S2 Chemical Formulae and Equations

Every element has a chemical symbol: one capital letter on its own, or a capital followed by a small letter. There is no element whose symbol is more than two letters, and the second letter is always lowercase. That single rule is what stops CO (carbon monoxide, one carbon and one oxygen) from being confused with Co (cobalt, a metal).

Most symbols are the first letter or the first two letters of the English name, but a small set of familiar metals take their symbols from Latin, because that was the language of science when the symbols were standardised. Those are the ones students lose marks on.

• Zn is zinc, a single element. ZN is nothing at all — symbols are never written in capitals.
• A number in front of a formula multiplies everything after it: 3CO₂ is three carbon dioxide molecules — three carbons and six oxygens.
• A number below and after a symbol belongs to that atom alone: the 2 in H₂O applies to the hydrogen only, not to the oxygen.
• A number in brackets multiplies the whole group: Ca(NO₃)₂ holds two nitrate groups, so two nitrogens and six oxygens.

A word alone is ambiguous; a formula is not. The word "soda" has meant at least four different chemicals at different points in history, and "spirits of salt" once meant hydrochloric acid. A formula removes that ambiguity in six characters or fewer. Write NaHCO₃ and a chemist in any country knows you mean one sodium ion, one hydrogen, one carbon and three oxygens, combined in that exact ratio — and can therefore predict what happens when it is heated.

That is the practical value of the notation: a formula is a compact, unambiguous, internationally readable statement of which atoms, and how many of each. Everything else on this page — ionic charges, prefixes, balancing, reaction patterns — is a rule for getting from a name or a reaction description to that statement, or for reading it back again.

Two substances can share the same set of atoms and yet be different compounds, because what matters is not only which atoms are present but in what ratio. Chemistry therefore uses two kinds of formula, and a question will usually tell you which one it wants.

Where a molecule's atoms are already in the smallest possible ratio, the two formulae are identical, which is the case for water (H₂O), carbon dioxide (CO₂) and ammonia (NH₃). Where they are not, the molecular formula is a whole-number multiple of the empirical one: hydrazine's N₂H₄ is exactly twice NH₂.

• To find the empirical formula from a molecular formula, divide every subscript by the highest common factor. C₄H₁₀ becomes C₂H₅ because both subscripts divide by 2.
• To find a molecular formula you need one extra fact — the relative molecular mass — because the ratio alone cannot tell you how many times the simplest unit repeats.
• The empirical formula of a compound is what you get from a composition-by-mass calculation; the molecular formula is what you get from a mass spectrometer.

Metals hold their outer electrons loosely; non-metals hold them tightly. Put the two together and electrons transfer, leaving charged particles called ions. A metal atom that loses electrons becomes positive; a non-metal atom that gains them becomes negative. The two opposite charges then attract, and the result is an ionic compound.

The size of the charge follows from the group the atom is in, so you can often work it out rather than memorise it. Sodium, in Group 1, has one outer electron to lose and forms Na⁺. Magnesium, in Group 2, loses two and forms Mg²⁺. Oxygen needs two electrons to complete its outer shell and forms O²⁻; chlorine needs one and forms Cl⁻.

Simple non-metal anions are built the same way, by adding electrons until the outer shell is full.

Some transition metals can lose different numbers of electrons in different compounds, so their charge has to be stated. Copper forms Cu⁺ and Cu²⁺; iron forms Fe²⁺ and Fe³⁺; lead forms Pb²⁺ and Pb⁴⁺. A Roman numeral in brackets after the name removes the ambiguity: iron(II) chloride is FeCl₂, while iron(III) chloride is FeCl₃. The numeral is not a multiplier; it is the charge on that one ion.

A polyatomic ion is a covalently bonded group with an overall charge. It is charged, so it behaves like a single ion in every ionic compound it appears in — and in every equation you write. Two consequences follow: if more than one is needed, it must go in brackets, and its internal bonds do not break when the compound dissolves.

• Simple non-metal ions take the ending –ide: chloride, oxide, nitride, sulfide.
• A polyatomic ion made of a non-metal with oxygen almost always takes the ending –ate: nitrate, sulfate, carbonate, phosphate. Hydroxide is the one common exception — it contains no oxygen per se in the sense the rule implies, and it is named –ide, not –ate.
• Where an element forms two such ions, the one with fewer oxygens usually takes –ite: nitrate (NO₃⁻) and nitrite (NO₂⁻); sulfate (SO₄²⁻) and sulfite (SO₃²⁻).
• Manganese and chromium add a Roman numeral to show the metal's oxidation state: manganate(VII) is MnO₄⁻, dichromate(VI) is Cr₂O₇²⁻.
• Ammonium is the only polyatomic cation you meet at this level, so it always sits first in a formula.

An ionic compound is electrically neutral: the total positive charge must exactly cancel the total negative charge. Every ionic formula you will ever be asked to write follows from that one requirement. The standard shortcut is the cross-over method.

And always finish by checking: does the total charge come to zero? That check takes ten seconds and catches almost every slip.

Most wrong formulae are not careless mistakes; they come from applying the right rule to the wrong kind of compound. Before writing anything, decide which of three families the substance belongs to. Each family has its own route to the formula, and once the family is identified the rest is mechanical.

The dividing line is the presence of a metal. If a metal is in the name, the compound is ionic and the cross-over method applies. If both parts are non-metals, the compound is covalent, charges are not involved, and the formula is decided either by prefixes in the name or by memory.

Reading a name off a formula is the reverse of the skill in section 6, and it follows a small set of rules. Learn these and you can name almost anything the syllabus shows you.

Copper(I) oxide is Cu₂O, not CuO. The numeral tells you the charge on the copper ion, and the formula then follows from the need for neutrality: two Cu⁺ ions are needed to balance one O²⁻. Students who read the numeral as a subscript write CuO and lose the mark.

Covalent compounds form between non-metals, and their names fall into two very different kinds. Some have only one possible formula, so the name needs no numbers. Others can exist in several different ratios of the same two elements, and then the name must state the numbers, which it does with prefixes.

The prefix sits immediately before the element it counts. The prefix mono– is used on the second element only, or dropped altogether where it would be clumsy: carbon monoxide is CO, and carbon dioxide is CO₂, but carbon monoxide is never called "monocarbon monoxide".

• Carbon dioxide — di– before oxide gives CO₂.
• Sulfur trioxide — tri– gives SO₃.
• Diphosphorus pentoxide — two phosphorus, five oxygen gives P₂O₅.
• Tetrachloromethane — one carbon with four chlorines gives CCl₄, the old dry-cleaning solvent.
• Dinitrogen tetroxide — the brown gas present in the exhaust of some rockets: N₂O₄.

Where two non-metals combine in only one possible way, prefixes are unnecessary and the name is simply "element –ide". Hydrogen and the halogens behave this way, because hydrogen forms exactly one compound with each of them.

A small number of covalent compounds have names that carry no numerical clue at all. There is no prefix in "ammonia" that tells you three hydrogens are attached to one nitrogen, and no rule that turns the word "methane" into CH₄. For these, the formula has to be learned. The list below is deliberately short: it covers the compounds that turn up again and again in equations later in this chapter.

An acid is a compound that releases hydrogen ions, H⁺, when it dissolves in water. Every acid you meet at this level is a source of one or more H⁺ ions paired with a negative ion, and that pairing is what predicts the salt the acid will make.

Two patterns are worth extracting from that table. First, an acid containing one replaceable hydrogen makes a salt with a 1− anion; sulfuric acid contains two and makes a sulfate; phosphoric acid contains three and makes a phosphate. Second, the name of the salt comes from the anion, not from the acid: hydrochloric acid makes chlorides, sulfuric acid makes sulfates, and the metal in front of it decides which particular salt it is.

Most elements exist as single atoms under ordinary conditions, but seven of them cannot bear to be alone. They always appear as pairs bonded to each other, and writing them as single atoms in an equation — H instead of H₂, or O instead of O₂ — is one of the most heavily penalised slips in the syllabus.

Two tricks help. The common ones are easy to picture: hydrogen, nitrogen, oxygen and the four halogens. If you arrange them so that the row reads hydrogen, nitrogen, oxygen along the top and fluorine, chlorine, bromine, iodine down the side, the seven spell out a set you can rebuild from memory. Our own mnemonic is "Have Nice Oxygens In Fluorine's Chlorine Bromine" — clumsy, but the initials H, N, O, F, Cl, Br, I are all that matters, and you will remember a clumsy mnemonic long after a tidy one.

• Solid metals such as iron, copper and aluminium are written as single symbols: Fe, Cu, Al.
• The noble gases — helium, neon, argon — are single atoms: He, Ne, Ar.
• Phosphorus and sulfur are molecular in the solid, but at this level they are written as P and S in equations. This is a convention, and the examination follows it.

A reaction can be described at two levels of detail: first the word equation, then the more precise symbol equation.

The arrow is read as yields or produces. Everything on its left is a reactant, everything on its right a product, and the reaction runs in one direction only — so never replace the arrow with an equals sign.

Method:

1. Underline the reactants and products in the question so you know which substances to write.
2. Convert every name to a formula using the ion charges and the covalent-name rules you learned earlier. Diatomic elements must be written as H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂ — never as a single atom.
3. Balance by placing coefficients in front of whole formulae. Work through the metals first, then the non-metals, and save hydrogen and oxygen for last.
4. Add state symbols, then re-count every element on both sides.

Applying the method to the reaction above: hydrogen and chlorine are both diatomic, so the reactants are H₂ and Cl₂. The product is hydrogen chloride, HCl. The left side carries two hydrogen atoms and two chlorine atoms, so the right side needs two HCl units — giving H₂(g) + Cl₂(g) → 2HCl(g).

State symbols show the physical form of each substance:

Atoms are not created or destroyed in a chemical reaction — they are only rearranged into new combinations. This is the Law of Conservation of Mass, and it is the reason an unbalanced equation is simply wrong: it would describe a reaction in which mass appeared from nowhere or vanished.

Count atoms as coefficient × subscript, and multiply everything inside a bracket by any subscript that follows it. In 2Al₂(SO₄)₃ there are 4 aluminium atoms, 2 × 3 = 6 sulphur atoms and 2 × 12 = 24 oxygen atoms.

There is one rule that cannot be broken while balancing: change coefficients, never subscripts. Water is H₂O. If you need more oxygen you may write 2H₂O, but you may never write H₂O₂ — that formula describes hydrogen peroxide, a completely different substance with completely different properties. Changing a subscript changes the identity of the substance; changing a coefficient only changes how much of it takes part.

Examiners rarely name the reaction type; they describe the substances and expect you to recognise the pattern, write the products and balance the equation.

Combination. Iron heated with sulphur gives the single compound iron(II) sulphide:

Fe(s) + S(s) → FeS(s)

Decomposition. Hydrogen peroxide breaks down slowly on its own and rapidly when manganese(IV) oxide is added:

2H₂O₂(aq) → 2H₂O(l) + O₂(g)

Thermal decomposition follows the same idea, driven by heat. A metal carbonate gives a metal oxide and carbon dioxide — for example lead(II) carbonate:

PbCO₃(s) → PbO(s) + CO₂(g)

Combustion. A hydrocarbon burning in excess oxygen gives only carbon dioxide and water:

2C₄H₁₀(g) + 13O₂(g) → 8CO₂(g) + 10H₂O(l)

Displacement. Iron is more reactive than copper, so it pushes copper out of its compound:

Fe(s) + CuSO₄(aq) → FeSO₄(aq) + Cu(s)

Neutralisation. An acid and an alkali always give a salt and water. The salt is named from the metal of the alkali and the acid:

HCl(aq) + KOH(aq) → KCl(aq) + H₂O(l)

Two relatives of neutralisation are worth keeping beside it. An acid reacting with a reactive metal gives a salt and hydrogen gas, and an acid reacting with a carbonate gives a salt, carbon dioxide and water — the fizzing you see in both cases is a gas escaping:

Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

2HCl(aq) + Na₂CO₃(aq) → 2NaCl(aq) + CO₂(g) + H₂O(l)

Precipitation. Mixing two clear solutions can produce a solid that cannot dissolve:

AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)

Silver chloride is the white precipitate; sodium nitrate stays dissolved.

Four checks, in this order, catch nearly every error:

A student writes:

2Fe(s) + CuSO₄(aq) → Fe₂(SO₄)₃(aq) + Cu(s)

The atoms balance, so the error survives a quick atom count. It is a formula error: iron here forms Fe²⁺, not Fe³⁺, so the equation should read Fe(s) + CuSO₄(aq) → FeSO₄(aq) + Cu(s). That is why check 1 comes first.

Most marks lost on formulae-and-equations questions in the Secondary 2 paper are not lost because a student cannot do the chemistry. They are lost through four habits that are easy to spot once you know what to look for, and easy to fix with a thirty-second check at the end of each question.

When a question gives you a word equation, a description, or a set of reagents and asks for the balanced symbol equation, always work in the same five steps. They take less time than rewriting the answer, and they stop the two mistakes that are hardest to see.

1. Write the names of the reactants and products in a row, so you know what you are aiming at and in what order.
2. Convert each name into a formula, using charges and brackets for ionic compounds and the prefixes for covalent compounds.
3. Write the state symbol for each species underneath its formula as you go.
4. Balance with coefficients only, and count atoms element by element after each change.
5. Check at the end: does each formula still describe a real substance, and are the atom totals equal on both sides?

A useful discipline is to keep a running tally. For Na₂CO₃ you are looking at two sodium, one carbon and three oxygen; for Al₂(SO₄)₃, two aluminium, three sulfur and twelve oxygen. Writing the tally in the margin beside the equation is not "extra work" — it is the evidence an examiner is looking for, and it earns the method marks even if you then slip on the final coefficient.

A student is given samples of magnesium and of a magnesium compound.

(a) The compound is magnesium nitrate. Write its chemical formula, showing clearly how the charges of the ions lead to your answer. [2]

(b) The student adds magnesium to dilute hydrochloric acid. Balance the equation for the reaction.

___ Mg + ___ HCl → ___ MgCl₂ + ___ H₂ [2]

(c) One product of the reaction in (b) is a gas that burns with a "pop". Rewrite the balanced equation from (b) with the correct state symbol for every substance, given that the acid is dilute and the salt formed is in solution. [2]

(d) On heating, the student's carbonate, ZnCO₃, breaks down into zinc oxide and carbon dioxide. Write the balanced chemical equation for this reaction, including the symbol for the condition needed. [2]

(e) A classmate balances the reaction between copper and oxygen as Cu + O₂ → CuO₂. State two separate things that are wrong with this answer. [2]

These are written the way a student should write them in the paper: the working visible, the units and symbols in place, and no step skipped.

1. (a) Magnesium forms the ion Mg²⁺ and nitrate is the polyatomic ion NO₃⁻. Two nitrate ions are needed to balance the charge of one magnesium ion (2+ and 2− cancel), so the formula is Mg(NO₃)₂. The brackets are needed because the nitrate ion is used twice as a single unit.
2. (b) Mg + 2HCl → MgCl₂ + H₂. Mg: 1 on each side. H: 2 on the left, 2 on the right. Cl: 2 on the left, 2 on the right. The equation is balanced with coefficients, and no formula was altered.
3. (c) Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g). Magnesium is a solid metal; the dilute acid is aqueous; magnesium chloride is dissolved in the water, so it is aqueous; hydrogen is the gas that burns with a pop.
4. (d) ZnCO₃(s) → ZnO(s) + CO₂(g), with "heat" written above the arrow. The formulae balance as they stand: Zn 1 : 1, C 1 : 1, O 3 : 3. No coefficient is needed.
5. (e) First, the product formula is wrong. Copper(II) oxide is CuO, because Cu²⁺ pairs with O²⁻ in a one-to-one ratio; CuO₂ is not the substance formed. Second, the formula has been altered in order to even up the oxygen atoms, which is not allowed — you balance with coefficients only. With the correct product the reaction is 2Cu + O₂ → 2CuO, which is balanced 2 : 2 for copper and 2 : 2 for oxygen.