Deduce the formula of an ionic compound from the relative numbers of the ions present in a model or a diagrammatic representation or from the charges on the ions

Stoichiometry – Formulae

What is an ionic compound?

An ionic compound is made up of positively charged ions (cations) and negatively charged ions (anions) held together by electrostatic forces.

The overall charge of the compound must be zero – the total positive charge must balance the total negative charge.

🔬 Think of it like a perfectly balanced see‑saw: every weight on one side has a matching weight on the other side.

Step‑by‑step guide to deducing the formula

  1. Write the ions and their charges.

    • Example: \$Na^+\$, \$Cl^-\$

    • Example: \$Fe^{3+}\$, \$O^{2-}\$

  2. Find the least common multiple (LCM) of the absolute values of the charges.

    LCM gives the total charge that each side must reach.

  3. Multiply each ion by the factor needed to reach the LCM.

    For \$Fe^{3+}\$ and \$O^{2-}\$, LCM = 6.

    \$Fe^{3+} \times 2 = +6\$, \$O^{2-} \times 3 = -6\$.

  4. Write the ratio of the ions.

    From the example above: \$Fe2O3\$.

  5. Reduce the ratio to the simplest whole‑number form.

    Always check if the numbers can be divided by a common factor.

Illustrative Examples

  • NaCl – 1 \$Na^+\$ : 1 \$Cl^-\$ (charges +1 and –1).

    \$Na^+ + Cl^- \;\Rightarrow\; NaCl\$

  • CaCl2 – 1 \$Ca^{2+}\$ : 2 \$Cl^-\$ (charges +2 and –1).

    \$Ca^{2+} + 2Cl^- \;\Rightarrow\; CaCl_2\$

  • Al2O3 – 2 \$Al^{3+}\$ : 3 \$O^{2-}\$ (charges +3 and –2).

    \$2Al^{3+} + 3O^{2-} \;\Rightarrow\; Al2O3\$

  • Fe2S3 – 2 \$Fe^{3+}\$ : 3 \$S^{2-}\$ (charges +3 and –2).

    \$2Fe^{3+} + 3S^{2-} \;\Rightarrow\; Fe2S3\$

Quick Reference Table

IonChargeTypical Counter‑Ion
\$Na^+\$+1\$Cl^-\$, \$Br^-\$, \$I^-\$
\$Ca^{2+}\$+2\$Cl^-\$, \$SO_4^{2-}\$
\$Al^{3+}\$+3\$O^{2-}\$, \$SO_4^{2-}\$
\$Fe^{3+}\$+3\$S^{2-}\$, \$O^{2-}\$

Practice Problems

  1. Determine the formula for a compound containing 3 \$Mg^{2+}\$ ions and 4 \$O^{2-}\$ ions.

  2. What is the formula of a salt that contains 2 \$Fe^{3+}\$ ions and 3 \$S^{2-}\$ ions?

  3. Write the formula for a compound made of 1 \$Cu^+\$ ion and 1 \$S^{2-}\$ ion.

  4. Given 1 \$Zn^{2+}\$ and 1 \$S^{2-}\$, what is the simplest formula?

Examination Tips

1. Balance the charges first. Always start by ensuring the total positive charge equals the total negative charge.

2. Use the LCM trick. Find the least common multiple of the charge magnitudes to decide how many of each ion you need.

3. Reduce to the simplest ratio. After writing the initial ratio, check if it can be simplified by dividing by a common factor.

4. Double‑check your work. Multiply the number of each ion by its charge and confirm the sum is zero.

💡 Remember: the formula is always written with the cation first, followed by the anion.