## 5.2 Formulas of Ionic Compounds

### Learning Objectives

By the end of this section, you will be able to:

• Determine formulas for simple ionic compounds

In every ionic compound, the total number of positive charges of the cations equals the total number of negative charges of the anions. Thus, ionic compounds are electrically neutral overall, even though they contain positive and negative ions. We can use this observation to help us write the formula of an ionic compound. The formula of an ionic compound must have a ratio of ions such that the numbers of positive and negative charges are equal.

### Example 1: Predicting the Formula of an Ionic Compound

The gemstone sapphire (Figure 1) is mostly a compound of aluminum and oxygen that contains aluminum cations, Al3+, and oxygen anions, O2−. What is the formula of this compound? Figure 1. Although pure aluminum oxide is colorless, trace amounts of iron and titanium give blue sapphire its characteristic color. (credit: modification of work by Stanislav Doronenko)

Predict the formula of the ionic compound formed between the sodium cation, Na+, and the sulfide anion, S2−.

Many ionic compounds contain polyatomic ions (Table 1) as the cation, the anion, or both. As with simple ionic compounds, these compounds must also be electrically neutral, so their formulas can be predicted by treating the polyatomic ions as discrete units. We use parentheses in a formula to indicate a group of atoms that behave as a unit. For example, the formula for calcium phosphate, one of the minerals in our bones, is Ca3(PO4)2. This formula indicates that there are three calcium ions (Ca2+) for every two phosphate $\left({\text{PO}}_{4}{}^{3-}\right)$ groups. The ${\text{PO}}_{4}{}^{3-}$ groups are discrete units, each consisting of one phosphorus atom and four oxygen atoms, and having an overall charge of 3-. The compound is electrically neutral, and its formula shows a total count of three Ca, two P, and eight O atoms.

Table 1. Common Polyatomic Ions
Charge Name Formula Charge Name Formula
1+ ammonium ${\text{NH}}_{4}{}^{+}$ 1− permanganate ${\text{MnO}}_{4}{}^{-}$
1− acetate ${\text{C}}_{2}{\text{H}}_{3}{\text{O}}_{2}{}^{-}$ 1− hydrogen carbonate, or bicarbonate ${\text{HCO}}_{3}{}^{-}$
1− cyanide $\text{CN}^-$ 2− carbonate ${\text{CO}}_{3}{}^{2-}$
1− hydroxide $\text{OH}^-$ 2− peroxide ${\text{O}}_{2}{}^{2-}$
1− nitrate ${\text{NO}}_{3}{}^{-}$ 1− hydrogen sulfate, or bisulfate ${\text{HSO}}_{4}{}^{-}$
1− nitrite ${\text{NO}}_{2}{}^{-}$ 2− sulfate ${\text{SO}}_{4}{}^{2-}$
1− perchlorate ${\text{ClO}}_{4}{}^{-}$ 2− sulfite ${\text{SO}}_{3}{}^{2-}$
1− chlorate ${\text{ClO}}_{3}{}^{-}$ 1− dihydrogen phosphate ${\text{H}}_{2}{\text{PO}}_{4}{}^{-}$
1− chlorite ${\text{ClO}}_{2}{}^{-}$ 2− hydrogen phosphate ${\text{HPO}}_{4}{}^{2-}$
1− hypochlorite $\text{ClO}^-$ 3− phosphate ${\text{PO}}_{4}{}^{3-}$

### Example 2: Predicting the Formula of a Compound with a Polyatomic Anion

Baking powder contains calcium dihydrogen phosphate, an ionic compound composed of the ions Ca2+ and ${\text{H}}_{2}{\text{PO}}_{4}{}^{-}$. What is the formula of this compound?

Predict the formula of the ionic compound formed between the lithium ion and the peroxide ion, ${\text{O}}_{2}{}^{2-}$ (Hint: Use the periodic table to predict the sign and the charge on the lithium ion.)

Because an ionic compound is not made up of single, discrete molecules, it may not be properly symbolized using a molecular formula. Instead, ionic compounds must be symbolized by a formula indicating the relative numbers of its constituent cations. For compounds containing only monatomic ions (such as NaCl) and for many compounds containing polyatomic ions (such as CaSO4), these formulas are just the empirical formulas introduced earlier in this chapter. However, the formulas for some ionic compounds containing polyatomic ions are not empirical formulas. For example, the ionic compound sodium oxalate is comprised of Na+ and ${\text{C}}_{2}{\text{O}}_{4}{}^{2-}$ ions combined in a 2:1 ratio, and its formula is written as Na2C2O4. The subscripts in this formula are not the smallest-possible whole numbers, as each can be divided by 2 to yield the empirical formula, NaCO2. This is not the accepted formula for sodium oxalate, however, as it does not accurately represent the compound’s polyatomic anion, ${\text{C}}_{2}{\text{O}}_{4}{}^{2-}$.

### Key Concepts and Summary

The total number of positive charges of the cations equals the total number of negative charges of the anions. Thus, ionic compounds are electrically neutral overall, even though they contain positive and negative ions.

### Exercises

1. For each of the following pairs of ions, write the symbol for the formula of the compound they will form:
1. Ca2+, S2-
2. ${\text{NH}}_{4}{}^{+}$, ${\text{SO}}_{4}{}^{2-}$
3. Al3+, Br–
4. Na+, ${\text{HPO}}_{4}{}^{2-}$
5. Mg2+, ${\text{PO}}_{4}{}^{3-}$
2. For each of the following pairs of ions, write the symbol for the formula of the compound they will form:
1. K+, O2-
2. ${\text{NH}}_{4}{}^{+}$, ${\text{PO}}_{4}{}^{3-}$
3. Al3+, O2-
4. Na+, ${\text{CO}}_{3}{}^{2-}$
5. Ba2+, ${\text{PO}}_{4}{}^{3-}$

## Glossary

ionic bond: electrostatic forces of attraction between the oppositely charged ions of an ionic compound

ionic compound: compound composed of cations and anions combined in ratios, yielding an electrically neutral substance

monatomic ion: ion composed of a single atom

oxyanion: polyatomic anion composed of a central atom bonded to oxygen atoms

polyatomic ion: ion composed of more than one atom