Calculating Relative Molecular Mass

Introduction

Knowing the definition of relative molecular mass is one thing; calculating it quickly and reliably is another. This page works carefully through three of the most important molecules in chemistry — water, carbon dioxide and ammonia — and shows a tidy method you can use for any molecule. Getting into good habits now will save you from errors in the longer calculations to come.

Core explanation

We use the rounded relative atomic masses H = 1, C = 12, N = 14 and O = 16.

Example 1: water, H₂O. One molecule contains 2 hydrogen atoms and 1 oxygen atom.

Element Number of atoms Ar Total --- --- --- --- H 2 1 2 O 1 16 16 Mr 18

Example 2: carbon dioxide, CO₂. One molecule contains 1 carbon atom and 2 oxygen atoms.

Element Number of atoms Ar Total --- --- --- --- C 1 12 12 O 2 16 32 Mr 44

Example 3: ammonia, NH₃. One molecule contains 1 nitrogen atom and 3 hydrogen atoms.

Element Number of atoms Ar Total --- --- --- --- N 1 14 14 H 3 1 3 Mr 17

Comparing the results. Water (18) and ammonia (17) have similar masses. Carbon dioxide (44) is much heavier, about two and a half times as heavy as a water molecule. These numbers already explain some everyday facts: carbon dioxide gas is denser than air (average Mr about 29), while ammonia gas is less dense than air.

Where the mass comes from. Notice that in each molecule most of the mass comes from the heavier atoms. In water, oxygen supplies 16 of the 18 units, even though there are twice as many hydrogen atoms. The number of atoms and their individual masses both matter.

The table method. Setting out each calculation as a table — element, number of atoms, Ar, total — makes it easy to check that every atom has been counted once, and makes working clear to anyone marking it.

Step-by-step reasoning

For any molecule:

1. Write the formula and read the subscripts (no subscript means 1). 2. Make a row for each element. 3. Enter the number of atoms and the Ar. 4. Multiply across each row. 5. Add the totals column to get Mr, with no units.

Visual explanation

Imagine building each molecule from coloured balls: a red oxygen worth 16 with two white hydrogens worth 1 each for water; a black carbon worth 12 between two red oxygens for carbon dioxide; a blue nitrogen worth 14 with three white hydrogens for ammonia. Totting up the ball values gives 18, 44 and 17.

Real-world analogy

A cashier adding up a till receipt lists each item, its quantity and its price, then totals the lines. The table method for Mr is exactly the same kind of itemised bill, but for atoms.

Real-world example

Fire extinguishers that use carbon dioxide work partly because CO₂ (Mr 44) is heavier than air and settles over a fire, pushing oxygen away. Ammonia (Mr 17), used in making fertilisers, is lighter than air, so leaked ammonia rises and disperses, which affects how factories ventilate and monitor it.

Why?

Why do we multiply by the subscript rather than just adding each Ar once? The subscript tells you how many of those atoms are actually present in one molecule, and each one contributes its own mass. Two oxygen atoms weigh twice as much as one.

Common misconception

"Mr of CO₂ is 12 + 16 = 28." This counts only one oxygen atom. The subscript 2 means two oxygen atoms, so Mr = 12 + 32 = 44. (28 is the Mr of carbon monoxide, CO.)

Worked example

Question: Calculate Mr for glucose, C₆H₁₂O₆. (Ar: C 12, H 1, O 16)

Reasoning: C: 6 × 12 = 72. H: 12 × 1 = 12. O: 6 × 16 = 96. Total = 72 + 12 + 96 = 180.

Answer: Mr(C₆H₁₂O₆) = 180.

Quick check

1. Calculate Mr for sulfur dioxide, SO₂. (Ar: S 32, O 16) Answer: 32 + (2 × 16) = 64.

Exam focus

Mr of H₂O (18), CO₂ (44) and NH₃ (17) appear constantly in exams, so be able to find them in seconds. Always show at least one line of working, as method marks are often available even if a slip affects the final answer.

Advanced insight

With more precise Ar values (H 1.008, C 12.011, N 14.007, O 15.999), the answers become H₂O 18.015, CO₂ 44.009 and NH₃ 17.031. The rounded values differ by less than 0.2%, which is why rounded values are fine for most school calculations.

Summary

To calculate Mr, list each element, multiply its Ar by its number of atoms, and add the totals. Water, H₂O, has Mr 18; carbon dioxide, CO₂, has Mr 44; ammonia, NH₃, has Mr 17. A table layout helps avoid missing atoms, and clear working earns marks.

Practice questions

1. Calculate Mr for methane, CH₄. (Ar: C 12, H 1) Answer: 12 + (4 × 1) = 16. 2. Calculate Mr for nitrogen dioxide, NO₂. (Ar: N 14, O 16) Answer: 14 + (2 × 16) = 46. 3. Calculate Mr for sulfuric acid, H₂SO₄. (Ar: H 1, S 32, O 16) Answer: (2 × 1) + 32 + (4 × 16) = 2 + 32 + 64 = 98. 4. How many times heavier is a CO₂ molecule than an NH₃ molecule? Give your answer to one decimal place. Answer: 44 ÷ 17 ≈ 2.6 times heavier.