Atomic Foundations of Matter · Lesson 10 of 14
Writing Chemical Formulae
“Valencies and ionic charges can be crossed, simplified and grouped to write correct compound formulae.”
• Write formulae of covalent compounds using valencies. • Write ionic formulae using cation and anion charges. • Apply the criss-cross method correctly. • Reduce crossed subscripts to the simplest whole-number ratio. • Use brackets correctly when more than one polyatomic ion is required. • Verify that the total positive and negative charges balance.
A formula is compact, but it contains precise information. The subscripts must show a composition that is consistent with the combining capacities of the atoms or with the charges of the ions. The chapter introduces a quick crossover method, but the method only works reliably when its meaning is understood.
Writing Chemical Formulae
Writing Chemical Formulae of Covalent Compounds
For the method presented here, first write the symbols of the constituent elements. Write their valencies. Cross the valency numbers so that each becomes the subscript of the other element. A subscript of one is not written.
Problem
Write the formula using H with valency one and Cl with valency one.
- 1.Write the symbols H and Cl.
- 2.Write valency 1 for H and 1 for Cl.
- 3.Cross the valencies. Each crossed value is 1.
- 4.A subscript of 1 is omitted.
- 5.The formula is HCl.
Problem
Write the formula using H with valency one and S with valency two.
- 1.Write H and S.
- 2.Write valencies 1 and 2.
- 3.Cross 2 to hydrogen and 1 to sulfur.
- 4.Omit the subscript 1 on sulfur.
- 5.The formula is H₂S.
Problem
Write the formula using carbon valency four and chlorine valency one.
- 1.Write C and Cl.
- 2.Write valencies 4 and 1.
- 3.Cross the valencies.
- 4.Carbon receives an unwritten 1, while chlorine receives 4.
- 5.The formula is CCl₄.
Writing Chemical Formulae of Ionic Compounds
For an ionic compound, write the cation first and the anion second. Write their charges as numerical magnitudes for the crossover step. Cross only the numbers, not the charge signs. Then simplify the subscripts if they share a common factor. The final formula must represent the simplest whole-number ratio and must be electrically neutral.
Problem
Write the formula for Ca²⁺ and Cl⁻.
- 1.Write the cation first: Ca²⁺, followed by Cl⁻.
- 2.Use the charge numbers 2 and 1.
- 3.Cross the 2 to chloride and the 1 to calcium.
- 4.Omit the subscript 1 on calcium.
- 5.The formula is CaCl₂.
- 6.Check: one Ca²⁺ gives +2 and two Cl⁻ give −2, so the total charge is zero.
Problem
Write the formula for Al³⁺ and O²⁻.
- 1.Write Al³⁺ and O²⁻.
- 2.Cross the numerical charges: aluminium receives 2 and oxygen receives 3.
- 3.The formula is Al₂O₃.
- 4.Check: 2 × (+3) = +6 and 3 × (−2) = −6.
- 5.The charges cancel.
Problem
Write the formula for Mg²⁺ and O²⁻.
- 1.Crossing gives Mg₂O₂.
- 2.Both subscripts share the common factor 2.
- 3.Divide both subscripts by 2 to obtain the simplest whole-number ratio 1:1.
- 4.Omit the written ones.
- 5.The formula is MgO.
Formulae With Polyatomic Ions
When a polyatomic ion is needed more than once, brackets keep the entire ion together. For magnesium hydroxide, Mg²⁺ requires two OH⁻ ions. Writing Mg(OH)₂ shows that two complete hydroxide groups are present.
Problem
Write the formula for Mg²⁺ and OH⁻.
- 1.Write Mg²⁺ followed by OH⁻.
- 2.Cross the numerical charges 2 and 1.
- 3.Magnesium receives an unwritten 1; hydroxide receives 2.
- 4.Because two hydroxide ions are required, place OH inside brackets before writing the subscript.
- 5.The formula is Mg(OH)₂.
Problem
Write the formula for Ca²⁺ and CO₃²⁻.
- 1.Crossing gives Ca₂(CO₃)₂.
- 2.Both subscripts contain the common factor 2.
- 3.Reduce the ratio to 1:1.
- 4.Only one carbonate ion is required, so brackets are unnecessary.
- 5.The formula is CaCO₃.
Problem
Write the formula for Al³⁺ and OH⁻.
- 1.Write Al³⁺ and OH⁻.
- 2.Cross the charge numbers to obtain one aluminium and three hydroxide ions.
- 3.Because three hydroxide ions are present, keep OH together in brackets.
- 4.The formula is Al(OH)₃.
- 5.AlOH₃ would incorrectly suggest that the subscript belongs only to hydrogen rather than to the whole hydroxide group.
Problem
Write the formula for Al³⁺ and SO₄²⁻.
- 1.Write Al³⁺ and SO₄²⁻.
- 2.Cross 3 and 2 so aluminium receives 2 and sulfate receives 3.
- 3.Three sulfate ions are required, so keep SO₄ inside brackets.
- 4.The formula is Al₂(SO₄)₃.
- 5.Charge check: 2 × (+3) = +6 and 3 × (−2) = −6.
Charges help determine the ratio of ions. Once a neutral compound formula is written, the ion charge signs are not shown as part of the formula.
The criss-cross method is a shortcut, not the reason the formula works. Always check the result by adding total positive and negative charge. Also simplify crossed numbers and use brackets only when a polyatomic ion appears more than once.
Quiz
Which statement is a key takeaway from this lesson?
Which additional statement is also a key takeaway from this lesson?
Which further statement is also a key takeaway from this lesson?
Which another statement is also a key takeaway from this lesson?
Which statement correctly applies to the lesson “Writing Chemical Formulae”?
Practice Problems
- Name CO₂, NO₂, SF₆ and PCl₃.
- Write formulae for sodium hydrogencarbonate, sulfur dioxide, ferric chloride and cuprous oxide.
- Write the formula formed from Fe³⁺ and OH⁻.
- Write the formula formed from K⁺ and CO₃²⁻.
- Explain why Mg₂O₂ is simplified to MgO.
- Explain why Al(OH)₃ requires brackets.
Key Takeaways
• A chemical formula shows the relative numbers of atoms or ions in a compound. • For an ionic compound, the total positive and negative charges must balance. • The criss-cross method can help determine subscripts, but the final formula must always be checked for neutrality. • Brackets are used when more than one polyatomic ion is required.