## Mass-to-Mole Conversions

#### Learning Objective

• Convert from grams to moles using a compound’s molar mass.

#### Key Points

• The mole is the universal measurement of quantity in chemistry. Although it is not possible to directly measure how many moles a substance contains, it is possible to first measure its mass and then convert that amount to moles.
• A substance’s molar mass is calculated by multiplying its relative atomic mass by the molar mass constant (1 g/mol).
• The molar mass constant can be used to convert mass to moles. By multiplying a given mass by the molar mass, the amount of moles of the substance can be calculated.

#### Terms

• molar massThe mass of a given substance (chemical element or chemical compound) divided by its amount (mol) of substance.
• moleIn the International System of Units, the base unit of the amount of substance; the amount of substance of a system that contains as many elementary entities as there are atoms in 12 g of carbon-12.

The mole is the universal measurement of quantity in chemistry. However, the measurements that researchers take every day provide answers not in moles but in more physically concrete units, such as grams or milliliters. Therefore, scientists need some way of comparing what can be physically measured to the amount of measurement they are interested in: moles.

## Molar Mass

Because scientists of the early 18th and 19th centuries could not determine the exact masses of the elements due to technology limitations, they instead assigned relative weights to each element. The relative atomic mass is a ratio between the average mass of an element and 1/12 of the mass of an atom of carbon-12. From this scale, hydrogen has an atomic weight of 1.0079 amu, and sodium has an atomic weight of 22.9997 amu.

From the relative atomic mass of each element, it is possible to determine each element’s molar mass by multiplying the molar mass constant (1 g/mol) by the atomic weight of that particular element. Multiplying by the molar mass constant ensures that the calculation is dimensionally correct because atomic weights are dimensionless. The molar mass value can be used as a conversion factor to facilitate mass-to-mole and mole-to-mass conversions.

## Converting Grams to Moles

The compound’s molar mass is necessary when converting from grams to moles.

• For a single element, the molar mass is equivalent to its atomic weight multiplied by the molar mass constant (1 g/mol).
• For a compound, the molar mass is the sum of the atomic weights of each element in the compound multiplied by the molar mass constant.

After the molar mass is determined, dimensional analysis can be used to convert from grams to moles.

## Example 1

For example, convert 18 grams of water to moles of water. The molar mass of water is 18 g/mol. Therefore:

$18 \ g \ H_2O \times \frac{1 \ mol}{18 \ g \ H_2O} = 1.0 \ mol \ H_2O$

## Example 2

If you have 34.5 g of NaCl, how many moles of NaCl do you have?

$34.5 \ g \ NaCl \cdot \frac {1 \ mol \ NaCl}{58.4 \ g\ NaCl} = 0.591 \ moles \ NaCl$