1.5.2Principles of Chemistry

Calculate Relative Mass

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Section 1 of 12Relative atomic mass and relative formula mass

Relative atomic mass, A_r

Relative atomic mass, A_r The A_r of an element is its average atom mass relative to carbon-12.
- It is the larger of the two numbers in each box of the Periodic Table.

Relative formula mass, M_r

Relative formula mass, M_r The M_r of a substance is the sum of the A_r values of all the atoms shown in its formula.
For a substance made of molecules it is also called the relative molecular mass.

Non-whole numbers

Non-whole numbers Use the exact values given in the question, such as 35.5 for chlorine and 63.5 for copper.

Section 2 of 12Method

Write down the formula and list each element in it.

Count how many atoms of each element there are, multiplying by the number outside any brackets.

Write the A_r of each element from the Periodic Table.

Multiply each A_r by its number of atoms and add all the results together.

Give the answer without units, because relative masses are ratios.

Section 3 of 12Worked examples

Substance	Atom count	Calculation	M_r
Water, H₂O	H: 2, O: 1	(2 × 1) + 16	18
Sodium chloride, NaCl	Na: 1, Cl: 1	23 + 35.5	58.5
Copper oxide, CuO	Cu: 1, O: 1	63.5 + 16	79.5
Calcium hydroxide, Ca(OH)₂	Ca: 1, O: 2, H: 2	40 + (2 × 16) + (2 × 1)	74
Magnesium nitrate, Mg(NO₃)₂	Mg: 1, N: 2, O: 6	24 + (2 × 14) + (6 × 16)	148

Section 4 of 12Dealing with brackets

Number outside bracket multiplies everything inside

Rule

Rule In Ca(OH)₂ the small 2 applies to both O and H, so there are 2 oxygen atoms and 2 hydrogen atoms.

Nested counts

Nested counts In (NH₄)₂SO₄ there are 2 nitrogen atoms and 2 × 4 = 8 hydrogen atoms, plus one sulfur and four oxygen atoms.
M_r = (2 × 14) + (8 × 1) + 32 + (4 × 16) = 132.

Check yourself

Check yourself Count the atoms of each element before adding anything, so none is missed.

Section 5 of 12Link to conservation of mass

Balanced equations

Balanced equations In a balanced equation the total M_r of the reactants (including the big numbers) equals the total M_r of the products.

Example

Example 2Mg + O₂ → 2MgO: reactants 2 × 24 + 32 = 80 and products 2 × 40 = 80.

Section 6 of 12Key Definitions

Relative masses are numbers without units, which allow substances to be compared.

Relative atomic mass, Ar

The weighted average mass of an atom of an element compared with one twelfth of a carbon-12 atom, given on the periodic table.

Relative formula mass, Mr

The sum of the relative atomic masses of all the atoms shown in the formula of a compound or element.

Diatomic molecule

An element existing as two atoms joined together, such as H₂, so its Mr is twice its Ar.

Brackets

A subscript outside a bracket multiplies every atom inside it, so Ca(OH)₂ contains one calcium, two oxygen and two hydrogen atoms.

Section 7 of 12Step-by-Step Method

Write down the formula and count how many atoms of each element it contains, including those inside brackets.

Look up the relative atomic mass of each element on the periodic table, using the value given rather than a rounded number.

Multiply each relative atomic mass by the number of atoms of that element, applying any brackets correctly.

Add the results together to give the relative formula mass, which has no units.

Substance	Formula	Atom count	Mr
Water	H₂O	H: 2, O: 1	18
Carbon dioxide	CO₂	C: 1, O: 2	44
Calcium hydroxide	Ca(OH)₂	Ca: 1, O: 2, H: 2	74
Aluminium sulfate	Al₂(SO₄)₃	Al: 2, S: 3, O: 12	342

Section 8 of 12Using Relative Masses

Using Relative Masses

Conservation

In a balanced equation the total Mr of the reactants equals the total Mr of the products, which follows from conservation of mass.

Comparing masses

Mr values allow the masses of substances to be compared, and they are the basis of reacting mass calculations.

Hydrated salts

The Mr of a hydrated salt such as CuSO₄·5H₂O is the Mr of the anhydrous salt plus five times the Mr of water.

Ar values

Ar values are often not whole numbers, such as 35.5 for chlorine, so use the values given rather than rounding them.

Section 9 of 12Worked Example

Question

Calculate the relative formula mass of aluminium sulfate, Al₂(SO₄)₃.
Use Ar values Al = 27, S = 32 and O = 16.

Count the atoms2 Al, 3 S, and 3 × 4 = 12 O.
Add the contributions(2 × 27) + (3 × 32) + (12 × 16).
Calculate54 + 96 + 192 = 342.

Answer The relative formula mass of aluminium sulfate is 342.

Section 10 of 12Exam Checklist & Tips

1.5.2 – Key Points for the Exam

Relative atomic mass (Ar) The weighted average mass of an atom of an element compared with one twelfth of carbon-12.
Relative formula mass (Mr) The sum of the relative atomic masses of the atoms in a formula.
Diatomic molecule A molecule made of two atoms of the same element, such as oxygen, O₂.
Law of Conservation of Mass The rule that mass is neither created nor destroyed in a chemical reaction.

Common Mistakes

Forgetting to multiply the atoms inside brackets by the subscript outside, for example in Ca(OH)₂.
Rounding Ar values to whole numbers when the periodic table gives values such as 35.5.
Adding units such as g to the relative formula mass, which is a ratio and has no units.
Using the mass number instead of the relative atomic mass from the periodic table.

Section 11 of 12Key terms

Term	Meaning
Relative atomic mass (A_r)	The average mass of an atom of an element compared with 1/12 of a carbon-12 atom.
Relative formula mass (M_r)	The sum of the relative atomic masses of the atoms in the formula.
Subscript	A small number after a symbol that shows how many atoms of that element are present.
Coefficient	The large number in front of a formula in an equation.

Section 12 of 12Exam technique

Using the atomic number instead of the mass number (A_r). The A_r is the larger number in the Periodic Table box.

Ignoring the number outside a bracket, so only one of the atoms in the bracket is counted.

Rounding chlorine to 35 or copper to 64 when the question gives 35.5 and 63.5.

Adding units such as grams. Relative formula mass has no units.