Constructing and Balancing Equations
This topic covers how to represent chemical changes using balanced equations. Mastering this skill is fundamental for describing reaction stoichiometry, ionic interactions, and electron transfer in redox processes.
Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- A balanced chemical equation conserves mass by ensuring the number of atoms of each element is identical on both the reactant and product sides.
- Stoichiometric coefficients (the numbers in front of formulae) are adjusted to balance the atoms; the chemical formulae themselves must never be changed.
- Ionic equations show only the species that are directly involved in the reaction by omitting 'spectator ions' which remain unchanged in solution.
- Half-equations describe either oxidation (loss of electrons) or reduction (gain of electrons) processes separately, showing the electrons explicitly.
- In ionic and half-equations, both the atoms and the overall electrical charge must be balanced on both sides of the arrow.
Formulae
Reactants → Products The general structure for all chemical equations, where the arrow indicates a chemical transformation.
Species → Oxidised Species + n e- The general form of an oxidation half-equation, where 'n' is the number of electrons lost.
Species + n e- → Reduced Species The general form of a reduction half-equation, where 'n' is the number of electrons gained.
Definitions
- Spectator Ion
- An ion that exists in the same form on both the reactant and product sides of a chemical equation, and thus does not actively participate in the chemical change.
- Ionic Equation
- A simplified chemical equation that only includes the particles (ions, atoms, or molecules) that undergo a chemical change in an aqueous reaction.
- Half-Equation
- An equation that represents either the oxidation or reduction part of a redox reaction, showing the explicit loss or gain of electrons.
Worked example
Aqueous solutions of iron(III) chloride (FeCl₃) and sodium hydroxide (NaOH) are mixed, forming a solid precipitate of iron(III) hydroxide and an aqueous solution of sodium chloride. Write the balanced net ionic equation for this reaction.
- 1
Step 1:
Write the full balanced molecular equation.
Start by writing the reactants and products:
FeCl₃(aq) + NaOH(aq) → Fe(OH)₃(s) + NaCl(aq).
- 2
Step 2:
Balance the atoms.
We need 3 Cl on the right, so 3 NaCl.
This gives 3 Na, so we need 3 NaOH.
This gives 3 OH, which matches Fe(OH)₃.
The equation is:
FeCl₃(aq) + 3NaOH(aq) → Fe(OH)₃(s) + 3NaCl(aq).
- 3
Step 3:
Write the full ionic equation by dissociating all aqueous (aq) species into their ions:
Fe³⁺(aq) + 3Cl⁻(aq) + 3Na⁺(aq) + 3OH⁻(aq) → Fe(OH)₃(s) + 3Na⁺(aq) + 3Cl⁻(aq).
- 4
Step 4:
Identify and cancel the spectator ions.
The Na⁺ and Cl⁻ ions appear on both sides and can be removed.
- 5
Step 5:
Write the final net ionic equation with the remaining species.
Check that atoms and charge are balanced (Reactants:
1 Fe, 3 O, 3 H, charge = 3+ + 3- = 0.
Products:
1 Fe, 3 O, 3 H, charge = 0).
Answer: Fe³⁺(aq) + 3OH⁻(aq) → Fe(OH)₃(s)
Common mistakes
- ×Using incorrect chemical formulae for common elements or polyatomic ions (e.g., writing O instead of O₂ for oxygen gas, or SO₄⁻ instead of SO₄²⁻ for sulfate).
- ×Making simple arithmetic errors when counting atoms on each side. Always perform a final check of every element once you think the equation is balanced.
- ×Forgetting to balance the net charge in ionic or half-equations. The sum of charges on the left must equal the sum of charges on the right.
- ×Leaving the final stoichiometric coefficients as a non-simplified ratio. If your final equation is 2A + 4B → 2C, it should be simplified to A + 2B → C.
No-calculator tips
- ✓Balance elements systematically. Start with elements that appear in only one compound on each side, and leave common elements like H and O until last.
- ✓Use the 'OIL RIG' mnemonic (Oxidation Is Loss, Reduction Is Gain) to remember where to place electrons in half-equations.
- ✓To balance complex equations, especially combustion, follow the order: C, then H, then O. This often simplifies the process.
- ✓When writing ionic equations, focus on what changes state (e.g., aqueous to solid) or what is formed (e.g., water from H⁺ and OH⁻). These are the key players.