Relative Molecular Mass

Introduction

Once we know the relative masses of atoms, we can find the relative masses of molecules. A molecule is simply a group of bonded atoms, so its mass is the total of the masses of its atoms. This total is called the relative molecular mass , Mr. It lets chemists compare molecules as easily as atoms: a carbon dioxide molecule, for instance, turns out to be almost two and a half times as heavy as a water molecule.

Core explanation

Definition. The relative molecular mass , symbol Mr , of a substance is the sum of the relative atomic masses of all the atoms shown in its molecular formula. Like Ar, it compares a mass with one-twelfth of the mass of a carbon-12 atom, and like Ar it has no units .

Why adding works. When atoms join to form a molecule, the mass of the molecule is (to a very good approximation) the sum of the masses of the atoms. The particles are simply rearranged; mass is conserved, as Dalton recognised. So adding Ar values gives the relative mass of the molecule.

Molecules of elements. Some elements exist as molecules of identical atoms:

Molecule Atoms Mr --- --- --- Hydrogen, H₂ 2 × H (1) 2 Oxygen, O₂ 2 × O (16) 32 Nitrogen, N₂ 2 × N (14) 28 Chlorine, Cl₂ 2 × Cl (35.5) 71 Sulfur, S₈ 8 × S (32) 256

This shows why the difference between O and O₂ matters. Ar(O) = 16 describes one oxygen atom; Mr(O₂) = 32 describes an oxygen molecule.

Molecules of compounds. For a compound, add the Ar of each element multiplied by the number of its atoms. Methane, CH₄, has one carbon and four hydrogen atoms: Mr = 12 + (4 × 1) = 16. Hydrogen chloride, HCl: Mr = 1 + 35.5 = 36.5.

Reading the formula correctly. A subscript applies only to the symbol directly before it. In CH₄, the 4 belongs to H, not to C. Accurate counting of atoms, which you practised earlier, is the key skill.

Using Mr. Mr lets us compare molecules directly. Mr(CO₂) = 44 and Mr(H₂O) = 18, so a carbon dioxide molecule is 44 ÷ 18 ≈ 2.4 times as heavy as a water molecule. Later, Mr will link the mass of a sample to the number of particles it contains.

Formulae

Mr = Σ (number of atoms of each element × Ar of that element)

Step-by-step reasoning

To find Mr of a molecule:

1. Write the molecular formula. 2. List each element and count its atoms from the subscripts. 3. Look up Ar for each element. 4. Multiply each Ar by its number of atoms. 5. Add the results. Give the answer without units.

Visual explanation

Picture a ball-and-stick model of methane: one black carbon ball in the centre with four white hydrogen balls around it. Put the whole model on an imaginary balance marked in atomic mass units. The carbon contributes 12, each hydrogen 1, and the pointer settles on 16.

Real-world analogy

A shopping basket's total cost is the sum of each item's price times the number bought. Three apples at 20p and one loaf at £1.20 cost £1.80. Molecular mass works the same way: number of atoms times each atom's mass, all added.

Real-world example

The air you breathe is mainly nitrogen (Mr 28) and oxygen (Mr 32), with a little carbon dioxide (Mr 44). Heavier gases tend to collect in low places, which is why carbon dioxide can build up in cellars and pits, a real safety hazard in breweries and wells.

Why?

Why does Mr have no units? Each Ar is a ratio compared with the carbon-12 unit, so adding ratios gives another ratio. The molecule is being compared with the same standard, so Mr is also a pure number.

Common misconception

"The Mr of oxygen gas is 16." Oxygen gas consists of O₂ molecules, so its Mr is 32. The value 16 is the Ar of a single oxygen atom.

Worked example

Question: Find the relative molecular mass of ethanol, C₂H₅OH. (Ar: C 12, H 1, O 16)

Reasoning: Count atoms: C = 2, H = 5 + 1 = 6, O = 1. Mr = (2 × 12) + (6 × 1) + (1 × 16) = 24 + 6 + 16 = 46.

Answer: Mr(C₂H₅OH) = 46.

Quick check

1. What is the Mr of nitrogen gas, N₂? (Ar: N 14) Answer: 2 × 14 = 28.

Exam focus

Show each multiplication, then the sum. Watch for elements that appear in two places in a formula, as H does in C₂H₅OH, and for diatomic elements such as H₂, O₂, N₂ and Cl₂. Never give units for Mr.

Advanced insight

Strictly, a molecule's mass is very slightly less than the sum of its atoms' masses, because energy is released when bonds form and energy has mass (E = mc²). For chemical bonds this mass change is about a billionth of the total, far too small to matter in any chemical calculation.

Summary

Relative molecular mass, Mr, is the sum of the relative atomic masses of all the atoms in a molecule. It has no units. For each element, multiply Ar by the number of atoms and add the totals. Diatomic elements such as O₂ have Mr twice their Ar. Mr lets us compare the masses of different molecules directly.

Practice questions

1. Define relative molecular mass. Answer: The sum of the relative atomic masses of all the atoms in one molecule of a substance. 2. Calculate Mr for methane, CH₄. (Ar: C 12, H 1) Answer: 12 + (4 × 1) = 16. 3. Calculate Mr for chlorine gas, Cl₂. (Ar: Cl 35.5) Answer: 2 × 35.5 = 71. 4. Calculate Mr for hydrogen peroxide, H₂O₂. (Ar: H 1, O 16) Answer: (2 × 1) + (2 × 16) = 2 + 32 = 34.