Ar & Mr
Section: 3. Stoichiometry | Syllabus: Cambridge IGCSE Chemistry (0620)
Relative Atomic Mass (Ar)
Relative atomic mass (Ar) is the average mass of the isotopes of an element compared to 1/12th the mass of an atom of 12C.
- It is a ratio, so it has no units
- Found in the periodic table for each element
- It is a weighted average that accounts for an element's naturally occurring isotopes and their abundances - see Isotopes earlier in this course for how this average is calculated
| Element | Symbol | Ar |
|---|---|---|
| Hydrogen | H | 1 |
| Carbon | C | 12 |
| Nitrogen | N | 14 |
| Oxygen | O | 16 |
| Sodium | Na | 23 |
| Magnesium | Mg | 24 |
| Aluminium | Al | 27 |
| Sulfur | S | 32 |
| Chlorine | Cl | 35.5 |
| Calcium | Ca | 40 |
| Iron | Fe | 56 |
| Copper | Cu | 64 |
Most Ar values are whole numbers or close to them. Chlorine (35.5) is a common exception, since it has two abundant isotopes (Cl-35 and Cl-37) in roughly a 3:1 ratio.
The relative atomic mass (Ar) is shown above the element's symbol in each periodic table box
Relative Formula Mass (Mr)
Relative formula mass (Mr) is the sum of the relative atomic masses of all the atoms shown in a formula. For simple molecular compounds it is sometimes called relative molecular mass; the same calculation is used for ionic compounds.
- Symbol: Mr - also has no units
- Mr = sum of (Ar × number of atoms) for every element in the formula
- Watch out for brackets - the subscript outside multiplies everything inside
Worked Example: Simple Mr Calculation
- Question: calculate the relative formula mass of sulfuric acid, H₂SO₄. (Ar: H = 1, S = 32, O = 16) [1]
- Answer: Mr = (2 × 1) + 32 + (4 × 16) = 2 + 32 + 64 = 98 [1]
Worked Example: Mr with Brackets
- Question: a fertiliser compound has the formula Ca₃P₂O₈. Calculate its relative formula mass. (Ar: Ca = 40, P = 31, O = 16) [2]
- Answer: count the atoms directly from the subscripts: Ca = 3, P = 2, O = 8; contributions: Ca = 3 × 40 = 120, P = 2 × 31 = 62, O = 8 × 16 = 128; Mr = 120 + 62 + 128 = 310 [2]
More Mr Examples
| Compound | Formula | Calculation | Mr |
|---|---|---|---|
| Calcium hydroxide | Ca(OH)₂ | 40 + (2×16) + (2×1) | 74 |
| Aluminium sulfate | Al₂(SO₄)₃ | (2×27) + (3×32) + (12×16) | 342 |
| Calcium carbonate | CaCO₃ | 40 + 12 + (3×16) | 100 |
| Glucose | C₆H₁₂O₆ | (6×12) + (12×1) + (6×16) | 180 |
Percentage Composition
Percentage composition is the percentage by mass of a given element within a compound.
% of element = (Ar × number of atoms ÷ Mr) × 100
Worked Example: Percentage Composition
- Question: calculate the percentage by mass of oxygen in carbon dioxide, CO₂. (Ar: C = 12, O = 16) [2]
- Answer: Mr of CO₂ = 12 + (2×16) = 44 [1]; % O = (32 ÷ 44) × 100 = 72.7% [1]
As a check, the percentages of every element in a compound should always add up to 100%.
Common Mistakes
- ❌ Giving Aᵣ or Mᵣ a unit such as grams
- ✓ Ar and Mr are ratios and have no units; only when using Mr to state the mass of one mole (in grams) do units appear
- ❌ In Ca(OH)₂, counting only 1 oxygen and 1 hydrogen
- ✓ the subscript 2 outside the bracket multiplies everything inside - Ca(OH)₂ has 2 oxygen and 2 hydrogen atoms, plus 1 calcium
Interactive revision notes, videos and practice questions load below.