship with gas volume.