IB Chemistry HLTopic 1 — Counting Particles by MassPaper 1 & 2Core skill~11 min read
Molar Mass
A balance tells you grams. Chemistry happens in moles. Molar mass is the bridge between the two, and once you can walk across it in both directions you can solve most of the calculations in Paper 2.
📘 What you need to know
Molar mass, M, is the mass of one mole of a substance. Units: g mol−1.
Its number is the same as the Ar or Mr — but molar mass has units and relative mass does not.
n = m ÷ M, where m is in grams. Rearranged: m = n × M and M = m ÷ n.
Find M by adding the Ar of every atom in the formula, including atoms inside brackets and inside water of crystallisation.
Molar mass is the hinge of nearly every calculation: grams in, moles out, then mole ratios do the chemistry.
Percentage by mass of an element = (total mass of that element in the formula ÷ Mr) × 100.
What molar mass actually is
The mole was defined so that one mole of a substance has a mass in grams equal to its relative mass. Carbon has Ar = 12.01, so one mole of carbon atoms weighs 12.01 g. Water has Mr = 18.02, so one mole of water weighs 18.02 g.
That is the whole idea. The periodic table is not really a list of atomic masses — it is a list of how many grams you need to weigh out to get 6.02 × 1023 atoms.
Bar heights are drawn to scale. A mole of copper is more than five times heavier than a mole of carbon, yet both contain exactly the same number of atoms.
Working out a molar mass
Adding up Ar values sounds trivial, and for CO2 it is. The errors appear when there are brackets or a dot in the formula.
🧩 Reading a formula properly
Split the formula into elements and count how many atoms of each there are.
A bracket multiplies everything inside it. In Ca(NO3)2 the subscript 2 applies to the N and all three O atoms — that is 2 N and 6 O.
A dot means “plus this many separate molecules”. In CuSO4·5H2O you add five whole waters, so 5 × 18.02.
Multiply each Ar by its count, then add everything.
Attach the units: g mol−1. Without them the answer is a relative mass, not a molar mass.
Formula
Atoms present
Working
Molar mass
H2O
2 H, 1 O
(2 × 1.01) + 16.00
18.02 g mol−1
K2CO3
2 K, 1 C, 3 O
(2 × 39.10) + 12.01 + (3 × 16.00)
138.21 g mol−1
Ca(OH)2
1 Ca, 2 O, 2 H
40.08 + (2 × 16.00) + (2 × 1.01)
74.10 g mol−1
(NH4)2SO4
2 N, 8 H, 1 S, 4 O
(2 × 14.01) + (8 × 1.01) + 32.07 + (4 × 16.00)
132.17 g mol−1
CuSO4·5H2O
1 Cu, 1 S, 4 O, plus 5 H2O
63.55 + 32.07 + (4 × 16.00) + (5 × 18.02)
249.72 g mol−1
The ammonium sulfate line is the one students get wrong. That outer 2 doubles the N and the four H atoms, giving 8 hydrogens in total. Say the formula out loud as “two lots of NH4, then SO4” and the count comes out right.
The link between mass and moles
One equation, three ways of using it. Learn it as a sentence rather than a triangle: moles equals mass divided by molar mass.
Mass and amountn = m ÷ Mm = n × MM = m ÷ n
If you would rather not memorise a triangle, check the units instead — only one arrangement of m and M gives an answer in mol.
Units are a free error-checker. Molar mass is g mol−1, so g ÷ (g mol−1) = mol. If your working leaves you with g2 mol−1 you multiplied when you should have divided.
Percentage by mass
Once you can build a molar mass, percentage composition falls straight out of it. This is the reverse of the empirical formula work coming next, so it is worth being comfortable with.
Percentage by mass of an element
% = (number of atoms × Ar) ÷ Mr × 100
Worked examples
WORKED EXAMPLE
Molar mass of a compound with brackets
Calculate the molar mass of calcium nitrate, Ca(NO3)2. Use Ar: Ca = 40.08, N = 14.01, O = 16.00.
Step 1: count the atoms carefullyThe bracket subscript 2 doubles both the N and the 3 O: 1 Ca, 2 N, 6 O.Step 2: multiply and addCa: 40.08N: 2 × 14.01 = 28.02O: 6 × 16.00 = 96.0040.08 + 28.02 + 96.00 = 164.10M = 164.10 g mol⁻¹6 oxygens, not 3 — that single slip is worth a mark
WORKED EXAMPLE
Mass to moles
Calculate the amount, in mol, in 4.60 g of ethanol, C2H5OH.
Step 1: molar mass first, alwaysC: 2 × 12.01 = 24.02H: 6 × 1.01 = 6.06O: 16.00M = 46.08 g mol⁻¹C₂H₅OH has 6 hydrogens in total, not 5Step 2: divide mass by molar massn = 4.60 ÷ 46.08 = 0.09983…n = 0.0998 mol
WORKED EXAMPLE
Moles to mass, with water of crystallisation
A student needs 0.0250 mol of hydrated copper(II) sulfate, CuSO4·5H2O. What mass should be weighed out?
Step 1: include the five waters in the molar massCuSO₄: 63.55 + 32.07 + 64.00 = 159.625H₂O: 5 × 18.02 = 90.10M = 249.72 g mol⁻¹Step 2: mass = moles × molar massm = 0.0250 × 249.72 = 6.243m = 6.24 gweighing out 3.99 g of the anhydrous salt instead would give the wrong amount
WORKED EXAMPLE
Percentage by mass
Ammonium nitrate, NH4NO3, is sold as a fertiliser. Calculate the percentage by mass of nitrogen in it.
Step 1: molar mass of the whole compoundN: 2 × 14.01 = 28.02H: 4 × 1.01 = 4.04O: 3 × 16.00 = 48.00Mr = 80.06Step 2: nitrogen as a fraction of that28.02 ÷ 80.06 = 0.350000.35000 × 100 = 35.0035.0 % nitrogen by massboth nitrogens count, even though they sit in different parts of the formula
💡 Exam tip
Write the molar mass down as a separate line before you do anything else. Examiners award marks for a correct M even when the final answer goes wrong.
Use the Ar values from the data booklet, to 2 decimal places. Using rounded whole numbers can shift a 3-significant-figure answer.
Do not round part-way through. Keep the full calculator value and round only the final answer.
Always write the units on molar mass. A bare number is a relative mass, and some questions test exactly that distinction.
If the formula has a dot (a hydrate), ask yourself whether the question wants the hydrated or anhydrous mass. It usually says.
Sense-check: for common laboratory masses, the number of moles is usually somewhere between 0.001 and 1.
⚠ Common mix-up
Ignoring the bracket subscript. Ca(OH)2 is 74.10, not 57.09. Everything inside the bracket gets doubled.
Leaving the water out of a hydrate. CuSO4·5H2O is 249.72, not 159.62.
Multiplying instead of dividing. Grams × g mol−1 gives nonsense units — check the units and the direction becomes obvious.
Confusing M with Mr. They are numerically identical, but only molar mass carries g mol−1.
Using the mass of the element instead of the compound. For percentage by mass, the denominator is the whole molar mass.
Forgetting hidden hydrogens. C2H5OH has 6 H atoms; CH3COOH has 4.
Up next: Empirical Formulae — running molar mass backwards, so that a set of masses from an experiment tells you what the compound actually is.
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