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  Edexcel IAL Chemistry — Unit 1

Formulae & Equations

Everything you need to go from "I've read it" to "I can actually do it" — moles, masses, equations, and formula calculations, explained properly.

💡 The Big Idea: Chemistry is really just careful counting — atoms can't be created, destroyed, or lost track of, so every formula and equation in this chapter is a tool for counting particles accurately, whether they're too small to see or too many to imagine.

Summary — What This Chapter Covers

  • Formulae & Mass: the difference between relative isotopic mass, relative atomic mass (Ar), and relative formula/molecular mass (Mr) — and how to calculate Mr from a formula.
  • Avogadro & the Mole: what a "mole" actually is, the Avogadro constant, and the core equation linking moles, mass, and molar mass.
  • Full & Ionic Equations: how to balance chemical equations, work out ionic compound formulae from charges, write ionic equations by cancelling spectator ions, and recognise reaction types (displacement, neutralisation, precipitation).
  • Calculating Formulae: finding empirical and molecular formulae from mass/percentage data, percentage composition by mass, water of crystallisation, and the ideal gas equation (PV = nRT).

Topic 1: Formulae & Mass

1Basic Terms You Must Know Cold

Before anything else clicks, you need rock-solid definitions of the basic vocabulary. These sound simple, but exam questions love testing the precise wording — "an atom that has become electrically charged" is NOT the same mark as "a charged particle" if the mark scheme wants the specific idea of gaining/losing electrons.

Atom
The smallest part of an element that can participate in a chemical reaction. Think of it as the smallest "chemically active" unit.
Element
A substance made of only one type of atom — it cannot be broken down into anything simpler by chemical means.
Ion
An atom (or group of atoms) that has become electrically charged by gaining or losing electrons.
Molecule
Two or more atoms chemically joined together (can be the same element, e.g. O₂, or different elements).
Compound
A substance made of two or more different elements chemically joined together.
Empirical formula
The smallest whole-number ratio of atoms of each element in a compound. Example: glucose's molecular formula is C₆H₁₂O₆, but its empirical formula is CH₂O.
Why "empirical" vs "molecular" matters Empirical formula is a ratio — it tells you the simplest proportion of atoms, but not necessarily how many atoms are actually in one molecule. Molecular formula is the real, actual count. Two very different compounds can share the same empirical formula (CH₂O is both formaldehyde AND part of the ratio for glucose), which is exactly why you sometimes need extra data (like relative molecular mass) to pin down the true molecular formula.

2Relative Isotopic Mass vs Relative Atomic Mass

This is one of the most commonly confused pairs in the whole chapter, so let's be really precise.

All relative masses in chemistry are measured against the same "ruler": 1/12th the mass of one atom of carbon-12. Carbon-12 was chosen as the international standard because it's stable, common, and gives convenient numbers to work with (rather than using the tiny, awkward actual mass in kilograms — 1.992646538 × 10⁻²⁶ kg — nobody wants to calculate with that every day).

Relative Isotopic Mass

This is the mass of one specific isotope of an element, relative to 1/12 of a carbon-12 atom. For example, the accurate isotopic mass of nitrogen-14 is 14.00307401, which we round to 14.0 for A-level purposes.

Relative Atomic Mass (Ar)

Most elements on the periodic table aren't just one isotope — they're a natural mixture of several isotopes in different proportions (called relative abundances). Relative atomic mass is the weighted average mass of all those isotopes, again relative to 1/12 of carbon-12.

Analogy that makes this click Imagine a bag of marbles where 75% weigh 35g and 25% weigh 37g. The "average marble mass" isn't just (35+37)/2 — it's weighted by how common each type is: (0.75 × 35) + (0.25 × 37) = 35.5g. That's exactly how Ar works with isotopes and their natural abundances — chlorine's Ar of 35.5 is a dead giveaway that it's a weighted mix of isotopes, not a whole number!

3Relative Formula Mass (Mr)

Once you know Ar values for individual atoms, Mr is just adding them all up according to the formula. The symbol Mr refers to the total mass of the whole substance as represented by its formula.

Which word to use — relative formula mass or relative molecular mass? Use "relative formula mass" for giant/ionic structures (like NaCl, which doesn't really exist as discrete molecules). Use "relative molecular mass" only for substances that genuinely exist as separate molecules (like H₂O or CO₂). If in doubt, always say "relative formula mass" — it's the safe, universally correct term that works for both ionic and covalent substances.
How to calculate Mr
Mr = Σ (Ar of each atom × number of that atom in the formula)
In plain English: multiply each element's Ar by how many atoms of it appear in the formula, then add all those totals together.
Worked Example

Calculate Mr for potassium carbonate, K₂CO₃ (Ar: K = 39.1, C = 12.0, O = 16.0)

ElementAtoms presentContribution
K22 × 39.1 = 78.2
C11 × 12.0 = 12.0
O33 × 16.0 = 48.0

Mr = 78.2 + 12.0 + 48.0 = 138.2

Practice Question
Calculate the relative formula mass of ammonium sulfate, (NH₄)₂SO₄. (Ar: N = 14.0, H = 1.0, S = 32.1, O = 16.0)

Topic 2: Avogadro & the Mole

4What Is a Mole, Really?

Atoms are unimaginably small and numerous — you can't weigh out "500 atoms" on a balance in a lab. So chemists needed a bridge between the tiny world of individual atoms and the everyday world of grams you can actually measure. That bridge is the mole.

The bakers' dozen analogy A "dozen" is just a word for the number 12 — it doesn't matter if it's a dozen eggs or a dozen cars, it's always 12 items. A "mole" works exactly the same way, except instead of 12, it's a mole of ANYTHING = 6.02 × 10²³ of that thing (atoms, molecules, ions — even electrons). It's just a giant, chemistry-scaled version of "a dozen."

This number, 6.02 × 10²³, is called the Avogadro constant (NA or L). It's defined so that one mole of any element weighs exactly its Ar in grams. So one mole of carbon (6.02 × 10²³ carbon atoms) weighs exactly 12.00g — which is precisely why carbon-12 was chosen as the reference standard in the first place. It all ties together.

The Core Mole Equation
n = m / M
Where n = number of moles (mol), m = mass of substance (g), M = molar mass (g mol⁻¹). In words: "moles equals mass divided by molar mass." This is arguably the single most-used equation in the entire course.
Worked Example

Q: How many moles are in 100g of water, and how many individual water molecules is that?

Step 1 — Molar mass of H₂O = (2 × 1.0) + 16.0 = 18.0 g mol⁻¹

Step 2 — Moles = mass ÷ molar mass = 100 ÷ 18.0 = 5.56 mol (3 s.f.)

Step 3 — Number of molecules = moles × NA = 5.56 × (6.02 × 10²³) = 3.35 × 10²⁴ molecules

Don't panic at huge or tiny numbers When you multiply or divide by Avogadro's constant, your answers naturally become extremely large or extremely small. 500 million atoms of platinum only weighs about 1.62 × 10⁻¹³ g — that's not a mistake, it's just how staggeringly small atoms really are. Trust the maths.
Practice Question
How many moles of ethanol (C₂H₅OH) are in 23.0g of ethanol, and how many molecules does that represent? (Ar: C = 12.0, H = 1.0, O = 16.0)

Topic 3: Full & Ionic Equations

5Balancing Equations

The golden rule underneath everything in this section: atoms cannot be created or destroyed in a chemical reaction (that's the Law of Conservation of Mass). So whatever atoms go in as reactants must come out as products — same number, same type, just rearranged. Balancing an equation is simply proving that this rule holds.

The one rule you must never break When balancing, you're only ever allowed to change the big numbers in front of formulae (called coefficients). You can NEVER change a subscript inside a formula — turning H₂O into H₂O₂ to "balance" oxygen doesn't balance the equation, it turns water into hydrogen peroxide, a totally different substance!
Worked Example — Step by Step

Balance: magnesium + oxygen → magnesium oxide

Step 1: Write the symbol equation: Mg + O₂ → MgO

Step 2: Count atoms each side — Reactants: 1 Mg, 2 O. Products: 1 Mg, 1 O. Oxygen doesn't balance!

Step 3: Fix it by adding coefficients: 2Mg + O₂ → 2MgO. Now both sides have 2 Mg and 2 O. ✓

Step 4: Add state symbols: 2Mg (s) + O₂ (g) → 2MgO (s)

State symbolMeaning
(s)Solid
(l)Liquid
(g)Gas
(aq)Aqueous (dissolved in water)

6Working Out Formulae for Ionic Compounds

Ionic compounds are electrically neutral overall — the positive and negative charges must exactly cancel out. So to find the formula, you just need to know each ion's charge and combine them in whatever ratio makes the total charge zero.

IonFormula & Charge
Iron(II)Fe²⁺
Copper(II)Cu²⁺
Chromium(III)Cr³⁺
AmmoniumNH₄⁺
HydroxideOH⁻
NitrateNO₃⁻
SulfateSO₄²⁻
CarbonateCO₃²⁻
Hydrogen carbonateHCO₃⁻
Worked Example — The "Swap the Numbers" Trick

Q: What's the formula of aluminium sulfate?

Write each ion with its charge: Al³⁺ and SO₄²⁻

Check by multiplying: Al³⁺ × 2 = +6, and SO₄²⁻ × 3 = −6. Total = 0 ✓

Formula: Al₂(SO₄)₃

Shortcut: just swap the charge numbers (3 and 2) and use them as the subscripts (2 and 3) — it works every time because it's exactly the same maths, just faster.

Practice Question
Work out the formula for iron(III) hydroxide.

7Ionic Equations & Spectator Ions

When ionic compounds dissolve in water, they split apart ("dissociate") into their separate ions floating freely in solution. But in many reactions, not every ion actually takes part — some just sit there unchanged on both sides of the equation. These bystanders are called spectator ions, and an ionic equation strips them out entirely, showing only the ions that actually react.

Why bother with ionic equations at all? They cut straight to the chemistry that matters. The full equation Zn + CuSO₄ → ZnSO₄ + Cu makes it look like sulfate is involved in the reaction — but it isn't! It's just along for the ride. The ionic equation Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s) reveals the real story: zinc atoms are giving electrons to copper ions.
Worked Example — 3-Step Method

Reaction: zinc + copper(II) sulfate → zinc sulfate + copper

Step 1 — Full balanced equation:
Zn(s) + CuSO₄(aq) → ZnSO₄(aq) + Cu(s)

Step 2 — Break aqueous compounds into ions:
Zn(s) + Cu²⁺(aq) + SO₄²⁻(aq) → Zn²⁺(aq) + SO₄²⁻(aq) + Cu(s)

Step 3 — Cancel identical ions on both sides (SO₄²⁻ appears unchanged on both sides, so cross it out):
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

Practice Question
Silver nitrate solution reacts with sodium chloride solution: AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq). Write the ionic equation.

8Recognising Reaction Types

Chemical equations aren't just calculations — they tell a story about what kind of reaction is happening. Learn to spot these three patterns instantly:

Reaction typeWhat to look forExample
DisplacementA more reactive element kicks out a less reactive one from a compoundBr₂(aq) + 2I⁻(aq) → I₂(aq) + 2Br⁻(aq)
NeutralisationAcid + base → salt + water (sometimes + CO₂)H⁺(aq) + OH⁻(aq) → H₂O(l)
PrecipitationTwo aqueous solutions react to form an insoluble solidBa²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s)
Exam link: hazards & safety Examiners love connecting equations to real lab safety. Bromine liquid is toxic, corrosive, and harmful to the environment. Bromine water above 0.2 mol dm⁻³ is corrosive; between 0.06–0.2 mol dm⁻³ it's an irritant; below 0.06 it's low hazard. For neutralisations, hazard depends on acid concentration, acid strength (strong vs weak), how many H⁺ it can donate (mono/di/triprotic), and whether the base is solid (more corrosive) or dilute solution.

Topic 4: Calculating Formulae

9Finding Empirical Formula

Empirical formula calculations always follow the same logical chain: mass → moles → ratio → simplest whole numbers. Whether you're given raw masses or percentages, the method barely changes.

The 3-Step Method
1. Divide each mass (or %) by that element's Ar → gives moles
2. Divide all mole values by the smallest one → gives a ratio
3. Round to whole numbers (or scale up if needed) → empirical formula
Percentages work exactly like masses here because "% by mass" for a 100g sample IS the mass in grams — that's the whole trick.
Worked Example

Q: Find the empirical formula of a compound with 85.7% carbon and 14.3% hydrogen.

CarbonHydrogen
% by mass85.714.3
÷ Ar85.7 ÷ 12.0 = 7.14214.3 ÷ 1.00 = 14.3
÷ smallest (7.142)1.002.00

Empirical formula: CH₂

Practice Question
A compound contains 40.0g carbon, 6.7g hydrogen, and 53.3g oxygen. Find its empirical formula. (Ar: C=12.0, H=1.0, O=16.0)

10From Empirical to Molecular Formula

Empirical formula only gives you the ratio — it might understate the real molecule by a factor of 2, 3, or more. To find the actual molecular formula, you need one more piece of information: the compound's relative molecular mass (Mr).

The Method
multiplier = Mr (molecular) ÷ Mr (empirical formula)
Then multiply every subscript in the empirical formula by that whole-number multiplier to get the molecular formula.
Worked Example

Empirical formula of X is C₄H₁₀S, and Mr of X is 180.2. Find the molecular formula. (Ar: C=12.0, H=1.0, S=32.1)

Step 1: Mass of empirical formula = (12.0×4)+(1.0×10)+(32.1×1) = 90.1

Step 2: Multiplier = 180.2 ÷ 90.1 = 2

Step 3: Multiply every subscript by 2 → C₈H₂₀S₂

Molecular formula: C₈H₂₀S₂

11Percentage Composition by Mass

The reverse question: given a formula, what percentage of its mass comes from one particular element? Useful for checking purity, comparing fertilisers, or verifying a compound's identity.

Formula
% mass of element = (Ar × number of atoms of that element) / Mr of compound × 100
Worked Example

Find the % by mass of calcium in CaCO₃. (Ar: Ca=40, C=12, O=16)

Mr of CaCO₃ = 40 + 12 + (3×16) = 100

% Ca = (1 × 40) ÷ 100 × 100 = 40%

Practice Question
Calculate the percentage by mass of nitrogen in ammonium nitrate, NH₄NO₃. (Ar: N=14.0, H=1.0, O=16.0)

12Water of Crystallisation

Some ionic compounds form crystals with water molecules locked into their structure — these are called hydrated compounds, and the trapped water is the "water of crystallisation." Written with a dot, e.g. CuSO₄·5H₂O (hydrated copper sulfate — vivid blue). Heat it strongly and it loses that water, becoming anhydrous CuSO₄ (white powder) — this is reversible, and it's a classic practical experiment.

How the experiment works 1) Weigh the hydrated salt. 2) Heat it until the mass stops changing (constant mass = all water driven off). 3) The mass lost = mass of water. 4) Convert both masses to moles and find the simplest ratio — that ratio becomes the "x" in the formula CuSO₄·xH₂O.
Worked Example

10.0g of hydrated copper sulfate is heated to a constant mass of 5.59g. Find the formula. (Mr: CuSO₄=159.6, H₂O=18.0)

CuSO₄H₂O
Mass5.59g10.0 − 5.59 = 4.41g
÷ Mr5.59 ÷ 159.6 = 0.0354.41 ÷ 18.0 = 0.245
÷ smallest17

Formula: CuSO₄·7H₂O

13The Ideal Gas Equation

This equation lets you find the number of moles of a gas (or a volatile liquid above its boiling point) just from its pressure, volume, and temperature — no need to know its identity in advance. It's the bridge that lets you combine empirical formula data with molar mass to nail down a molecular formula, even for gases.

Ideal Gas Equation
PV = nRT
P = pressure (Pa)  |  V = volume (m³)  |  n = moles (mol)  |  R = gas constant, 8.31 J mol⁻¹ K⁻¹  |  T = temperature (K)
⚠️ The #1 mistake with this equation: UNITS All quantities MUST be in SI units before you plug them in, or your answer will be wrong by orders of magnitude.

• Pressure: kPa → Pa means × 1000
• Volume: cm³ → m³ means ÷ 1,000,000 (× 10⁻⁶); dm³ → m³ means ÷ 1000 (× 10⁻³)
• Temperature: Celsius → Kelvin means + 273
Worked Example — Full Multi-Step Problem

A compound is 66.7% C, 11.1% H, remainder O. 0.135g of it occupies 56.0 cm³ at 90°C and 101 kPa. Find the molecular formula.

Step 1 — Moles of each element (per 100g): C: 66.7÷12.0=5.558, H: 11.1÷1.00=11.1, O: (100−66.7−11.1)÷16.0=1.3875

Step 2 — Divide by smallest (1.3875): C=4, H=8, O=1 → empirical formula C₄H₈O

Step 3 — Convert units: P = 101×10³ Pa, V = 56.0×10⁻⁶ m³, T = 90+273 = 363 K

Step 4 — Find n: n = PV/RT = (101×10³ × 56.0×10⁻⁶) / (8.31 × 363) = 1.875×10⁻³ mol

Step 5 — Find molar mass: M = mass ÷ n = 0.135 ÷ 1.875×10⁻³ = 72 g mol⁻¹

Step 6 — Compare to empirical mass: C₄H₈O has mass (4×12.0)+(8×1.0)+16.0 = 72.0 — matches exactly!

Molecular formula: C₄H₈O (multiplier = 72÷72 = 1, so molecular = empirical here)

Practice Question
Calculate the number of moles of gas in a 250 cm³ container at 200 kPa and 25°C. (R = 8.31 J mol⁻¹ K⁻¹)

What to Memorise

n = m / M
Moles = mass ÷ molar mass. The single most-used equation in this chapter.
NA = 6.02 × 10²³ mol⁻¹
Avogadro's constant — number of particles in one mole of anything.
PV = nRT
Ideal gas equation. R = 8.31 J mol⁻¹ K⁻¹. Remember: Pa, m³, K only!
% mass = (Ar × atoms) / Mr × 100
Percentage composition by mass of one element in a compound.
Relative isotopic mass
Mass of ONE isotope relative to 1/12 of a carbon-12 atom.
Relative atomic mass (Ar)
Weighted average mass of all isotopes of an element, relative to 1/12 of carbon-12.
Empirical formula
Simplest whole-number ratio of atoms in a compound. Method: mass → moles → ratio.
Molecular formula
Actual number of atoms in one molecule. Found via multiplier = Mr(molecular) ÷ Mr(empirical).
Spectator ions
Ions present but NOT involved in the actual reaction — cancelled out to form the ionic equation.
Hydrated vs anhydrous
Hydrated = contains water of crystallisation (·xH₂O). Anhydrous = water removed by heating.

Concepts Checklist

Exam Tips & Common Mistakes

Unit errors in PV = nRT are the #1 mark-loser Always convert pressure to Pa, volume to m³, and temperature to Kelvin BEFORE substituting into the equation. Show this conversion as a separate line of working — if your final answer is wrong but your method and unit conversions are visible, you still pick up method marks.
Always show your working Examiners cannot award "all or nothing" marks for a single arithmetic slip if your method is visible. A wrong final answer with correct method still earns most of the marks. A correct final answer with no working shown can lose marks if the mark scheme is method-based.
Never change a subscript to balance an equation Only adjust the big coefficient numbers in front of formulae. Changing H₂O to H₂O₂ isn't "balancing" — it's inventing a different chemical. This is one of the most common silly mistakes under exam pressure.
Only split AQUEOUS ionic compounds into ions When writing ionic equations, only substances marked (aq) get broken into separate ions. Solids (s), liquids (l), and gases (g) stay whole — this is a very common error, especially with precipitates which are (s), not (aq).
Use Ar values from the periodic table, not rounded whole numbers For example, potassium's Ar is 39.1, not 39. Using the more precise periodic table value gives more accurate final answers, and mark schemes are written expecting this level of precision.
Don't forget to count ALL atoms of an element, even split across a formula In NH₄NO₃, nitrogen appears twice — once in the ammonium ion and once in the nitrate ion. Students often only count one and get the percentage composition wrong.
Empirical ≠ Molecular unless the ratio is already lowest terms If a question gives you Mr data, that's your cue that they want the molecular formula, not just the empirical one — always check whether the empirical formula's mass matches the given Mr, and multiply up if it doesn't.
Water of crystallisation experiments need "constant mass" If asked to describe the experimental method, you must state that the sample is heated, cooled, and re-weighed repeatedly until the mass stops changing — this proves all the water has been driven off. Missing this step is a common lost mark in practical-based questions.
Formulae & Equations — Revision Guide  |  Edexcel International A Level Chemistry  |  Made for offline study
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Also in the full note
  • Topic 1: Formulae & Mass
  • Topic 2: Avogadro & the Mole
  • Topic 3: Full & Ionic Equations
  • Exam Tips & Common Mistakes
  • 7Ionic Equations & Spectator Ions
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