Relative Atomic Mass (Ar) and Relative Formula Mass (Mr)

Relative Atomic Mass (Ar)

Relative Atomic Mass, symbolised as Ar, is the weighted average mass of an atom of an element compared to 1/12th of the mass of a carbon-12 atom. It takes into account the different isotopes of an element and their relative abundances in nature.

Key points about Ar:

• It is a weighted average based on the abundance of each isotope.
• It has no units because it is a ratio compared to carbon-12.
• The value is found on the periodic table for each element.

For example, chlorine has two main isotopes: chlorine-35 and chlorine-37. The relative atomic mass of chlorine reflects the average mass of these isotopes weighted by how common each is.

If chlorine-35 makes up 75% of chlorine atoms and chlorine-37 makes up 25%, the Ar is calculated roughly as:

$$Ar = (0.75 \times 35) + (0.25 \times 37) = 26.25 + 9.25 = 35.5$$

Relative Formula Mass (Mr)

Relative Formula Mass, symbolised as Mr, is the sum of the relative atomic masses of all the atoms in a chemical formula of a compound or molecule.

Key points about Mr:

• It applies to compounds and molecules, including ionic compounds and covalent molecules.
• It is calculated by adding the Ar values of each atom in the formula.
• It has no units, as it is a relative measure.

For example, for water (H₂O), the Mr is calculated by adding the Ar of 2 hydrogen atoms and 1 oxygen atom.

Using approximate Ar values from the periodic table, Mr for water is:

Mr = (2 \times 1) + (1 \times 16) = 2 + 16 = 18

Calculating Ar and Mr

To calculate Ar or Mr, use the relative atomic masses from the periodic table. Add the Ar values for each atom in the formula to find Mr.

For example, the Ar of hydrogen (H) is approximately 1, and oxygen (O) is approximately 16.

So, for water (H₂O):

$$Mr = (2 \times Ar_{\text{H}}) + (1 \times Ar_{\text{O}}) = (2 \times 1) + (1 \times 16) = 2 + 16 = 18$$

This means one molecule of water has a relative formula mass of 18.

Another example is sodium chloride (NaCl). Sodium (Na) has an Ar of approximately 23, and chlorine (Cl) has an Ar of approximately 35.5.

$$Mr = 23 + 35.5 = 58.5$$