Relative Formula Mass of Molecules

Introduction

Relative atomic masses describe single atoms, but most substances are made of atoms joined together. To weigh out a mole of water, sugar or carbon dioxide, we first need the relative mass of one whole molecule. Fortunately, this is just addition: the mass of a molecule is the total mass of the atoms it contains. This page shows how to do that addition quickly and without slips.

Core explanation

Definition. The relative formula mass, Mᵣ, of a substance is the sum of the relative atomic masses of all the atoms shown in its formula. For substances made of molecules, it is also called the relative molecular mass. Like Aᵣ, it is a ratio on the carbon-12 scale, so it has no units.

The method. Count the atoms of each element (as you did when counting atoms inside molecules), multiply each count by the element's Aᵣ, then add.

For water, H₂O: 2 × 1.0 + 1 × 16.0 = 18.0.

For carbon dioxide, CO₂: 1 × 12.0 + 2 × 16.0 = 44.0.

Setting out. A small table keeps longer calculations tidy. For glucose, C₆H₁₂O₆:

Element Number of atoms Aᵣ Total --- --- --- --- C 6 12.0 72.0 H 12 1.0 12.0 O 6 16.0 96.0 Mᵣ 180.0

More examples.

Substance Formula Mᵣ --- --- --- Oxygen O₂ 32.0 Chlorine Cl₂ 71.0 Ammonia NH₃ 17.0 Methane CH₄ 16.0 Hydrogen chloride HCl 36.5 Ethanol C₂H₅OH 46.0 Sulfuric acid H₂SO₄ 98.1 Octane C₈H₁₈ 114.0 Sucrose C₁₂H₂₂O₁₁ 342.0

Elements count too. Diatomic elements such as O₂ and Cl₂ are molecules, so their Mᵣ is twice their Aᵣ. Oxygen gas has Mᵣ = 32.0, not 16.0.

Same Mᵣ, different substances. Carbon dioxide (CO₂) and propane (C₃H₈) both have Mᵣ = 44.0. An Mᵣ alone cannot identify a compound; the formula is needed.

Step-by-step reasoning

1. Write the formula and list every element in it. 2. Count the atoms of each element, including hidden 1s and repeated symbols. 3. Multiply each count by the Aᵣ of that element. 4. Add all the products to get Mᵣ. 5. Check the answer is at least as large as the heaviest single atom present.

Visual explanation

Imagine building a model of ethanol from atoms that each carry a mass label: two carbon balls marked 12.0, six hydrogen balls marked 1.0 and one oxygen ball marked 16.0. Putting the whole model on a balance shows the sum of the labels, 46.0.

Real-world analogy

A shopping bill is the sum of each item's price multiplied by how many you bought. Three apples at 20p and two pears at 30p cost 3 × 20 + 2 × 30 = 120p. Finding Mᵣ is the same calculation, with atoms as items and Aᵣ as prices.

Real-world example

Brewers and fuel chemists often need the Mᵣ of ethanol (46.0) and of octane, a major component of petrol (114.0). These values are the first step in working out how much carbon dioxide a given amount of fuel releases when it burns.

Why?

Why can we simply add the atomic masses? When atoms bond covalently, they share electrons but no significant mass is gained or lost. The mass of the molecule is therefore just the total of the atoms' masses, to the precision used in chemistry.

Common misconception

"The Mᵣ of oxygen is 16." That is the Aᵣ of an oxygen atom. Oxygen gas is made of O₂ molecules, so its Mᵣ is 32.0. Always check whether the question refers to atoms or to the element as it normally exists.

Worked example

Question: Calculate the relative formula mass of aspirin, C₉H₈O₄.

Reasoning: C: 9 × 12.0 = 108.0. H: 8 × 1.0 = 8.0. O: 4 × 16.0 = 64.0. Total = 108.0 + 8.0 + 64.0 = 180.0.

Answer: Mᵣ(C₉H₈O₄) = 180.0 (no units).

Quick check

1. Calculate the Mᵣ of nitrogen dioxide, NO₂. Answer: 14.0 + 2 × 16.0 = 46.0.

Exam focus

Show the multiplication for each element before adding; this earns method marks if you slip. Do not give Mᵣ units. Watch for formulae where an element appears twice, such as C₂H₅OH or CH₃COOH, and count every atom.

Advanced insight

A mass spectrometer measures the mass of individual molecules, which contain particular isotopes. The peak for the molecular ion of chlorine therefore appears at 70, 72 and 74 rather than 71.0, because Cl₂ molecules are made from different combinations of chlorine-35 and chlorine-37. Mᵣ is the weighted average of these.

Summary

The relative formula mass, Mᵣ, of a molecule is the sum of the Aᵣ values of all its atoms, found by multiplying each atom count by its Aᵣ and adding. It has no units. Diatomic elements have Mᵣ equal to twice their Aᵣ, and different molecules can share the same Mᵣ.

Practice questions

1. Calculate the Mᵣ of sulfuric acid, H₂SO₄. Answer: 2 × 1.0 + 32.1 + 4 × 16.0 = 98.1. 2. Calculate the Mᵣ of ethanoic acid, CH₃COOH. Answer: C: 2 × 12.0 = 24.0; H: 4 × 1.0 = 4.0; O: 2 × 16.0 = 32.0; total 60.0. 3. Find the Mᵣ of sucrose, C₁₂H₂₂O₁₁. Answer: 144.0 + 22.0 + 176.0 = 342.0. 4. Show that carbon dioxide and propane, C₃H₈, have the same Mᵣ. Answer: CO₂: 12.0 + 32.0 = 44.0. C₃H₈: 36.0 + 8.0 = 44.0. Both are 44.0.