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

Atoms are extremely light, so chemists compare their masses on a scale. The scale is based on carbon-12. One unit on this scale is 1/12 of the mass of a carbon-12 atom.

Relative Atomic Mass (Ar)

Definition: The average mass of the atoms of an element compared to 1/12 of a carbon-12 atom. It is a weighted average because many elements have isotopes (atoms of the same element with different masses).

Key points:

• Read Ar from the Periodic Table (often a decimal, e.g. Cl ≈ 35.5).
• Ar has no units; it is a relative number.

Relative Molecular/Formula Mass (Mr)

Definition: The sum of the Ar values of all atoms in a substance.

For molecules (like CO₂) we say relative molecular mass. For ionic compounds (like NaCl) we say relative formula mass. Both are written Mr.

In symbols: $M_r = \sum A_r(\text{each atom})$.

How to calculate Mr

1. Write the formula clearly.
2. Count how many of each atom there are (use brackets and subscripts carefully).
3. Multiply each atom count by its Ar, then add them all.

Common mistakes to avoid

• Confusing Ar with mass number. Ar is an average from the Periodic Table; mass number is protons + neutrons in one atom.
• Forgetting brackets: multiply everything inside by the subscript outside, e.g. (NH₄)₂ = 2 N and 8 H.
• Ignoring decimals: use values like Cl = 35.5 when given.
• Diatomic elements (H₂, O₂, N₂, Cl₂) have two atoms per molecule.