We have already encountered some chemical formulas for simple ionic compounds. A chemical formula is a concise list of the elements in a compound and the ratios of these elements. To better understand what a chemical formula means, we must consider how an ionic compound is constructed from its ions.

Ionic compounds exist as positive and negative ions in regular, three-dimensional arrays called crystals (Figure 3.6 “A Sodium Chloride Crystal”). As you can see, there are no individual NaCl “molecules” in the array; instead, there is a continuous lattice of alternating sodium and chloride ions. However, we can use the ratio of sodium ions to chloride ions, expressed in the lowest possible whole numbers, as a way of describing the compound in terms of a formula unit. In the case of sodium chloride, the ratio of sodium ions to chloride ions, expressed in lowest whole numbers, is 1:1, so we use NaCl (one Na symbol and one Cl symbol) to represent the compound. Thus, NaCl is the chemical formula for sodium chloride, which is a concise way of describing the ratio of different ions in the compound. A macroscopic sample is composed of myriads of NaCl pairs; each pair called a formula unit. Although it is convenient to think that NaCl crystals are composed of individual NaCl units, Figure 3.6 “A Sodium Chloride Crystal” shows that no single ion is exclusively associated with any other single ion. Each ion is surrounded by ions of opposite charge.

Figure 3.6 A Sodium Chloride Crystal. A crystal contains a three-dimensional array of alternating positive and negative ions. The precise pattern depends on the compound. A crystal of sodium chloride, shown here, is a collection of alternating sodium and chlorine ions.

The formula for an ionic compound follows several conventions. First, the cation is written before the anion. Because most metals form cations and most nonmetals form anions, formulas typically list the metal first and then the nonmetal. Second, charges are not written in a formula. Remember that in an ionic compound, the component species are ions, not neutral atoms, even though the formula does not contain charges. Finally, the proper formula for an ionic compound always obeys the following rule: the total positive charge must equal the total negative charge. To determine the proper formula of any combination of ions, determine the smallest whole number ratio of cations and anions to balance the total positive and negative charges in the compound.

If we look at the ionic compound consisting of lithium ions and bromide ions, we see that the lithium ion has a 1⁺ charge and the bromide ion has a 1⁻ charge. Only one ion of each is needed to balance these charges. The formula for lithium bromide is LiBr.

When an ionic compound is formed from magnesium and oxygen, the magnesium ion has a 2⁺ charge, and the oxygen atom has a 2⁻ charge. Although both of these ions have higher charges than the ions in lithium bromide, they still balance each other in a one-to-one ratio. Therefore, the proper formula for this ionic compound is MgO.

Now consider the ionic compound formed by magnesium and chlorine. A magnesium ion has a 2⁺ charge, while a chlorine ion has a 1⁻ charge:

Mg²⁺ Cl⁻

Combining one ion of each does not completely balance the positive and negative charges. The easiest way to balance these charges is to assume the presence of two chloride ions for each magnesium ion:

Mg²⁺ Cl⁻ Cl⁻

Now the positive and negative charges are balanced. We could write the chemical formula for this ionic compound as MgClCl, but the convention is to use a numerical subscript when there is more than one ion of a given type: MgCl₂. This chemical formula says that there are one magnesium ion and two chloride ions in this formula. By convention, the lowest whole number ratio is used in the formulas of ionic compounds. The formula Mg₂Cl₄ has balanced charges with the ions in a 1:2 ratio, but it is not the lowest whole number ratio.