# 7.8: Formulas for Binary Ionic Compounds

Shorthand was a very popular way of recording speech, especially in dictating letters and in court testimony. Instead of trying to write out all the words, the person taking the dictation would use a set of symbols that represented syllables or words. Unless you know shorthand, passages written in shorthand are meaningless. But knowing shorthand allows you to read such passages. Different professions also use a type of shorthand in communication to save time. Chemists use chemical symbols in combination to indicate specific compounds. There are two advantages to this approach:

1. The compound under discussion is clearly described so there can be no confusion about its identity.
2. Chemical symbols represent a universal language that all chemists can understand, no matter what their native language is.

## Writing Formulas for Binary Ionic Compounds

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 charge to cancel each other out. Consider the compound aluminum nitride. The ions are:

$\ce{Al^{3+}} \: \: \: \: \: \ce{N^{3-}}$

Since the ions have charges that are equal in magnitude, one of each will be the lowest ratio of ions in the formula. The formula for aluminum nitride is $$\ce{AlN}$$.

The ions for the compound lithium oxide are:

$\ce{Li^+} \: \: \: \: \: \ce{O^{2-}}$

In this case, two lithium ions are required to balance out the charge of one oxide ion. The formula of lithium oxide is $$\ce{Li_2O}$$.

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. Shown below is the crisscross method for aluminum oxide.

The red arrows indicate that the 3 from the $$3+$$ charge will cross over to become the subscript of the $$\ce{O}$$. The 2 from the $$2-$$ charge will cross over to become the subscript of the $$\ce{Al}$$. The formula for aluminum oxide is $$\ce{Al_2O_3}$$.

Be aware that ionic compounds are empirical formulas and so must be written as the lowest ratio of the ions. In the case of aluminum nitride, the crisscross method would yield a formula of $$\ce{Al_3N_3}$$, which is not correct. It must be reduced to $$\ce{AlN}$$. Following the crisscross method to write the formula for lead (IV) oxide would involve the following steps:

The crisscross first yields $$\ce{Pb_2O_4}$$ for the formula, but that must be reduced to the lower ratio and $$\ce{PbO_2}$$ is the correct formula.

## Summary

• Formulas for binary compounds begin with the metal followed by the nonmetal.
• Positive and negative charges must cancel each other out.
• Ionic compound formulas are written using the lowest ratio of ions.

## Contributors

• CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.