Formulae and Balanced Equations

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 1.25 — Writing word and balanced chemical equations, including state symbols
• 1.26 — Calculating relative formula masses from relative atomic masses

Specification section 1(d) The Periodic Table — also taught in Electronic Configurations and the Periodic Table.

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

Burn a strip of magnesium and weigh what is left. The white ash weighs MORE than the metal you started with. For a long time that looked like matter being created out of nothing, and it was one of the observations that held chemistry back. The resolution is simple once you see it: something joined in that you were not weighing. Oxygen from the air became part of the product, and if you had weighed the air too, nothing would have been gained at all. Atoms are never created or destroyed in a chemical reaction — they are only rearranged.

A balanced equation is the bookkeeping that makes that statement checkable. It is not a puzzle invented to be difficult; it is a claim that the atoms you finished with are exactly the atoms you started with, and balancing is how you prove it. If the two sides do not match, the equation is saying atoms appeared or vanished, which did not happen.

The one rule that makes balancing work — and the one that ruins it

1. You may put a BIG NUMBER in front of a formula. That means 'this many of these', and it changes only how many you have.
2. You may NEVER change a small subscript inside a formula. That changes what the substance IS.
3. H₂O is water. H₂O₂ is hydrogen peroxide — a bleach that will burn your skin. Changing that little 2 has not given you more water; it has silently swapped the substance for a different one.
4. So when an equation will not balance, the answer is always another coefficient at the front, never an adjusted subscript.
5. Balance the most complicated formula first, leave elements that appear on their own until last, and count again at the end.

Balancing the combustion of methane

Balance CH₄ + O₂ → CO₂ + H₂O

1. Count as written. Left: 1 C, 4 H, 2 O. Right: 1 C, 2 H, 3 O. Carbon is fine; hydrogen and oxygen are not.
2. Fix hydrogen first, because it appears in only one formula on each side. Four H on the left needs 2H₂O on the right.
3. Recount oxygen on the right: 2 in CO₂ plus 2 in 2H₂O makes 4.
4. Oxygen is the element on its own, so it goes last: 2O₂ on the left gives 4.
5. Final check. Left: 1 C, 4 H, 4 O. Right: 1 C, 4 H, 4 O. Balanced.

Answer: CH₄ + 2O₂ → CO₂ + 2H₂O

State symbols finish the sentence: (s) solid, (l) liquid, (g) gas, (aq) aqueous, meaning dissolved in water. The pair worth being careful about is (l) and (aq). Water itself is (l) because it is a pure liquid; sodium chloride solution is (aq) because the salt is dissolved IN water. NaCl(l) would be molten salt at over 800 °C, which is a completely different thing from NaCl(aq) in a beaker at room temperature — and the distinction matters enormously once you reach electrolysis.

Finally, the mass of a formula. Every element has a relative atomic mass, Ar, from the Periodic Table, and the relative formula mass, Mr, is simply all of them added up for one formula. A subscript multiplies the atom before it, and a bracket multiplies everything inside it — that bracket is where nearly all lost marks live. In Ca(NO₃)₂ the subscript 2 applies to the whole bracket, so there are two nitrogens and six oxygens, not one and three.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

Learn this definition · Relative formula mass (Mr)

The sum of the relative atomic masses of all the atoms shown in the formula of a substance. It has no units, because it is a comparison rather than a measurement.

Balancing any equation

1. Write the correct formulae for every reactant and product, and do not change them afterwards.
2. Count each type of atom on both sides.
3. Balance the most complicated formula first, adding coefficients in front only.
4. Leave any element appearing on its own, such as O₂ or Mg, until last.
5. Recount every atom on both sides, then add state symbols.

Calculating a relative formula mass

1. Write out every element in the formula with its Ar from the Periodic Table.
2. Multiply each Ar by the subscript immediately after that atom.
3. Where there is a bracket, multiply everything inside it by the number after the bracket.
4. Add all the totals together. The answer has no unit.

State symbols — and the pair that is examined against itself

(s)

solid

(l)

liquid — a pure substance in its liquid state, such as water or molten lead

(g)

gas

(aq)

aqueous — dissolved in water. This is a solution, not a pure liquid

(l) against (aq)

H₂O(l) is pure water; NaCl(aq) is salt dissolved in water; NaCl(l) is molten salt above 800 °C

2Mg(s) + O₂(g) → 2MgO(s)

Conditions: burning in air. The product is heavier than the magnesium because the oxygen that joined it was never weighed.

CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)

Conditions: note the three different state symbols in the products — and that mass appears to fall here, because the carbon dioxide escapes.

Model answer [3 marks]

A student burns magnesium in a crucible and finds the product weighs more than the magnesium did. Explain this observation. [3]

The magnesium reacts with oxygen from the air to form magnesium oxide. The oxygen atoms become part of the product, so the product contains everything the magnesium did plus the oxygen that joined it. The oxygen came from the air and was not weighed at the start, so mass appears to increase — although no atoms were created.

Model answer [3 marks]

Calculate the relative formula mass of Ca(NO₃)₂. Ar: Ca = 40, N = 14, O = 16. [3]

The subscript 2 applies to everything inside the bracket, so there are 1 Ca, 2 N and 6 O. Ca is 40. N is 2 × 14 = 28. O is 6 × 16 = 96. Total Mr = 40 + 28 + 96 = 164.

Mark-losing trap. Never change a subscript to balance an equation. Changing H₂O to H₂O₂ swaps water for bleach — only the front coefficients may change.

Mark-losing trap. A bracket multiplies everything inside it. Ca(NO₃)₂ has six oxygens, not three, and that is the most common Mr error there is.

Mark-losing trap. (l) is a pure liquid; (aq) is dissolved in water. NaCl(l) is molten salt above 800 °C, which is not what is in the beaker.

Mark-losing trap. Mass seems to fall when a gas escapes and to rise when a gas joins in. In a sealed container it never changes at all.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · Calculate [1 mark] — Calculate the relative formula mass of carbon dioxide, CO₂. Ar: C = 12, O = 16.
2. Grade 7 · State [2 marks] — Balance the equation for the reaction of hydrogen with oxygen: __ H₂ + O₂ → __ H₂O. State the number that must go in front of BOTH gaps.
3. Grade 8 · Explain [4 marks] — A student heats magnesium in an open crucible and finds the mass has increased. Another student heats calcium carbonate in an open crucible and finds the mass has decreased. Select every statement that belongs in a full-mark explanation of both results.
4. Grade 9 · Calculate [3 marks] — Calculate the relative formula mass of aluminium sulfate, Al₂(SO₄)₃. Ar: Al = 27, S = 32, O = 16.
5. 9+ · Analyse [5 marks] — A student reacts marble chips with hydrochloric acid in an open conical flask standing on a balance, and records the mass falling steadily for several minutes. She repeats the experiment with the identical quantities in a sealed flask, and the balance reading does not change at all. She concludes that mass is conserved only in sealed containers. Select every statement that belongs in a full-mark response.

The people behind this science

Two ways into the same idea — the one who built a whole system on relative masses, and the one who put the balance at the centre of chemistry. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Dmitri Mendeleev — the one who built a whole system on relative masses

Mendeleev arranged the elements by relative atomic mass and found that their properties repeated — and where a mass did not fit the pattern he was prepared to say the measured mass was WRONG rather than the pattern. Several times he turned out to be right. The Ar values you add up in this lesson are the numbers he staked his reputation on.

• “Why did you trust your pattern more than a measured atomic mass?”
• “What does it mean to say one atom is twelve times heavier than another?”
• “How can you compare the masses of atoms nobody has ever seen?”
• “Which measured mass did you most doubt, and were you right to doubt it?”

Antoine Lavoisier — the one who put the balance at the centre of chemistry

This lesson opens with magnesium ash weighing more than the metal it came from, and Lavoisier is the man who resolved exactly that. He heated metals in sealed vessels and weighed before and after, showing the extra mass came out of the air rather than from nowhere — which destroyed the phlogiston theory and established the principle that makes balancing an equation mean anything at all.

• “Why did sealing the vessel matter so much to your argument?”
• “How did weighing things show that phlogiston could not exist?”
• “Where does the extra mass come from when a metal is burned?”
• “Why did chemistry need a whole new naming system before it could progress?”

Carry on through the course

• Previous lesson: Solubility and Solubility Curves
• Next lesson: The Mole
• The Three States of Matter — What the particles are doing in a solid, a liquid and a gas — and what really changes when ice melts.
• Pure Substances, Mixtures and How to Separate Them — Why a pure substance melts at one temperature, and which separation technique to reach for when.
• Inside the Atom — Protons, neutrons and electrons — where they are, what they weigh, what they carry, and how isotopes give an element a decimal mass.
• Electronic Configurations and the Periodic Table — Why the table has the shape it has: the group number IS the outer-shell electron count, and everything follows from that.
• Solubility and Solubility Curves — Why a solution can be full, why hot water holds more, and how one curve tells you exactly how many crystals you will get back.
• All of Chemistry · Chemistry key terms · required practicals · equations · Incandio Science · The 4CH1 specification