Relative masses
Section: 2 Atoms, Molecules and Stoichiometry | Syllabus: Cambridge AS Level Chemistry (9701)
The Unified Atomic Mass Unit
Unified Atomic Mass Unit (u or amu) One twelfth of the mass of a carbon-12 atom. It is the standard unit used to express the masses of atoms and molecules on a relative scale.- The actual mass of one carbon-12 atom is approximately 1.993 × 10⁻²⁶ kg.
- Therefore 1 u = (1.993 × 10⁻²⁶) ÷ 12 ≈ 1.661 × 10⁻²⁷ kg.
- Carbon-12 was chosen as the reference standard because it is stable, abundant, and gives a convenient scale where most elements have near-integer atomic masses.
All relative masses are dimensionless (they have no units) because they are ratios - the mass of an atom compared to 1/12 the mass of a ¹²C atom.
Relative Atomic Mass, Aᵣ
Relative Atomic Mass, Aᵣ The weighted mean mass of an atom of an element, relative to 1/12 of the mass of a carbon-12 atom.- Aᵣ is a weighted mean - it accounts for the natural abundance of all isotopes of the element.
- It is not necessarily a whole number (e.g. Aᵣ of Cl = 35.5, reflecting the ~75:25 ratio of ³⁵Cl to ³⁷Cl).
Chlorine has two isotopes: ³⁵Cl (75.0% abundance) and ³⁷Cl (25.0% abundance).
Aᵣ = (35 × 75.0 + 37 × 25.0) ÷ 100 = (2625 + 925) ÷ 100 = 35.5
Relative Isotopic Mass
Relative Isotopic Mass The mass of an atom of a specific isotope relative to 1/12 of the mass of a carbon-12 atom.- Unlike Aᵣ, relative isotopic mass refers to one specific isotope, not a weighted average.
- For example, the relative isotopic mass of ³⁵Cl = 34.97 (approximately 35).
- Relative isotopic masses are close to whole numbers (the mass number) but not exactly, due to nuclear binding energy.
Relative Molecular Mass, Mᵣ
Relative Molecular Mass, Mᵣ The weighted mean mass of a molecule relative to 1/12 of the mass of a carbon-12 atom. It is the sum of the relative atomic masses of all atoms in the molecular formula. Calculating Mᵣ of Water, H₂OAᵣ(H) = 1, Aᵣ(O) = 16
Mᵣ(H₂O) = (2 × 1) + 16 = 18
Calculating Mᵣ of Sulfuric Acid, H₂SO₄Aᵣ(H) = 1, Aᵣ(S) = 32, Aᵣ(O) = 16
Mᵣ(H₂SO₄) = (2 × 1) + 32 + (4 × 16) = 2 + 32 + 64 = 98
Relative Formula Mass
Relative Formula Mass The sum of the relative atomic masses of all atoms in the empirical formula of an ionic compound. Used instead of relative molecular mass for ionic compounds, which do not exist as discrete molecules.- The calculation method is identical to Mᵣ - sum the Aᵣ values for all atoms in the formula.
- For ionic compounds (e.g. NaCl, MgSO₄), use the formula unit, not a molecular formula.
Aᵣ(Na) = 23, Aᵣ(Cl) = 35.5
Relative formula mass = 23 + 35.5 = 58.5
Relative Formula Mass of Calcium Nitrate, Ca(NO₃)₂Aᵣ(Ca) = 40, Aᵣ(N) = 14, Aᵣ(O) = 16
= 40 + 2 × (14 + 3 × 16) = 40 + 2 × 62 = 40 + 124 = 164
Figure 2.1: Summary of Relative Mass Terms
(Flowchart or table: Unified atomic mass unit (1/12 of ¹²C) → used to define → Relative Isotopic Mass (one isotope) → weighted average → Relative Atomic Mass Aᵣ (element). Separately: Aᵣ values summed → Relative Molecular Mass Mᵣ (covalent) or Relative Formula Mass (ionic).)
Exam TipAᵣ, Mᵣ and relative formula mass are all dimensionless ratios - never attach units to them. They should not be confused with molar mass (g mol⁻¹), which numerically has the same value but carries units.
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