Relative Formula Mass

Introduction

Once you know how heavy each type of atom is on the relative scale, you can work out how heavy a whole molecule or formula unit is. Just add up the relative atomic masses of every atom in the formula. The result is the relative formula mass , Mr. It tells you, for example, that a water molecule is 18 times heavier than one-twelfth of a carbon-12 atom — and it is the number you need for almost every chemical calculation that follows.

Core explanation

Definition. The relative formula mass ( Mr ) of a substance is the sum of the relative atomic masses of all the atoms in its formula. Like Ar, it has no units .

For substances made of molecules, such as water or carbon dioxide, Mr is also called the relative molecular mass . For ionic compounds such as sodium chloride, which do not contain molecules, "relative formula mass" is the correct term because the formula shows a formula unit rather than a molecule. The calculation is the same in both cases.

The basic method. Write the formula, count each type of atom, multiply by its Ar and add.

Water, H₂O: 2 hydrogen atoms and 1 oxygen atom. Mr = (2 × 1) + (1 × 16) = 18.

Carbon dioxide, CO₂: 1 carbon and 2 oxygen. Mr = 12 + (2 × 16) = 44.

Handling brackets. A subscript after brackets multiplies every atom inside. In calcium hydroxide, Ca(OH)₂, there are 1 Ca, 2 O and 2 H. Mr = 40 + (2 × 16) + (2 × 1) = 74.

In aluminium sulfate, Al₂(SO₄)₃, there are 2 Al, 3 S and 12 O. Mr = (2 × 27) + (3 × 32) + (12 × 16) = 54 + 96 + 192 = 342.

Using a table. For longer formulae, a small table keeps your working tidy and reduces errors:

Element Number of atoms Ar Total --- --- --- --- Ca 1 40 40 C 1 12 12 O 3 16 48 CaCO₃ 100

Elements too. Mr can be found for elements that exist as molecules. Oxygen gas is O₂, so its Mr is 2 × 16 = 32. Chlorine gas, Cl₂, has Mr = 2 × 35.5 = 71. Be careful to use the formula of the actual substance.

Useful values of Ar: H 1, C 12, N 14, O 16, Na 23, Mg 24, Al 27, S 32, Cl 35.5, K 39, Ca 40, Fe 56, Cu 63.5.

Step-by-step reasoning

To find Mr of ammonium nitrate, NH₄NO₃:

1. Count atoms: N appears twice (once in NH₄, once in NO₃), H four times, O three times. 2. Nitrogen: 2 × 14 = 28. 3. Hydrogen: 4 × 1 = 4. 4. Oxygen: 3 × 16 = 48. 5. Add: 28 + 4 + 48 = 80.

Visual explanation

Imagine building a model of a sulfuric acid molecule, H₂SO₄, from coloured balls, each labelled with its Ar. Place all seven balls on a scale: two marked 1, one marked 32 and four marked 16. The scale reads 98 — the Mr.

Real-world analogy

Working out Mr is like totalling a shopping bill. Each item (atom) has a price (Ar), and the formula tells you the quantity of each. Multiply quantity by price, add the lines together, and you have the total — the formula mass.

Real-world example

Farmers compare fertilisers partly by how much nitrogen they supply per kilogram. Urea, CO(NH₂)₂, has Mr = 60 and ammonium nitrate has Mr = 80. Knowing these values lets agricultural chemists calculate which product delivers more nitrogen for its mass.

Why?

Why can we simply add atomic masses? When atoms join to form a compound, the total mass is conserved: no atoms are gained or lost, and the tiny mass changes from bonding are far too small to matter at this level. So the mass of a formula unit is effectively the sum of the masses of its atoms.

Common misconception

"In Ca(OH)₂ the 2 applies only to hydrogen." It applies to everything inside the brackets, so there are two oxygen atoms as well as two hydrogen atoms. Getting this wrong gives Mr = 58 instead of the correct 74.

Worked example

Question: Calculate the relative formula mass of magnesium nitrate, Mg(NO₃)₂.

Reasoning: Atoms: 1 Mg, 2 N, 6 O. Mg: 1 × 24 = 24. N: 2 × 14 = 28. O: 6 × 16 = 96. Total = 24 + 28 + 96.

Answer: Mr = 148.

Quick check

1. What is the Mr of methane, CH₄? Answer: 12 + (4 × 1) = 16.

Exam focus

Show your working line by line so method marks can be awarded even if an arithmetic slip occurs. Take special care with brackets and with repeated elements such as nitrogen in NH₄NO₃. Give Mr without units, and use 35.5 for chlorine.

Advanced insight

For a hydrated salt, the water of crystallisation is included. Copper(II) sulfate crystals, CuSO₄·5H₂O, have Mr = 159.5 + (5 × 18) = 249.5. Heating removes the water and the mass falls — a difference that can be used to find how many water molecules each formula unit contains.

Summary

Relative formula mass (Mr) is the sum of the relative atomic masses of all atoms in a formula, and it has no units. For molecular substances it is also called relative molecular mass. Count every atom carefully, remembering that a subscript after brackets multiplies everything inside, then multiply by Ar and add.

Practice questions

1. Calculate Mr for sodium chloride, NaCl. Answer: 23 + 35.5 = 58.5. 2. Calculate Mr for sulfuric acid, H₂SO₄. Answer: (2 × 1) + 32 + (4 × 16) = 98. 3. Calculate Mr for iron(III) oxide, Fe₂O₃. Answer: (2 × 56) + (3 × 16) = 112 + 48 = 160. 4. Calculate Mr for ammonium sulfate, (NH₄)₂SO₄. Answer: N 2 × 14 = 28, H 8 × 1 = 8, S 32, O 4 × 16 = 64; total 132. 5. Explain why the Mr of oxygen gas is 32, not 16. Answer: Oxygen gas exists as O₂ molecules containing two atoms, so Mr = 2 × 16 = 32.