Structure 1.4.2 — Relative Atomic Mass \( A_r \) and Relative Formula Mass \( M_r \)

Relative Atomic Mass (\( A_r \))

The relative atomic mass \( A_r \) of an element is the weighted average mass of the atoms of an element, compared to 1/12 of the mass of a carbon-12 atom.

Key Features:

• \( A_r \) is dimensionless (has no units)
• Based on the carbon-12 scale where \( ^{12}\text{C} \) has a value of exactly 12.000
• Weighted average accounts for isotopic abundances
• Values are taken from the data booklet (to two decimal places)

Relative Formula Mass (\( M_r \))

The relative formula mass \( M_r \) of a compound is the sum of the relative atomic masses of all the atoms in the chemical formula.

• For molecules (covalent compounds), \( M_r \) is the relative molecular mass
• For ionic compounds, it’s referred to as relative formula mass (same symbol, \( M_r \))
• Also dimensionless (no units)

Important:

• Use values of \( A_r \) from the IB Chemistry Data Booklet (not periodic table values from other sources)
• Always round only at the final step of the calculation to maintain accuracy

Common \( A_r \) Values (from Data Booklet):

• H = 1.01
• C = 12.01
• O = 16.00
• Na = 22.99
• Cl = 35.45
• Mg = 24.31
• S = 32.07

Formula to Calculate \( M_r \):

Add the atomic masses (from the data booklet) of each atom in the formula:

\( M_r = \sum (A_r \times \text{number of atoms}) \)

Example: Sodium Hydrogen Carbonate is a common household chemical, otherwise known as bicarbonate of soda. Its molecular formula is NaHCO₃.