The Mole Concept

Lessons

Senior 2 · Chemistry

The Mole Concept

5 lessons

Lesson 2 of 5

Relative Atomic, Molecular and Formula Masses; Molar Mass

25 min

Why this matters

You cannot count 6.02 × 10²³ atoms, but you can weigh a sample on a balance. To turn a mass into a number of moles, you need to know how heavy each kind of particle is. An agro-dealer selling a 50 kg bag of urea, a pharmacist weighing out a medicine and a chemist planning a reaction all rely on this link between mass and moles.

By the end of this lesson you will be able to calculate relative formula masses and molar masses, and use n = m ÷ M to move between mass and moles.

Relative atomic mass, A_r

Atoms are compared with the carbon-12 atom. The relative atomic mass (A_r) of an element is the average mass of its atoms compared with one-twelfth of the mass of a carbon-12 atom. Because it is a ratio, it has no units.

It is an average because most elements are mixtures of isotopes. Chlorine is about 75% chlorine-35 and 25% chlorine-37, so its A_r = 0.75 × 35 + 0.25 × 37 = 35.5.

Use these values in this unit:

Element	H	C	N	O	Na	Mg	Al	P	S	Cl	K	Ca	Fe	Cu	Zn
A_r	1	12	14	16	23	24	27	31	32	35.5	39	40	56	63.5	65

Relative molecular mass and relative formula mass

Add up the A_r values of all the atoms in the formula.

For a substance made of molecules, the total is the relative molecular mass, M_r: H₂O = 2 × 1 + 16 = 18; CO₂ = 12 + 2 × 16 = 44; CH₄ = 12 + 4 × 1 = 16; sucrose, C₁₂H₂₂O₁₁ = 12 × 12 + 22 × 1 + 11 × 16 = 342.
An ionic compound has no molecules, so the total is called the relative formula mass (the same symbol, M_r, is used): NaCl = 23 + 35.5 = 58.5; CaCO₃ = 40 + 12 + 3 × 16 = 100.

Worked example 1: formulae with brackets and water

Calculate M_r for (a) Ca(NO₃)₂, (b) (NH₄)₂SO₄, (c) CuSO₄·5H₂O.

Solution.

(a) The bracket is doubled: 40 + 2 × (14 + 3 × 16) = 40 + 2 × 62 = 164.
(b) 2 × (14 + 4 × 1) + 32 + 4 × 16 = 36 + 32 + 64 = 132.
(c) CuSO₄ = 63.5 + 32 + 64 = 159.5, and 5H₂O = 5 × 18 = 90, so the total is 249.5.

Molar mass, M

The molar mass (M) of a substance is the mass of one mole of it, in grams per mole (g/mol). It has the same number as A_r or M_r: the molar mass of water is 18 g/mol, so 18 g of water contains 6.02 × 10²³ molecules.

The key relationship

n = m ÷ M where n = moles (mol), m = mass (g), M = molar mass (g/mol). Rearranged: m = n × M.

Worked example 2: mass to moles

How many moles are there in 11 g of carbon dioxide?

Solution. M(CO₂) = 44 g/mol. n = 11 ÷ 44 = 0.25 mol.

Worked example 3: moles to mass

What is the mass of 0.20 mol of calcium carbonate?

Solution. m = 0.20 × 100 = 20 g.

Worked example 4: mass to particles

How many molecules are there in 9.0 g of water?

Solution. n = 9.0 ÷ 18 = 0.50 mol. N = 0.50 × 6.02 × 10²³ = 3.01 × 10²³ molecules.

Worked example 5: a bag of fertiliser

How many moles of urea, CO(NH₂)₂, are in a 50 kg bag?

Solution. M = 12 + 16 + 2 × (14 + 2) = 60 g/mol. Convert the mass to grams: 50 kg = 50 000 g. n = 50 000 ÷ 60 = 833 mol.

Tip

Units check: g ÷ (g/mol) = mol. If your units do not cancel to the unit you want, the formula is upside down.

Kilograms first: n = m ÷ M needs the mass in grams, so multiply kilograms by 1000 (and tonnes by 1 000 000) before you divide.

✦

Practice

Use the A_r table in this lesson. Try each item before you read the solution.

Calculate M_r of sulfuric acid, H₂SO₄.

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Solution: 2 × 1 + 32 + 4 × 16 = 98.

How many moles are in 4.9 g of sulfuric acid?

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Solution: 4.9 ÷ 98 = 0.050 mol.

What is the mass of 0.25 mol of sodium hydroxide, NaOH?

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Solution: M = 23 + 16 + 1 = 40 g/mol. m = 0.25 × 40 = 10 g.

How many sodium ions are there in 117 g of sodium chloride?

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Solution: n = 117 ÷ 58.5 = 2.00 mol of NaCl, which contains 2.00 mol of Na⁺. Number of ions = 2.00 × 6.02 × 10²³ = 1.20 × 10²⁴.

What is the mass of 3.01 × 10²³ molecules of oxygen, O₂?

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Solution: n = 3.01 × 10²³ ÷ 6.02 × 10²³ = 0.500 mol. M(O₂) = 32 g/mol, so m = 0.500 × 32 = 16 g.

Summary

A_r compares an atom's average mass with 112 of a carbon-12 atom; it has no units and averages the isotopes.
M_r is the sum of the A_r values in the formula (relative formula mass for ionic compounds); remember brackets and water of crystallisation.
Molar mass M is the mass of one mole in g/mol, numerically equal to M_r.
n = m ÷ M, with the mass in grams.

Sources and credits

Chemistry 2e, 3.1: Formula Mass and the Mole Concept (formula mass for covalent and ionic substances, molar mass and mass–mole conversions) by Paul Flowers, Klaus Theopold, Richard Langley and William R. Robinson, OpenStax, via LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
The worked examples, Practice items and exercises were written by Ganzaa.

1Why this matters

2Relative atomic mass, Ar

3Relative molecular mass and relative formula mass

Worked example 1: formulae with brackets and water

4Molar mass, M

5The key relationship

Worked example 2: mass to moles

Worked example 3: moles to mass

Worked example 4: mass to particles

Worked example 5: a bag of fertiliser

Practice

Why this matters

Relative atomic mass, A_r

Relative molecular mass and relative formula mass

Molar mass, M

The key relationship