Construct symbol equations with state symbols, including ionic equations

Constructing Symbol Equations with State Symbols (including Ionic Equations)

Learning Objectives (Cambridge AO1‑AO3)

• AO1: Recall and use correct chemical symbols, formulae, state symbols, ion charges, isotopes and oxidation numbers.
• AO2: Apply the law of conservation of mass to balance chemical equations and use mole‑ratio calculations.
• AO3: Analyse reactions by writing complete and net ionic equations, identifying spectator ions and, where relevant, half‑equations for redox processes.

How This Topic Links to the Rest of the Syllabus

1. States of Matter & the Kinetic‑Particle Model

• Solids (s): Particles vibrate in fixed positions; definite shape and volume.
• Liquids (l): Particles are close together but can move past one another; take the shape of the container but retain a fixed volume.
• Gases (g): Particles are far apart and move rapidly in all directions; fill any container (diffusion, effusion).
• Aqueous (aq): Species dissolved in water; ionic compounds are present as separated ions that can move freely.

These ideas explain why a precipitate is written (s) – particles have lost the freedom to move – and why a gas that bubbles out of solution is written (g).

2. Atoms, Ions, Isotopes & the Periodic Table

2.1 Key Concepts

• Atoms consist of protons (+), neutrons (0) and electrons (–). The number of protons = atomic number.
• Isotopes: Same number of protons, different numbers of neutrons. Chemically identical, but have different atomic masses.
• Electrons occupy shells (K, L, M …). The outer‑most shell (valence shell) determines chemical reactivity.
• Ions form when atoms gain (–) or lose (+) electrons. The charge on an ion equals the difference between protons and electrons.
• Oxidation number = charge on the ion in an ionic compound; useful for identifying redox changes.

2.2 Electronic‑Configuration Cheat‑Sheet (IGCSE level)

2.3 Common Ions (selected for IGCSE)

2.4 Periodic‑Group Highlights (reaction relevance)

• Group 1: Very reactive, form soluble +1 cations; always appear as spectator ions unless they form an insoluble salt (e.g., AgCl).
• Group 2: Form +2 cations; carbonates become less soluble down the group – useful for predicting precipitation.
• Group 7: Form –1 anions; most of their salts are soluble, exceptions include Ag⁺, Pb²⁺, Hg₂²⁺.
• Transition metals: Variable charges, coloured ions and precipitates (e.g., Cu²⁺ → Cu(OH)₂(s)).

3. Writing Chemical Formulae

1. Identify the charges of the constituent ions.
2. Cross‑multiply to obtain the smallest whole‑number ratio that gives a neutral compound.
3. Write the cation first, the anion second; use subscripts for numbers > 1 and parentheses for polyatomic ions that appear more than once.

Example: Calcium nitrate → Ca²⁺ + 2 NO₃⁻ ⇒ Ca(NO₃)₂

4. State Symbols

Use solubility rules (see the box below) to decide whether an ionic compound is written (aq) or (s).

Solubility Quick‑Reference (IGCSE)

5. The Mole Concept & Stoichiometry

• Mole (mol): The amount of substance containing 6.022 × 10²³ entities (Avogadro’s number).
• Molar mass (M): Mass (in g) of one mole of a substance; numerically equal to the relative atomic/molecular mass.
• From a balanced symbol equation you obtain the **mole ratio** between any two species.
• Typical calculations:
  • Mass ↔ moles (using M)
  • Limiting‑reactant determination
  • Theoretical yield → % yield

Worked Example – Mass‑Mass Calculation

Given the balanced equation
$$\mathrm{2H_2}(g)+\mathrm{O_2}(g)\rightarrow\mathrm{2H_2O}(l)$$

How many grams of water are produced from 10.0 g of H₂?

1. Calculate moles of H₂: \(n=\frac{10.0\ \text{g}}{2.02\ \text{g mol}^{-1}}=4.95\ \text{mol}\).
2. From the mole ratio, 2 mol H₂ → 2 mol H₂O, so moles H₂O = 4.95 mol.
3. Mass of H₂O = \(4.95\ \text{mol}\times18.02\ \text{g mol}^{-1}=89.2\ \text{g}\).

6. Steps to Write a Balanced Symbol Equation

1. Identify reactants and products. Use correct formulas (Section 3).
2. Write the un‑balanced equation.
3. Balance atoms. Start with the most complex species; then balance the simpler ones.
4. Balance total charge. Only necessary for ionic equations; the sum of oxidation numbers on each side must be equal.
5. Attach state symbols. Apply the solubility rules (see Section 4).

7. From Symbol Equation to Ionic Equations

7.1 Complete Ionic Equation

• Split every strong electrolyte (soluble salt, strong acid, strong base) into its constituent ions.
• Keep insoluble solids, gases and weak electrolytes in molecular form.

7.2 Spectator Ions

• Ions that appear unchanged on both sides of the complete ionic equation.
• They do not participate in the actual chemical change.

7.3 Net Ionic Equation

• Cancel the spectator ions.
• The remaining species represent the observable change (precipitate, gas, colour change, etc.).

8. Redox Reactions & Half‑Equations

1. Assign oxidation numbers to all atoms in the reactants and products.
2. Identify which atoms are oxidised (increase in oxidation number) and which are reduced (decrease).
3. Write separate oxidation and reduction half‑equations, balancing O atoms with H₂O and H atoms with H⁺ (or OH⁻ in basic media).
4. Balance charge in each half‑equation by adding electrons.
5. Multiply the half‑equations to equalise the number of electrons transferred and add them together.
6. Combine with the spectator ions to give the full balanced redox (symbol) equation; then derive the ionic forms if required.

Redox Example – Zinc displaces copper

Balanced symbol equation:

Oxidation numbers: Zn 0 → Zn²⁺ (+2), Cu²⁺ → Cu 0 (‑2).

Half‑equations:

• Oxidation: \(\mathrm{Zn}(s)\rightarrow\mathrm{Zn^{2+}}(aq)+2e^-\)
• Reduction: \(\mathrm{Cu^{2+}}(aq)+2e^-\rightarrow\mathrm{Cu}(s)\)

Adding gives the same overall equation; the net ionic form is:

9. Common Types of Reactions Tested

9.1 Acid‑Base Neutralisation

General form: acid(aq) + base(aq) → salt(aq) + water(l)

Example:

9.2 Precipitation (Double‑Replacement) Reactions

When two aqueous solutions are mixed, an insoluble product (precipitate) may form.

Example: Silver nitrate + sodium chloride

9.3 Gas‑Evolution Reactions

Typical when an acid reacts with a carbonate, bicarbonate or a metal.

Example: Hydrochloric acid + calcium carbonate

9.4 Redox (Displacement) Reactions

Identify oxidation‑reduction, write half‑equations, combine.

Example: Iron(II) sulphate + potassium permanganate in acidic medium

10. Practical Tips for the Exam

• Check solubility rules before assigning (aq) or (s).
• Strong acids (HCl, H₂SO₄, HNO₃, HBr, HI) and strong bases (NaOH, KOH, Ca(OH)₂) dissociate completely – treat them as ions in the complete ionic equation.
• Write gases as (g) even if they are observed as bubbles.
• Keep solids that do not dissolve (e.g., CaCO₃) as (s).
• Balance atoms first, then balance the total charge.
• Use the “spectator‑ion” method: write the complete ionic equation, cancel identical ions on both sides, and record the net ionic equation.
• For redox, always show the half‑equations in your working – examiners award marks for correct identification of oxidation and reduction.

11. Quick Checklist (before finalising an answer)

1. Correct formulas (subscripts, parentheses, polyatomic ions)?
2. All atoms balanced?
3. Total charge balanced?
4. State symbols correct using solubility rules?
5. Identify strong electrolytes → split into ions for the complete ionic equation.
6. Cancel spectator ions → net ionic equation.
7. If redox, have oxidation numbers and half‑equations been shown?
8. Does the net ionic equation represent the observable change (precipitate, gas, colour change)?

12. Practice Questions (with Answers)

1. Reaction: Potassium sulphate K₂SO₄(aq) + barium nitrate Ba(NO₃)₂(aq).
   1. Symbol equation:
      $$\mathrm{K_2SO_4}(aq)+\mathrm{Ba(NO_3)_2}(aq)\rightarrow\mathrm{BaSO_4}(s)+2\mathrm{KNO_3}(aq)$$
   2. Complete ionic equation:
      $$2\mathrm{K^+}(aq)+\mathrm{SO_4^{2-}}(aq)+\mathrm{Ba^{2+}}(aq)+2\mathrm{NO_3^-}(aq)\rightarrow\mathrm{BaSO_4}(s)+2\mathrm{K^+}(aq)+2\mathrm{NO_3^-}(aq)$$
   3. Net ionic equation:
      $$\mathrm{Ba^{2+}}(aq)+\mathrm{SO_4^{2-}}(aq)\rightarrow\mathrm{BaSO_4}(s)$$
2. Reaction: Hydrochloric acid HCl(aq) with magnesium metal Mg(s).
   1. Balanced symbol equation:
      $$2\mathrm{HCl}(aq)+\mathrm{Mg}(s)\rightarrow\mathrm{MgCl_2}(aq)+\mathrm{H_2}(g)$$
   2. Complete ionic equation:
      $$2\mathrm{H^+}(aq)+2\mathrm{Cl^-}(aq)+\mathrm{Mg}(s)\rightarrow\mathrm{Mg^{2+}}(aq)+2\mathrm{Cl^-}(aq)+\mathrm{H_2}(g)$$
   3. Net ionic equation:
      $$2\mathrm{H^+}(aq)+\mathrm{Mg}(s)\rightarrow\mathrm{Mg^{2+}}(aq)+\mathrm{H_2}(g)$$
3. Quantitative problem (stoichiometry): 5.00 g of Na₂CO₃(s) reacts with excess HCl(aq). Calculate the mass of CO₂(g) produced.
   
   1. Balanced equation:
      $$\mathrm{Na_2CO_3}(s)+2\mathrm{HCl}(aq)\rightarrow2\mathrm{NaCl}(aq)+\mathrm{CO_2}(g)+\mathrm{H_2O}(l)$$
   2. Moles of Na₂CO₃: \(n=\frac{5.00\ \text{g}}{105.99\ \text{g mol}^{-1}}=0.0472\ \text{mol}\).
   3. From the mole ratio, 1 mol Na₂CO₃ → 1 mol CO₂, so \(n_{\text{CO}_2}=0.0472\ \text{mol}\).
   4. Mass of CO₂: \(0.0472\ \text{mol}\times44.01\ \text{g mol}^{-1}=2.08\ \text{g}\).
4. Redox half‑equation practice: Write the half‑equations for the reaction of zinc metal with copper(II) sulphate.
   
   • Oxidation (Zn → Zn²⁺):
     \(\mathrm{Zn}(s)\rightarrow\mathrm{Zn^{2+}}(aq)+2e^-\)
   • Reduction (Cu²⁺ → Cu):
     \(\mathrm{Cu^{2+}}(aq)+2e^-\rightarrow\mathrm{Cu}(s)\)