Formulae, equations and state symbols

Writing the formula of an ionic compound

Copper(II) sulfate is CuSO₄ and aluminium sulfate is Al₂(SO₄)₃. Both contain the sulfate ion, SO₄²⁻, yet one formula has one sulfate and the other has three. The difference is the metal ion. Copper(II) is Cu²⁺, and one 2+ ion balances one 2− ion. Aluminium is Al³⁺, and the smallest whole numbers that balance 3+ against 2− are two aluminium ions, 6+, and three sulfate ions, 6−.

An ionic compound has no overall charge, so its formula is the lowest whole-number ratio of ions in which the positive charges equal the negative. The charges on main-group ions follow from the group: Group 1 metals form 1+ ions, Group 2 metals 2+ and aluminium 3+, while nitrogen forms 3−, oxygen and sulfur 2− and the halogens 1−. Transition metals can form more than one ion, and the Roman numeral in the name gives the charge: iron(II) is Fe²⁺ and iron(III) is Fe³⁺.

Describe the drawing

An outline periodic table of the first five periods. Group 1 is shaded and marked 1+, Group 2 2+ and aluminium 3+, in one colour; nitrogen and phosphorus 3−, oxygen and sulfur 2− and the halogens 1−, in a second colour. Group 0, carbon and silicon are unshaded, Group 0 marked no ions. The d block is hatched, labelled more than one ion, with arrows to Fe²⁺/Fe³⁺, Cu²⁺, Zn²⁺ and Ag⁺.

Many common ions contain more than one atom, held together by covalent bonds, with a charge on the group as a whole. Their formulae and charges cannot be read off the periodic table and are learned as a set.

Where a formula needs more than one polyatomic ion, the ion goes in brackets with the number outside. Calcium hydroxide is Ca(OH)₂: one calcium ion and two whole hydroxide ions. Written CaOH₂, it would mean one oxygen atom and two hydrogen atoms, which is not calcium hydroxide. A single polyatomic ion takes no brackets, as in NaOH, CaCO₃ and NH₄Cl. Ammonium sulfate needs two ammonium ions for each sulfate, so it is (NH₄)₂SO₄.

The blue of copper(II) sulfate crystals comes from water held in the lattice. Crystalline copper(II) sulfate is a hydrated salt, CuSO₄·5H₂O, with five molecules of water of crystallisation for each CuSO₄, joined to the formula by a raised dot. Heated, the crystals lose that water as steam and crumble to white anhydrous CuSO₄. The dot is not a multiplication sign, and the 5 multiplies only the water: one CuSO₄·5H₂O holds nine oxygen atoms, four in the sulfate and five in the water. The number of waters in a hydrated salt is found by heating it to constant mass and comparing the moles of water lost with the moles of anhydrous salt left.

CuSO₄·5H₂O(s) → CuSO₄(s) + 5H₂O(g)Blue hydrated crystals become a white anhydrous powder on heating.

Polyatomic ion

An ion made of two or more atoms covalently bonded together and carrying an overall charge, such as SO₄²⁻ or NH₄⁺.

Water of crystallisation

Water molecules held in a fixed ratio within the crystal lattice of a hydrated salt.

Elements, balanced equations and state symbols

Seven elements exist as molecules of two atoms at room temperature and are always written that way when they appear as the element: hydrogen H₂, nitrogen N₂, oxygen O₂, and the halogens F₂, Cl₂, Br₂ and I₂. Hydrogen gas in an equation is H₂(g), never H. The noble gases are single atoms, He and Ar.

Metals, and non-metals with giant structures such as carbon and silicon, are written as the symbol alone, Mg(s) or C(s), because there is no small molecule to write. Sulfur and phosphorus form S₈ and P₄ molecules. Equations usually write sulfur as S(s), and phosphorus as P(s), or as P₄(s) when it burns to P₄O₁₀.

Diatomic molecule

A molecule made of two atoms, as in the elements hydrogen, nitrogen, oxygen and the halogens.

A balanced equation has the same number of atoms of each element on both sides, because in a chemical reaction atoms are rearranged, never created or lost.

The only numbers that may change while balancing are the large ones in front of each formula, the coefficients. The small subscripts belong to the formula and fix which substance it is. Changing H₂O to H₂O₂ to get more oxygen on the right does balance the oxygen, but it changes the product from water to hydrogen peroxide, which the reaction does not make.

Balancing goes faster in a sensible order. Start with an element that appears in only one formula on each side. Leave until last any element that appears on its own, such as O₂ or H₂, because its coefficient can be changed without upsetting anything else. Fractions are allowed while working. Multiply through at the end to clear them, unless one mole of a particular substance is wanted, as in the definitions of enthalpy change, where ½O₂ is kept.

The water in that equation is (l) because a state symbol describes the substance under the conditions the equation refers to, usually room temperature, as in an enthalpy of combustion. In the flame itself the water leaves as steam, and an equation written for the hot gases uses H₂O(g).

Balanced equation

An equation with the same number of atoms of each element, and the same total charge, on each side.

Coefficient

The number written in front of a formula in an equation, giving how many units of that substance react or form.

Every species in the equation for a reaction carries a state symbol: (s) solid, (l) liquid, (g) gas, (aq) aqueous. Without them an equation cannot say whether hydrogen chloride is a gas or a solution, and the two behave differently. HCl(g) is a gas of covalent molecules; HCl(aq) is hydrochloric acid, in which the molecules have given up H⁺ ions to the water.

HCl(g) + H₂O(l) → H₃O⁺(aq) + Cl⁻(aq)Hydrogen chloride dissolving in water is itself a reaction, and the state symbols show the change from gas to aqueous ions.

Aqueous means dissolved in water, which is not the same as liquid. Pure ethanol is C₂H₅OH(l); ethanol mixed with water is C₂H₅OH(aq). Water itself is H₂O(l) and is never (aq), because water cannot be dissolved in itself. Molten sodium chloride, as in electrolysis, is NaCl(l); a solution of it in water is NaCl(aq).

A solid that forms when two solutions are mixed is a precipitate, and it is written (s). Deciding which product precipitates needs a short list of solubility rules.

State symbols can often be read straight from a test tube. Fizzing means a gas is forming, (g). A solid appearing in a clear solution is a precipitate, (s). A solid that disappears as it reacts has gone into solution as aqueous ions. A solution changing colour means a coloured ion is forming or being used up, as when the blue of Cu²⁺(aq) fades. Writing the state symbols from what was seen is the reverse of predicting what will be seen, and a question can ask for either.

State symbol

A symbol after a formula giving its physical state: (s) solid, (l) liquid, (g) gas or (aq) dissolved in water.

Aqueous

Dissolved in water, shown by the state symbol (aq) in an equation.

Precipitate

An insoluble solid formed when two solutions are mixed and react.

Ionic equations and spectator ions

Barium chloride solution and sodium sulfate solution give a thick white precipitate the moment they meet. The full equation is BaCl₂(aq) + Na₂SO₄(aq) → BaSO₄(s) + 2NaCl(aq). But before mixing, the two solutions hold free ions, Ba²⁺, Cl⁻, Na⁺ and SO₄²⁻, moving about in water. Afterwards the sodium and chloride ions are still there, still dissolved, exactly as they were. They are spectator ions: present, but unchanged by the reaction.

Describe the drawing

Before and after mixing. On the left, a beaker of barium chloride solution holding 2 Ba²⁺ and 4 Cl⁻ ions, and a beaker of sodium sulfate solution holding 4 Na⁺ and 2 SO₄²⁻ ions. An arrow labelled mix leads to one beaker where 2 Ba²⁺ and 2 SO₄²⁻ are packed together as a white solid of BaSO₄ at the bottom, while 4 Na⁺ and 4 Cl⁻, each ringed as spectator ions, are still spread through the solution. Underneath: Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s).

An ionic equation leaves the spectators out and shows only what changes. For any soluble barium salt mixed with any soluble sulfate it is the same equation, Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s). Acidified barium chloride solution therefore tests for sulfate ions whatever compound they come from.

The method is the same every time. Write the balanced full equation with state symbols. Split every aqueous ionic compound, and every strong acid, into its ions, keeping the coefficients. Leave solids, liquids, gases and covalent molecules whole, because they have no free ions in solution. Cross out any ion that appears unchanged on both sides. Check that the atoms and the total charge balance.

Describe the drawing

A vertical flow of five boxes joined by arrows, with the barium sulfate example beside each. One: the full equation BaCl₂(aq) + Na₂SO₄(aq) → BaSO₄(s) + 2NaCl(aq). Two: every aqueous ionic compound split into ions. Three: BaSO₄(s) highlighted and kept whole. Four: 2Na⁺ and 2Cl⁻ struck through on both sides as spectators. Five: Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s), checked for atoms and for charge, 0 = 0.

Neutralisation simplifies in the same manner. Hydrochloric acid with sodium hydroxide, nitric acid with potassium hydroxide, any strong acid with any alkali: once the spectators are cancelled, every one is the same reaction.

H⁺(aq) + OH⁻(aq) → H₂O(l)The ionic equation for any strong acid with any alkali. Their enthalpy changes of neutralisation are all close to −57 kJ mol⁻¹ because the reaction is the same.

Spectator ion

An ion present in the reaction mixture that is unchanged by the reaction and appears identically on both sides of the equation.

Ionic equation

An equation showing only the ions and other species that take part in a reaction, with spectator ions left out.

Acids, alkalis and their salts

Four acids run through the whole course: hydrochloric acid, HCl, sulfuric acid, H₂SO₄, nitric acid, HNO₃, and ethanoic acid, CH₃COOH. In water each releases H⁺ ions. A salt forms when that hydrogen is replaced by a metal ion or an ammonium ion, so each acid gives its own family of salts. The common alkalis are sodium hydroxide, NaOH, potassium hydroxide, KOH, and aqueous ammonia, NH₃(aq), which takes H⁺ to become NH₄⁺ and so makes ammonium salts: NH₃(aq) + HCl(aq) → NH₄Cl(aq).

Acids react with metal oxides to give a salt and water, and with carbonates to give a salt, water and carbon dioxide, which is the fizz. Ionic equations for these follow the same method, with one caution. Ethanoic acid is a weak acid: most of its molecules stay whole in water, so it is written CH₃COOH(aq) and not split. Only the strong acids, hydrochloric, sulfuric and nitric, are split into H⁺(aq) and their negative ions.

CuO(s) + H₂SO₄(aq) → CuSO₄(aq) + H₂O(l)A metal oxide and an acid: black solid dissolves to a blue solution.

Salt

A compound formed when the hydrogen ions of an acid are replaced by metal ions or ammonium ions.

Half-equations: a first look

Magnesium displaces copper from copper(II) sulfate solution: the metal is coated with brown copper as the blue fades. With sulfate cancelled as a spectator, the ionic equation is Mg(s) + Cu²⁺(aq) → Mg²⁺(aq) + Cu(s). Each magnesium atom has lost two electrons, and each copper(II) ion has gained two.

A half-equation shows one of those changes on its own, with the electrons written in.

Mg(s) → Mg²⁺(aq) + 2e⁻Magnesium loses electrons, which is oxidation.

Cu²⁺(aq) + 2e⁻ → Cu(s)Copper(II) ions gain electrons, which is reduction.

A half-equation balances charge as well as atoms, and the electrons make the two sides equal. In the first, the charge on the left is 0, and on the right it is +2 + 2 × (−1) = 0. In the second, the left is +2 + 2 × (−1) = 0 and the right is 0.

Adding two half-equations with the same number of electrons cancels the electrons and gives the ionic equation back. When the numbers differ, one or both are multiplied first. Aluminium loses three electrons per atom and copper(II) gains two, so 2Al and 3Cu²⁺ transfer six electrons between them: 2Al(s) + 3Cu²⁺(aq) → 2Al³⁺(aq) + 3Cu(s). Half-equations for ions such as manganate(VII) also balance oxygen with water and hydrogen with H⁺ ions, and follow the same rule: atoms first, then electrons to balance the charge.

Half-equation

An equation for the oxidation or the reduction half of a redox reaction on its own, with electrons shown to balance the charge.

Other boards: the acids list and equations from observations

OCR A names the four acids and three alkalis of the acids table in its acids statement, 2.1.4: hydrochloric, sulfuric, nitric and ethanoic acids, and sodium hydroxide, potassium hydroxide and aqueous ammonia. The same statement asks for the full and ionic equations of acids with carbonates, metal oxides and alkalis, so an OCR question can name any of those reactions and expect both equations with state symbols.

Edexcel sets writing equations from observations as a statement of its own, 5.15. A question describes a test tube, fizzing, a precipitate, a colour fading, and the state symbols follow from what was seen: fizzing gives (g), a solid appearing gives (s), a solid dissolving gives aqueous ions. Cambridge sets formulae and equations in 2.3 with the same expectations as AQA.