Balancing chemical equations

A balanced chemical equation has equal numbers of atoms for each element on both sides of the equation.

To balance an equation:

1. Write out the unbalanced equation.
2. Count the number of atoms of each element on both sides.
3. Add coefficients before formulas to balance atom numbers.
4. Check if atom numbers are equal on both sides.

You cannot alter the chemical formulas themselves.

Balanced equations obey the law of conservation of mass, showing that the same mass is retained before and after a reaction.

Worked example 1 - Balancing the complete combustion of propane

Balance the equation for the complete combustion of propane (C_3_H_8_) with oxygen to form carbon dioxide and water.

Step 1: Write out the unbalanced equation

C₃H₈ + O₂ ➔ CO₂ + H₂O

Step 2: Count the number of atoms of each element on both sides

Step 3: Add coefficients before formulas to balance atom numbers

• Start with carbon: To balance 3 C atoms in propane, add a coefficient of 3 to CO₂.
• Next, balance hydrogen: To balance 8 H atoms, H₂O needs a coefficient of 4 (since each molecule has 2 H atoms).
• Finally, balance oxygen: There are now 3(2) + 4 = 10 O atoms required for CO₂ and H₂O. Since O₂ has 2 O atoms, you need 5 molecules of O₂ to provide 10 O atoms.

Step 4: Check if atom numbers are equal on both sides

The balanced equation is:

C₃H₈ + 5O₂ ➔ 3CO₂ + 4H₂O

This balances the equation, ensuring the law of conservation of mass is satisfied.

State symbols

State symbols are written after chemical formulas or names of substances in chemical equations. They indicate the physical state of each reactant and product.

Common state symbols are:

• (s) - solid
• (l) - liquid
• (g) - gas
• (aq) - aqueous (dissolved in water)

For example:

CaCO_3(s) + 2HCl_(aq) ➔ CaCl_2(aq) + H₂O_(l) + CO_2(g)

The state symbols show that:

• Calcium carbonate (CaCO₃) is a solid.
• Hydrochloric acid (HCl) and calcium chloride (CaCl₂) are aqueous solutions.
• Water (H₂O) is a liquid
• Carbon dioxide (CO₂) is a gas.

Ionic equations for reactions in aqueous solution

Many reactions occur between ions dissolved in aqueous solution. For these reactions, you can write an ionic equation which shows only the particles directly involved in the reaction.

To write an ionic equation:

1. Write out the full balanced equation.
2. Split soluble ionic compounds into their component ions.
3. Cancel out any ions that appear unchanged on both sides (called spectator ions).
4. Check ionic charges balance on both sides.

Worked example 2 - Writing an ionic equation for the precipitation of silver chloride

A solution of silver nitrate reacts with sodium chloride to form silver chloride precipitate and sodium nitrate solution.

Write the ionic equation.

Step 1: Write out the full balanced equation including state symbols

AgNO_3(aq) + NaCl_(aq) ➔ AgCl_(s) + NaNO_3(aq)

Step 2: Split soluble ionic compounds into their component ions

Ag⁺_(aq) + NO₃⁻_(aq) + Na⁺_(aq) + Cl⁻_(aq) ➔ AgCl_(s) + Na⁺_(aq) + NO₃⁻_(aq)

Step 3: Cancel out spectator ions

Ag⁺_(aq) + Cl⁻_(aq) ➔ AgCl_(s)

Step 4: Check ionic charges balance on both sides

Charges balance: +1 from Ag⁺ and -1 from Cl⁻ equals 0, indicating a neutral compound is formed.

Acids react with metals and metal compounds

1. Acids with metals - Acids react with sufficiently reactive metals in a redox reaction, producing a salt and hydrogen: Metal + acid ➔ salt + hydrogen

For example, calcium reacting with sulfuric acid: Ca_(s)_ + H_2_SO_4(aq)_ ➔ CaSO_4(aq)_ + H_2(g)_

The ionic equation is: Ca_(s) + 2H⁺_(aq) ➔ Ca²⁺_(aq) + H_2(g)

1. Acids with metal oxides - These neutralisation reactions yield a salt and water: Metal oxide + acid ➔ salt + water

For example, zinc oxide with hydrochloric acid: ZnO_(s)_ + 2HCl_(aq)_ ➔ ZnCl_2(aq)_ + H_2_O_(l)_

The ionic equation is: ZnO_(s) + 2H⁺_(aq) ➔ Zn²⁺_(aq) + H₂O_(l)

1. Acids with metal hydroxides - These neutralisation reactions also yield a salt and water. Metal hydroxides that dissolve in water are called alkalis. Metal hydroxide + acid ➔ salt + water

Alkali + acid ➔ salt + water

For example, zinc hydroxide with hydrochloric acid: Zn(OH)2(s) + 2HCl_(aq)_ ➔ ZnCl_2(aq)_ + 2H_2_O_(l)_

The ionic equation is: Zn(OH)_2(s) + 2H⁺_(aq) ➔ Zn²⁺_(aq) + 2H₂O_(l)

Alternatively, alkali sodium hydroxide reacts with sulfuric acid: 2NaOH_(aq)_ + H_2_SO_4(aq)_ ➔ Na_2_SO_4(aq)_ + 2H_2_O_(l)_

The ionic equation is: OH^-_(aq) + H⁺_(aq) ➔ H₂O_(l)

1. Acids with metal carbonates - These neutralisation reactions produce a salt, water, and carbon dioxide: Metal carbonate + acid ➔ salt + water + carbon dioxide

For example, sodium carbonate with hydrochloric acid: Na_2_CO_3(s)_ + 2HCl_(aq)_ ➔ 2NaCl_(aq)_ + H_2_O_(l)_ + CO_2(g)_

The ionic equation is: CO₃^2-_(aq) + 2H⁺_(aq) ➔ H₂O_(l) + CO_2(g)

1. Acids with metal hydrogencarbonates - These neutralisation reactions also produce a salt, water and carbon dioxide: Metal hydrogencarbonate + acid ➔ salt + water + carbon dioxide

For example, sodium hydrogencarbonate with hydrochloric acid: NaHCO_3(s)_ + HCl_(aq)_ ➔ NaCl_(aq)_ + H_2_O_(l)_ + CO_2(g)_

The ionic equation is: HCO₃^-_(aq) + H⁺_(aq) ➔ H₂O_(l) + CO_2(g)

Displacement reactions

Displacement reactions are redox reactions in which one element replaces another, less reactive, element in a compound.

Displacement reactions involving metals

A more reactive metal displaces a less reactive metal from one of its salts.

For example, magnesium will displace copper from a copper sulfate solution: Mg_(s) + CuSO_4(aq) ➔ MgSO_4(aq) + Cu_(s)

The ionic equation is: Mg_(s) + Cu²⁺_(aq) ➔ Mg²⁺_(aq) + Cu_(s)

In this reaction:

• The blue colour of the copper(II) sulfate solution fades.
• Magnesium metal becomes coated with brown copper.
• Colourless magnesium sulfate forms in the solution.

Displacement reactions involving halogens

A more reactive halogen displaces a less reactive halogen from one of its salts.

For example, chlorine will displace bromine from a sodium bromide solution: Cl_2(aq) + 2NaBr_(aq) ➔ 2NaCl_(aq) + Br_2(aq)

The ionic equation is: Cl_2(aq) + 2Br^-_(aq) ➔ 2Cl^-_(aq) + Br_2(aq)

In this reaction:

• The colourless potassium bromide solution turns yellow-orange.
• If an organic solvent like hexane is added and shaken, an orange layer forms on top.

Precipitation reactions

Precipitation reactions are reactions in which an insoluble solid is formed when two solutions are mixed. Precipitation reactions are used in the chemical tests for carbon dioxide, sulfate ions and halide ions.

1. Test for carbon dioxide When carbon dioxide is bubbled through calcium hydroxide solution (limewater), the limewater turns cloudy due to the formation of a white precipitate of calcium carbonate.

The equation is: Ca(OH)_2(aq) + CO_2(g) ➔ CaCO_3(s) + H₂O_(l)

1. Test for sulfate ions The presence of sulfate ions can be shown by the addition of aqueous barium ions (from solutions of barium chloride or barium nitrate).The white precipitate that forms is barium sulfate.

For example, when barium chloride is added to sodium sulfate, the equation is: Na₂SO_4(aq) + BaCl_2(aq) ➔ BaSO_4(s) + 2NaCl_(aq)

The ionic equation is: SO₄^2-_(aq) + Ba²⁺_(aq) ➔ BaSO_4(s)

1. Test for halide ions The presence of halide ions can be shown by the addition of aqueous silver ions (from a solution of silver nitrate). The precipitates that form are silver halides.

For example, when silver nitrate is added to sodium chloride, the equation is: NaCl_(aq) + AgNO_3(aq) ➔ AgCl_(s) + NaNO_3(aq)

The ionic equation is: Cl^-_(aq) + Ag⁺_(aq) ➔ AgCl_(s)

The halide ion can be identified by the colour of the precipitate: