1.9: Formulas for Ionic Compounds

Learning Objectives

• Write the chemical formula for a simple ionic compound.
• Recognize polyatomic ions in chemical formulas.

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

Ionic compounds exist as alternating positive and negative ions in regular, three-dimensional patterns called crystals (Figure \(\PageIndex{1}\)). There are no individual NaCl “particles” in the crystal; instead, there is a continuous pattern of alternating sodium and chloride ions. In order to identify this compound using a chemical formula we use the ratio of sodium ions to chloride ions, expressed in the lowest possible whole numbers. 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. The term molecule is not applicable to an ionic compound; instead the lowest ratio is called a formula unit. Although it is convenient to think that NaCl crystals are composed of individual NaCl units, Figure \(\PageIndex{1}\) shows that no single ion is exclusively associated with any other single ion. Each ion is surrounded by several ions of opposite charge.

Figure \(\PageIndex{1}\) A Sodium Chloride Crystal. A crystal contains a three-dimensional pattern 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 how many of each ion is needed to balance the total positive and negative charges in the compound.

This rule is ultimately based on the fact that matter is, overall, electrically neutral.

By convention, assume that there is only one atom if a subscript is not present. We do not use 1 as a subscript.

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. Instead of writing the chemical formula for this ionic compound as MgClCl, we 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.

By convention, the lowest whole-number ratio of the ions is used in ionic formulas. There are exceptions for certain ions, such as Hg₂²⁺

Example \(\PageIndex{1}\)

Write the chemical formula for an ionic compound composed of each pair of ions.

1. the sodium ion and the sulfur ion
2. the aluminum ion and the fluoride ion
3. the 3+ iron ion and the oxygen ion

Solution

1. To obtain a valence shell octet, sodium forms an ion with a 1+ charge, while the sulfur ion has a 2− charge. Two sodium 1+ ions are needed to balance the 2− charge on the sulfur ion. The formula is Na₂S which indicates two sodium ions and one sulfide ion.
2. The aluminum ion has a 3+ charge, while the fluoride ion formed by fluorine has a 1− charge. Three fluorine 1− ions are needed to balance the 3+ charge on the aluminum ion. This combination is written as AlF₃.
3. Iron can form two possible ions, but the ion with a 3+ charge is specified here. The oxygen atom has a 2− charge as an ion. To balance the positive and negative charges, we look to the least common multiple—6: two iron 3+ ions will give 6+, while three 2− oxygen ions will give 6−, thereby balancing the overall positive and negative charges. Thus, the formula for this ionic compound is Fe₂O₃.

Exercise \(\PageIndex{1}\)

Write the chemical formula for an ionic compound composed of each pair of ions.

1. the calcium ion and the oxygen ion
2. the 2+ copper ion and the sulfur ion
3. the 1+ copper ion and the sulfur ion

Polyatomic Ions

Some ions consist of groups of atoms bonded together and have an overall electric charge. Because these ions contain more than one atom, they are called polyatomic ions. Polyatomic ions have characteristic formulas, names, and charges that should be memorized. For example, NO₃⁻ is the nitrate ion; it has one nitrogen atom and three oxygen atoms and an overall 1− charge. Table \(\PageIndex{1}\) lists the most common polyatomic ions.

Table \(\PageIndex{1}\): Some Biologically Important Polyatomic Ions

Name	Formula
ammonium ion	NH4^+
acetate ion	C2H3O2^−
carbonate ion	CO3^2^−
hydrogen carbonate ion (bicarbonate ion)	HCO3^−
cyanide ion	CN^−
hydroxide ion	OH^−
phosphate ion	PO4^3^−
hydrogen phosphate ion	HPO4^2^−
dihydrogen phosphate ion	H2PO4^−
nitrate ion	NO3^−
sulfite ion	SO3^2^−

The rule for constructing formulas for ionic compounds containing polyatomic ions is the same as for formulas containing monatomic (single-atom) ions: the positive and negative charges must balance. If more than one of a particular polyatomic ion is needed to balance the charge, the entire formula for the polyatomic ion must be enclosed in parentheses, and the numerical subscript is placed outside the parentheses. This is to show that the subscript applies to the entire polyatomic ion. An example is Ba(NO₃)₂.

Example \(\PageIndex{2}\)

Write the chemical formula for an ionic compound composed of each pair of ions.

1. the potassium ion and the sulfate ion
2. the calcium ion and the nitrate ion

Solution

1. Potassium ions have a charge of 1+, while sulfate ions have a charge of 2−. We will need two potassium ions to balance the charge on the sulfate ion, so the proper chemical formula is K₂SO₄.
2. Calcium ions have a charge of 2+, while nitrate ions have a charge of 1−. We will need two nitrate ions to balance the charge on each calcium ion. The formula for nitrate must be enclosed in parentheses. Thus, we write Ca(NO₃)₂ as the formula for this ionic compound.

Exercise \(\PageIndex{2}\)

Write the chemical formula for an ionic compound composed of each pair of ions.

1. the magnesium ion and the carbonate ion
2. the aluminum ion and the acetate ion

Interpreting Names of Ionic Compounds

Each ionic compound has a name consisting of the name of the cation followed by the name of the anion. 

Cation Names

Many cation names are the same as the name of the corresponding element on the periodic table. For example, sodium can form sodium ions and magnesium can form magnesium ions. 

However, most transition metals (Groups 3 - 12) and post-transition metals (at the bottom of Groups 13 - 16) can form ions with different charges in different environments, so we need a way of distinguishing these possibilities. For example, iron can form cations with a +2 charge and with a +3 charge. It would be confusing if we called both of those iron ions. 

Instead, when multiple different charges are possible we use Roman numerals as part of the name of the ion to indicate which one we are referring to. The two types of iron ions are called iron(II) ions and iron(III) ions. The Roman numeral tells the charge of the ion. The most common Roman numerals used to represent charges are: 1 = I, 2 = II,  3 = III, and 4 = IV. The charges represented by Roman numerals are always positive (they are only used for cations). 

It is possible to have polyatomic cations. A common one is the ammonium ion, NH₄⁺. Unlike most cations, ammonium is not made from a metal.

Anion Names

Unlike cations, element names are modified when a substance becomes an anion. For monatomic anions (monatomic means "one atom"), the ending of the element name is removed and replaced by -ide. For example, toothpaste contains fluoride ions, not fluorine atoms.

Polyatomic anions are much more common than polyatomic cations. Luckily you can generally recognize them by the last three letters of their names: -ate and -ite. Unfortunately there are some exceptions like hydroxide ions and cyanide ions which are polyatomic despite having an -ide ending. 

Example \(\PageIndex{3}\)

Write the formula for each compound. 

1. Sodium oxide
2. Ammonium chloride
3. Iron(III) sulfide

Solution

1. Sodium ions have a charge of +1 ; oxide ions have a charge of +2. Therefore, twice as many sodium ions as oxide ions are needed and the formula is Na₂O.
2. Ammonium is a polyatomic cation with the formula NH₄⁺ where the charge is +1 (represented by the + sign written as a superscript). The subscript 4 is not part of the charge, it tells the number of hydrogen atoms in each ammonium ion. Chloride ions have a -1 charge. Since these ions have charges of +1 and -1 they can combine at a 1:1 ratio and the formula is NH₄Cl.
3. The Roman numeral tells us that in this case the iron has a charge of +3. The sulfide ion has a charge of -2. Finding the ratio on this one is tricky! The formula is Fe₂S₃. Two iron(III) ions add up to a total positive charge of +6 and three sulfide ions add up to a total negative charge of -6. This makes a charge of zero overall. 

Looking Closer: Blood and Seawater

Science has long recognized that blood and seawater have similar compositions. After all, both liquids have ionic compounds dissolved in them. The similarity may be more than mere coincidence; many scientists think that the first forms of life on Earth arose in the oceans. A closer look, however, shows that blood and seawater are quite different. A 0.9% solution of sodium chloride approximates the salt concentration found in blood. In contrast, seawater is principally a 3% sodium chloride solution, over three times the concentration in blood. Here is a comparison of the amounts of ions in blood and seawater:

Ion	Percent in Seawater	Percent in Blood
Na^+	2.36	0.322
Cl^−	1.94	0.366
Mg^2^+	0.13	0.002
SO4^2^−	0.09	—
K^+	0.04	0.016
Ca^2^+	0.04	0.0096
HCO3^−	0.002	0.165
HPO4^2^−, H2PO4^−	—	0.01

Most ions are more abundant in seawater than they are in blood, with some important exceptions. There are far more hydrogen carbonate ions (HCO₃⁻) in blood than in seawater. This difference is significant because the hydrogen carbonate ion and some related ions have a crucial role in controlling the acid-base properties of blood. The amount of hydrogen phosphate ions—HPO₄²⁻ and H₂PO₄⁻—in seawater is very low, but they are present in higher amounts in blood, where they also affect acid-base properties. Another notable difference is that blood does not have significant amounts of the sulfate ion (SO₄²⁻), but this ion is present in seawater.

Key Takeaways

• Proper chemical formulas for ionic compounds balance the total positive charge with the total negative charge.
• Groups of atoms with an overall charge, called polyatomic ions, also exist.

Contributors and Attributions

• Anonymous