Formulae and Equations

This lesson covers: 

  1. How to balance chemical equations
  2. State symbols
  3. How to write ionic equations
  4. Using balanced equations to calculate reactant and product masses

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 (C3H8) 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

C3H8O2➔CO2H2O
C31
H82
O221


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

C3H85O2➔3CO24H2O
C33
H88
O1064

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:

CaCO3(s) + 2HCl(aq) ➔ CaCl2(aq) + H2O(l) + CO2(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

AgNO3(aq) + NaCl(aq) ➔ AgCl(s) + NaNO3(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.

Using balanced equations to calculate masses

Balanced equations show molar ratios between reactants and products. By rearranging ratios and using molar masses, you can calculate:

  • Mass of product from given mass of reactant.
  • Mass of reactant needed to produce a given mass of product.


The steps to calculate reacting masses are:

  1. Write out the balanced equation.
  2. Convert given mass into moles.
  3. Use the mole ratio from the equation to calculate moles of the desired species.
  4. Convert moles of the desired species into mass.

Worked example 3 - Calculating mass of product

50.0 g of calcium carbonate reacts with excess hydrochloric acid to produce calcium chloride, water, and carbon dioxide.

Calculate the mass (in g) of carbon dioxide produced.


Step 1: Write out the balanced equation

CaCO3(s) + 2HCl(aq) ➔ CaCl2(aq) + H2O(l) + CO2(g)


Step 2: Calculate moles of CaCO3

moles of CaCO3​=Mr​mass​=100.150.0​=0.4995 mol


Step 3: Calculate moles of CO2 produced

CaCO3 : CO2 mole ratio = 1:1

Moles of CO2 = 0.4995 mol


Step 4: Calculate mass of CO2

mass of CO2 = moles x Mr = 0.4995 x 44.0 = 22.0 g

Worked example 4 - Calculating mass of reactant

Calculate the mass (in g) of aluminium (Al) required to react completely with oxygen (O2) to produce 100.0 g of aluminium oxide (Al2O3).


Step 1: Write out the balanced equation

4Al(s) + 3O2(g) ➔ 2Al2O3(s)


Step 2: Calculate moles of Al2O3

moles of Al2​O3​=Mr​ mass​=102.0100.0​=0.980 mol


Step 3: Calculate moles of Al required

Al2O3 : Al mole ratio = 2:4 = 1:2

Moles of Al required = 0.980 × 2 = 1.960 mol


Step 4: Calculate mass of Al

mass of Al = moles x Ar = 1.960 x 27.0 = 52.9 g