Topic 06 · Chemical Formulae and Equations

Chemical Formulae and Equations

1

Chemical Formulae

1.1What a formula tells you

A chemical formula shows the elements in a substance and the ratio of their atoms.
OOCcarbon dioxide, CO₂1 carbon atom, 2 oxygen atomsHHOwater, H₂O2 hydrogen atoms, 1 oxygen atom
  • The symbols show which elements are present. The subscripts show how many atoms of each.
  • CO2: one carbon atom and two oxygen atoms. H2O: two hydrogen atoms and one oxygen atom.
  • The prefix di- means two. Carbon dioxide has two oxygen atoms.

1.2Formulae of elements

Monoatomic

Single, uncombined atoms. The Group 18 elements, such as neon (Ne) and argon (Ar), have full outer shells.

Diatomic

Two atoms joined: H2, N2, O2, F2, Cl2, Br2, I2.

Polyatomic

Three or more atoms joined, such as phosphorus and ozone (O3).

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Chemical Formulae (continued)

1.3Formulae of compounds

  • A subscript outside brackets multiplies everything inside them. Ca(NO3)2 has 1 calcium, 2 nitrogen and 6 oxygen atoms.
Ca(NO₃)₂=Ca+OOON+OOONCa²⁺NO₃⁻NO₃⁻2+−−1 Ca2 N6 O
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Constructing Formulae

2.1Valency

Valency is the number of electrons an atom must lose, gain or share to get a noble gas configuration. The valency of an ion is its charge without the sign.
Group121314151617
ExamplesLi, Na, KBe, Mg, CaB, AlC, SiN, PO, SF, Cl, Br, I
Valency1234321
NoteTransition metals can form more than one ion. A Roman numeral shows the valency: iron(II) is Fe2+, iron(III) is Fe3+, copper(II) is Cu2+, copper(I) is Cu+. Zinc (Zn2+) and silver (Ag+) have only one common ion.

2.2Polyatomic ions

NameFormulaValencyNameFormulaValency
ammoniumNH4+1sulfateSO42−2
hydroxideOH−1carbonateCO32−2
nitrateNO3−1phosphatePO43−3
NoteA polyatomic ion stays together as one unit. Put it in brackets when more than one is needed, e.g. Mg(NO3)2.
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Constructing Formulae (continued)

2.3The crossing method

CO42241write the valencies, then cross them over: C₂O₄CO₂2simplify 2 : 4 to 1 : 2
  1. Write the symbols and their valencies below.
  2. Cross the valencies: each valency becomes the subscript of the other element.
  3. Simplify the ratio if possible. C2O4 becomes CO2.

2.4Worked examples

Worked exampleWrite the formula of sodium phosphate.

Sodium has valency 1 (Na+). Phosphate is a polyatomic ion with valency 3 (PO43−).Three Na+ are needed to cancel one PO43−.The formula is Na3PO4.

Worked exampleWrite the formula of magnesium nitrate.

Magnesium has valency 2 (Mg2+). Nitrate has valency 1 (NO3−).Two NO3− are needed. Put the polyatomic ion in brackets before the subscript 2.The formula is Mg(NO3)2.

2.5Finding a charge from a formula

Worked exampleFind the charge on the Al ion in KAl(SO4)2.

The compound is neutral, so the total charge is 0.Let the charge on Al be x: 0 = (+1) + x + 2(−2).So x = +3.
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Constructing Formulae (continued)

2.6Practice with formulae

CompoundIons and valenciesFormula
calcium chlorideCa2+ (2) and Cl− (1)CaCl2
silver phosphateAg+ (1) and PO43− (3)Ag3PO4
iron(III) sulfateFe3+ (3) and SO42− (2)Fe2(SO4)3
aluminium oxideAl3+ (3) and O2− (2)Al2O3
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Chemical Equations

3.1Word and chemical equations

sodium + chlorine → sodium chloride

2Na(s) + Cl2(g) → 2NaCl(s)

NaNa+ClClNaClNaCl2NaCl₂2NaCl
  • Reactants go on the left of the arrow and products on the right.
  • The number in front of a formula is the number of units reacting or formed.
  • State symbols show the physical state: (s) solid, (l) liquid, (g) gas, (aq) aqueous, which means dissolved in water.
NoteThe same substance can have a different state in different reactions. Sodium chloride is (s) when it forms from sodium and chlorine, but (aq) when it forms in a solution.

3.2Balancing an equation

HH+OOHHOH₂ + O₂ → H₂O: 2 O on the left, 1 O on the rightHHHHOHH+OOHHO2H₂ + O₂ → 2H₂O: 4 H and 2 O on each side
  1. From the word equation (hydrogen + oxygen → water), write the correct formulae for reactants and products.
  2. Count the atoms of each element on both sides.
  3. Add numbers in front of formulae to balance. Never change a subscript.
  4. Add the state symbols: 2H2(g) + O2(g) → 2H2O(l).
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Chemical Equations (continued)

3.3Balancing with a solid and a gas

Worked exampleIron(III) oxide reacts with carbon monoxide to form iron and carbon dioxide. Write the balanced equation with state symbols.

Formulae: Fe2O3 + CO → Fe + CO2.Two iron atoms on the left need 2Fe. Three oxygen atoms in Fe2O3 are removed as CO2, so use 3CO and 3CO2.Fe2O3(s) + 3CO(g) → 2Fe(s) + 3CO2(g)

3.4A harder equation

Worked exampleAqueous iron(III) sulfate reacts with aqueous barium nitrate to form aqueous iron(III) nitrate and solid barium sulfate. Write the equation with state symbols.

Formulae: Fe2(SO4)3 + Ba(NO3)2 → Fe(NO3)3 + BaSO4.Balance the ions. Two Fe3+ need 2Fe(NO3)3. Three SO42− need 3BaSO4, so 3Ba(NO3)2.Fe2(SO4)3(aq) + 3Ba(NO3)2(aq) → 2Fe(NO3)3(aq) + 3BaSO4(s)

3.5Ionic equations

  1. Write the balanced equation with state symbols.
    NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)
  2. Split the aqueous substances into ions.
    Na+ + OH− + H+ + Cl− → Na+ + Cl− + H2O(l)
  3. Cancel the spectator ions, which appear unchanged on both sides.
  4. What remains is the ionic equation: H+(aq) + OH−(aq) → H2O(l)
Na⁺OH⁻H⁺Cl⁻Na⁺Cl⁻HHOspectator ions Na⁺ and Cl⁻ are unchanged, so they cancel
  • Solids, gases and liquids such as water are not split into ions.
  • Write the quantity in front of an ion: H2SO4(aq) splits into 2H+(aq) + SO42−(aq).
  • Aqueous covalent substances such as aqueous chlorine are not split: Cl2(g) + 2I−(aq) → 2Cl−(aq) + I2(aq).
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Chemical Equations (continued)

3.6An ionic equation with a solid and a gas

Worked exampleWrite the ionic equation for ZnCO3(s) + 2HNO3(aq) → Zn(NO3)2(aq) + CO2(g) + H2O(l).

Split only the aqueous substances: 2H+ + 2NO3− and Zn2+ + 2NO3−. Keep ZnCO3(s), CO2(g) and H2O(l) whole.Cancel the spectator ions, 2NO3−(aq).ZnCO3(s) + 2H+(aq) → Zn2+(aq) + CO2(g) + H2O(l)

3.7A precipitation reaction

Worked exampleWrite the ionic equation for AgNO3(aq) + HCl(aq) → AgCl(s) + HNO3(aq).

Split the aqueous substances: Ag+ + NO3− + H+ + Cl− → AgCl(s) + H+ + NO3−.Cancel the spectator ions, H+ and NO3−. The solid AgCl stays whole.Ag+(aq) + Cl−(aq) → AgCl(s)

3.8Common mistakes to avoid

  • Changing a subscript to balance an equation. Subscripts belong to the formula of the substance, so only change the number in front.
  • Forgetting the brackets in a formula such as Mg(NO3)2.
  • Writing hydrogen as H instead of H2. The diatomic elements are H2, N2, O2, F2, Cl2, Br2 and I2.
  • Splitting a solid, a gas or water into ions in an ionic equation.
  • Leaving the state symbols out when the question asks for them.
Exam tipAfter you balance, count the atoms of every element one last time. Check the charges too in an ionic equation.
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