Writing Formulas (Criss-cross Method)

5.5: Writing Formulas for Ionic Compounds

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Learning Objectives

Write the correct formula for an ionic compound.
Recognize polyatomic ions in chemical formulas.

Ionic compounds do not exist as molecules. In the solid state, ionic compounds are in crystal lattice containing many ions each of the cation and anion. An ionic formula, like \(\ce{NaCl}\), is an empirical formula. This formula merely indicates that sodium chloride is made of an equal number of sodium and chloride ions. Sodium sulfide, another ionic compound, has the formula \(\ce{Na_2S}\). This formula indicates that this compound is made up of twice as many sodium ions as sulfide ions. This section will teach you how to find the correct ratio of ions, so that you can write a correct formula.

If you know the name of a binary ionic compound, you can write its chemical formula. Start by writing the metal ion with its charge, followed by the nonmetal ion with its charge. Because the overall compound must be electrically neutral, decide how many of each ion is needed in order for the positive and negative charges to cancel each other out.

Example \(\PageIndex{1}\): Aluminum Nitride and Lithium Oxide

Write the formulas for aluminum nitride and lithium oxide.

Solution

	Write the formula for aluminum nitride	Write the formula for lithium oxide
1. Write the symbol and charge of the cation (metal) first and the anion (nonmetal) second.	\(\ce{Al^{3+}} \: \: \: \: \: \ce{N^{3-}}\)	\(\ce{Li^+} \: \: \: \: \: \ce{O^{2-}}\)
2. Use a multiplier to make the total charge of the cations and anions equal to each other.	total charge of cations = total charge of anions 1(3+) = 1(3-) +3 = -3	total charge of cations = total charge of anions 2(1+) = 1(2-) +2 = -2
3. Use the multipliers as subscript for each ion.	\(\ce{Al_1N_1}\)	\(\ce{Li_2O_1}\)
4. Write the final formula. Leave out all charges and all subscripts that are 1.	\(\ce{AlN}\)	\(\ce{Li_2O}\)

An alternative way to writing a correct formula for an ionic compound is to use the crisscross method. In this method, the numerical value of each of the ion charges is crossed over to become the subscript of the other ion. Signs of the charges are dropped.

Example \(\PageIndex{2}\): The Crisscross Method for Lead (IV) Oxide

Write the formula for lead (IV) oxide.

Solution

Crisscross Method	Write the formula for lead (IV) oxide
1. Write the symbol and charge of the cation (metal) first and the anion (nonmetal) second.	\(\ce{Pb^{4+}} \: \: \: \: \: \ce{O^{2-}}\)
2. Transpose only the number of the positive charge to become the subscript of the anion and the number only of the negative charge to become the subscript of the cation.
3. Reduce to the lowest ratio.	\(\ce{Pb_2O_4}\)
4. Write the final formula. Leave out all subscripts that are 1.	\(\ce{PbO_2}\)

Exercise \(\PageIndex{2}\)

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

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

Answer a:: CaO
Answer b:: CuS
Answer c:: Cu₂S

Be aware that ionic compounds are empirical formulas and so must be written as the lowest ratio of the ions.

Example \(\PageIndex{3}\): Sulfur Compound

Write the formula for sodium combined with sulfur.

Solution

Crisscross Method	Write the formula for sodium combined with sulfur
1. Write the symbol and charge of the cation (metal) first and the anion (nonmetal) second.	\(\ce{Na^{+}} \: \: \: \: \: \ce{S^{2-}}\)
2. Transpose only the number of the positive charge to become the subscript of the anion and the number only of the negative charge to become the subscript of the cation.
3. Reduce to the lowest ratio.	This step is not necessary.
4. Write the final formula. Leave out all subscripts that are 1.	\(\ce{Na_2S}\)

Exercise \(\PageIndex{3}\)

Write the formula for each ionic compound.

sodium bromide
lithium chloride
magnesium oxide

Answer a:: NaBr
Answer b:: LiCl
Answer c:: MgO

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 Polyatomic Ions
Name	Formula
ammonium ion	NH₄ ⁺
acetate ion	C₂H₃O₂ ⁻ (also written CH₃CO₂ ⁻)
carbonate ion	CO₃ ²⁻
chromate ion	CrO₄ ²⁻
dichromate ion	Cr₂O₇ ²⁻
hydrogen carbonate ion (bicarbonate ion)	HCO₃ ⁻
cyanide ion	CN⁻
hydroxide ion	OH⁻
nitrate ion	NO₃ ⁻
nitrite ion	NO₂ ⁻
permanganate ion	MnO₄ ⁻
phosphate ion	PO₄ ³⁻
hydrogen phosphate ion	HPO₄ ²⁻
dihydrogen phosphate ion	H₂PO₄ ⁻
sulfate ion	SO₄ ²⁻
hydrogen sulfate ion (bisulfate ion)	HSO₄ ⁻
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.

Writing Formulas for Ionic Compounds Containing Polyatomic Ions

Writing a formula for ionic compounds containing polyatomic ions also involves the same steps as for a binary ionic compound. Write the symbol and charge of the cation followed by the symbol and charge of the anion.

Example \(\PageIndex{4}\): Calcium Nitrate

Write the formula for calcium nitrate.

Solution

Crisscross Method	Write the formula for calcium nitrate
1. Write the symbol and charge of the cation (metal) first and the anion (nonmetal) second.	\(\ce{Ca^{2+}} \: \: \: \: \: \ce{NO_3^-}\)
2. Transpose only the number of the positive charge to become the subscript of the anion and the number only of the negative charge to become the subscript of the cation.
3. Reduce to the lowest ratio.	\(\ce{Ca_1(NO_3)_2}\)
4. Write the final formula. Leave out all subscripts that are 1. If there is only 1 of the polyatomic ion, leave off parentheses.	\(\ce{Ca(NO_3)_2}\)

Example \(\PageIndex{5}\)

Write the chemical formula for an ionic compound composed of the potassium ion and the sulfate ion.

Solution

Explanation	Answer
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.	\(K_2SO_4\)

Exercise \(\PageIndex{5}\)

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

the magnesium ion and the carbonate ion
the aluminum ion and the acetate ion

Answer a:: MgCO₃
Answer b:: Al(CH₃COO)₃

Recognizing Ionic Compounds

There are two ways to recognize ionic compounds. First, compounds between metal and nonmetal elements are usually ionic. For example, CaBr₂ contains a metallic element (calcium, a group 2 [or 2A] metal) and a nonmetallic element (bromine, a group 17 [or 7A] nonmetal). Therefore, it is most likely an ionic compound. (In fact, it is ionic.) In contrast, the compound NO₂ contains two elements that are both nonmetals (nitrogen, from group 15 [or 5A], and oxygen, from group 16 [or 6A]. It is not an ionic compound; it belongs to the category of covalent compounds discussed elsewhere. Also note that this combination of nitrogen and oxygen has no electric charge specified, so it is not the nitrite ion.

Second, if you recognize the formula of a polyatomic ion in a compound, the compound is ionic. For example, if you see the formula Ba(NO₃)₂, you may recognize the "NO₃" part as the nitrate ion, NO₃ ⁻. (Remember that the convention for writing formulas for ionic compounds is not to include the ionic charge.) This is a clue that the other part of the formula, Ba, is actually the Ba²⁺ ion, with the 2+ charge balancing the overall 2− charge from the two nitrate ions. Thus, this compound is also ionic.

Example \(\PageIndex{6}\)

Identify each compound as ionic or not ionic.

Na₂O
PCl₃
NH₄Cl
OF₂

Solution

Explanation	Answer
a. Sodium is a metal, and oxygen is a nonmetal. Therefore, Na₂O is expected to be ionic.	\(Na_2O\), ionic
b. Both phosphorus and chlorine are nonmetals. Therefore, PCl₃ is not ionic.	\(PCl_3\), not ionic
c. The NH₄ in the formula represents the ammonium ion, NH₄ ⁺, which indicates that this compound is ionic.	\(NH_4Cl\), ionic
d. Both oxygen and fluorine are nonmetals. Therefore, OF₂ is not ionic.	\(OF_2\), ionic

Exercise \(\PageIndex{6}\)

Identify each compound as ionic or not ionic.

N₂O
FeCl₃
(NH₄)₃PO₄
SOCl₂

Answer a:: not ionic
Answer b:: ionic

Answer c:: ionic
Answer d:: not ionic

Summary

Formulas for ionic compounds contain the symbols and number of each atom present in a compound in the lowest whole number ratio.

Contributions & Attributions

This page was constructed from content via the following contributor(s) and edited (topically or extensively) by the LibreTexts development team to meet platform style, presentation, and quality:

CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.
Marisa Alviar-Agnew (Sacramento City College)
Henry Agnew (UC Davis)

Writing Formulas (Criss-cross Method)

Source: https://chem.libretexts.org/Courses/College_of_Marin/CHEM_114%3A_Introductory_Chemistry/05%3A_Molecules_and_Compounds/5.05%3A_Writing_Formulas_for_Ionic_Compounds

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