You can work out a formula
Last lesson you learned that the valences in a compound add up to zero. Turn that around: if you know the valences of the two parts, you can work out the ratio of atoms and write the formula.
Four steps
Take the compound of aluminum and oxygen (Al is +3, O is −2):
- Write the valences: write the symbols, positive part first, and mark each valence:
- Cross over: the size of each valence becomes the other part’s subscript. Al gets a 2 and O gets a 3, giving .
- Reduce: if the subscripts share a factor, reduce them to the lowest ratio. 2 and 3 are already as low as they go.
- Check: (+3) × 2 + (−2) × 3 = 0 ✓
This is often called the criss-cross method. Pick any positive part and negative part below to see the four steps:
Example 1: Reducing
Write the formula of the compound of calcium (+2) and oxygen (−2).
- Write the valences.
- Cross over. This gives .
- Reduce. 2 : 2 = 1 : 1, so the formula is .
- Check. (+2) × 1 + (−2) × 1 = 0 ✓
Example 2: A polyatomic group
Write the formula of ammonium sulfate (ammonium, , is +1; sulfate, , is −2).
- Write the valences.
- Cross over. You need 2 and 1 .
- Add parentheses. When you need more than one of a polyatomic group, put it in parentheses and write the number outside: .
- Check. (+1) × 2 + (−2) × 1 = 0 ✓
Common mistakes
Mistake 1: Forgetting to reduce. should be . That said, a formula always has to match what the substance is actually made of: hydrogen peroxide really is , and you can’t reduce it to HO.
Mistake 2: Leaving out the parentheses. Writing calcium hydroxide as CaOH2 is wrong, because it looks like 1 O and 2 H. The correct formula is .
Mistake 3: Putting the parts in the wrong order. Sodium chloride is , not ClNa. The positive part usually comes first (a few exceptions, like and , come later).
Quick check
What is the formula of the compound of magnesium (+2) and nitrogen (−3)?
Cross over: Mg gets a 3 and N gets a 2. Check: (+2) × 3 + (−3) × 2 = 0.
Which formula is written correctly?
A should be . B needs parentheses: . D should be . For : (+1) × 2 + (−2) × 1 = 0 ✓
Summary
- Four steps: write the valences, cross over, reduce, check.
- Put the positive part first. Use parentheses when there’s more than one of a polyatomic group.
- Always check that the valences add up to zero.
On to AP (for later)
AP Chemistry predicts ion charges from an element’s group in the periodic table (Group 1: +1, Group 2: +2, Group 16: −2, Group 17: −1), then uses the same charge balance to write formulas for ionic compounds (topic 1.8).