Relative formula mass

Atoms have very little mass. So instead of using their actual masses in kilograms, their relative atomic masses are used.

The relative atomic mass of an element, symbol Ar, is the mean mass of its atoms compared to the mass of an atom of the carbon-12 isotope. The Ar values for elements are often stated in the periodic table. As Ar is a measure of the relative masses of atoms, it has no units.

The relative atomic masses of elements are proportional measures. For example, the Ar for helium is 4.0, and the Ar for carbon is 12.0. This means that carbon atoms have three times the mass of helium atoms.

Calculating relative formula mass

The relative formula mass, symbol Mr, is used for a substance made up of molecules. This is calculated by adding up the relative atomic masses of all the atoms in the formula for the substance.

To calculate the Mr for a substance:

  1. work out how many atoms of each element are in the chemical formula
  2. add together the Ar values for all the atoms of each element

For example, the formula for carbon dioxide is CO2. It has one carbon atom (relative atomic mass = 12.0) and two oxygen atoms (relative atomic mass = 16.0):

Mr of CO2 = 12.0 + 16.0 + 16.0 = 44.0

It could also be calculated this way:

Mr of CO2 = (1 × 12.0) + (2 × 16.0) = 12.0 + 32.0 = 44.0

Like Ar values, Mr values also have no units.

Relative formula masses of ionic compounds

Ionic compounds such as sodium chloride do not exist as molecules. However, their relative formula masses are calculated in the same way. The formulae used are their empirical formulae.

Question

Calculate the relative formula mass, Mr, of calcium hydroxide, Ca(OH)2.

(Relative atomic masses: Ca = 40.1, O = 16.0, H = 1.0)

Mr = 40.1 + (2 × 16.0) + (2 × 1.0)

= 40.1 + 32.0 + 2.0

= 74.1

It could also be calculated this way:

Mr = 40.1 + 2 × (16.0 + 1.0)

= 40.1 + 34.0 = 74.1

Masses in balanced chemical equations

Relative atomic masses and relative formula masses may be used to show that mass is conserved during a reaction.

1. Write down the balanced chemical equation

Zn + 2HCl \rightarrow ZnCl2 + H2

2. Write down the relative atomic masses and relative formula masses of the reactants and products. Relative atomic masses may be found in the periodic table.

Relative atomic mass of Zn = 65.4

Relative formula masses:

HCl = 1.0 + 35.5 = 36.5

ZnCl2 = 65.4 + (2 × 35.5) = 136.4

H2 = 2 × 1.0 = 2.0

3. Calculate the relative mass of the reactants and of the products. The large numbers in the equation show the ratio in which the substances react and are produced. Masses should be multiplied by these numbers.

Relative mass of reactants

= (Ar of Zn) + (2 × Mr of HCl)

= 65.4 + (2 × 36.5)

= 138.4

Relative mass of products

= (Mr of ZnCl2) + (Mr of H2)

= 136.4 + 2.0

= 138.4

4. Compare the relative masses of the reactants and products.

The relative masses of the reactants and products is the same. Mass is conserved.