3.12: Ionic Bonding: Writing Chemical Formulas of Ionic Compounds Containing Polyatomic Ions

Learning Objectives

• Write the chemical formulas of ionic compounds containing polyatomic ions.

Several common polyatomic ions, which have defined formulas, names, and charges that cannot be modified in any way, were introduced in Section 3.11. These charged units can form ionic bonds with oppositely-charged ions, which can be either monatomic or polyatomic. The processes for writing the chemical formula and the chemical name of an ionic compound containing a polyatomic ion will be presented and applied in the current and following sections of this chapter, respectively.

Writing Chemical Formulas of Ionic Compounds Containing Polyatomic Ions

The procedure for determining the chemical formula of an ionic compound containing exclusively main group elements or a combination of main group and transition metal elements can also be utilized to establish the chemical formula of an ionic compound that contains a polyatomic ion.

For example, consider the cyanide ion and beryllium.

Based on the combinations listed in Section 3.2, the cyanide ion and beryllium will combine to form an ionic compound. Recall that an ionic bond is produced when a cation exists in close physical proximity to an anion, creating an electrostatic attractive force. In the given combination, the cyanide ion is classified as a polyatomic anion, and beryllium, a metal, ionizes to form a cation. After establishing that a pair of chemicals will form an ionic bond, a five-step process can be employed to determine the chemical formula of the resultant ionic compound.

1. Write the ion symbols for any indicated polyatomic ions and for any monatomic ion that results upon the ionization of a main group or transition metal element. Based on the information presented in the previous sections of this chapter, the cyanide ion is symbolized as CN^–1, and beryllium ionizes to form Be⁺².
   
2. In order to ensure consistent formatting in all ionic chemical formulas, the symbol for the cation is written first. In this example, Be⁺² will be written before CN^–1 in the final chemical formula.
   
3. The signs of the ions are only used to determine the relative order in which the ion symbols are written. As this information was established in the previous step, the "+" and "–" signs can be removed, so that only the base elemental symbols and numerical superscripts remain. In this example, the "+" sign is removed from Be⁺² and the "–" sign is removed from CN^–1. The revised symbols are written as Be² and CN¹, respectively.
   
4. Use subscripts to indicate how many of each of the given ions are present in the base chemical formula. Two different processes, both of which are presented below, can be used to determine this information.
   
   1. The first process, which is considered the more "scientifically-correct" method, is known as the "Ratio Method," as it establishes the correct cation-to-anion ratio by equating the total charges of the cations to the sum of the charges of the anions, in order to ensure that the final compound will be a net-neutral species. To determine this ratio, a mini-equation, in which the larger superscript value is multiplied by 1, and the smaller superscript value is multiplied by a variable, such as x, is solved. In the current example, the larger superscript value is "2," and the smaller superscript value is "1." Therefore,

      2(1) = 1(x)
      2 = x

      This result indicates that for every 1 of the ions with the larger superscript value, in this case, Be², 2 of the other ions, CN¹, are required to achieve charge-balance between them.
      
      To apply this information, remove the numerical superscripts from each symbol and instead utilize subscripts to indicate the ratio established above. Completion of this step results in a base formula of Be₁CN₂. However, this formula does not accurately reflect the intended meaning of the second subscript. As written, the "2" indicates that 2 nitrogens are present, but the base formula should actually contain 2 cyanide ions. Because a polyatomic ion is an indivisible unit, its chemical formula must be enclosed inside of two parentheses when incorporated into an ionic chemical formula. The subscript that specifies how many of that ion are present within a compound must be written after the closing parenthesis. A subscript in this position refers to the entire polyatomic ion, not simply the last element that it contains, which accurately reflects its intended meaning. Additionally, a subscript that is written outside of a parenthetical unit does not impact the identity of the polyatomic ion, which cannot be modified, by definition. Therefore, the true base formula for this ionic compound is Be₁(CN)₂.
      
   2. The alternative process for establishing this chemical formula is a "shortcut" known as the "Criss-Cross Method." In this system, the superscript on the first symbol becomes the subscript on the second symbol, and the superscript on the second symbol is repositioned as the subscript on the first symbol, as shown below.

      

      This "shortcut" is known as the "Criss-Cross Method" because the numerical values effectively "criss-cross" over one another when they are moved to their new positions. However, this formula does not accurately reflect the intended meaning of the second subscript. As written, the "2" indicates that 2 nitrogens are present, but the base formula should actually contain 2 cyanide ions. Because a polyatomic ion is an indivisible unit, its chemical formula must be enclosed inside of two parentheses when incorporated into an ionic chemical formula. The subscript that specifies how many of that ion are present within a compound must be written after the closing parenthesis. A subscript in this position refers to the entire polyatomic ion, not simply the last element that it contains, which accurately reflects its intended meaning. Additionally, a subscript that is written outside of a parenthetical unit does not impact the identity of the polyatomic ion, which cannot be modified, by definition. Therefore, the true base formula for this ionic compound is Be₁(CN)₂.
      
5. The final step in this process is to ensure that the subscripts in the base formula are mathematically-appropriate for inclusion in an ionic compound.
   
   1. If possible, the subscripts that are written outside of the parentheses must be reduced to the lowest-common ratio of whole numbers by dividing both of the subscripts by the same numerical value. Any subscripts that are written inside of the parentheses may not be modified in any way, as those subscripts are defined by and, therefore, are integral to, the identity of the polyatomic ion. This division should only be performed if both of the resultant subscripts remain whole numbers. In the current example, no such division is possible. Therefore, the chemical formula remains unchanged: Be₁(CN)₂.
   
   
   2. If a "1" has been explicitly-written as a subscript, it must be removed. As indicated previously, values of "1" are usually implicitly-understood in chemistry and, therefore, should not be written in a chemical formula. In this example, the formula shown above does include an explicitly-written "1" and, therefore, should be revised to Be(CN)₂.

The chemical formula that results upon the completion of this final step is a chemically-correct formula for an ionic compound. Therefore, Be(CN)₂ is the chemical formula for the compound formed when the cyanide ion and beryllium bond with one another.

Example \(\PageIndex{1}\)

Write the chemical formula for the compound that is formed when lithium and the sulfate ion bond with one another.

Solution

Based on the combinations listed in Section 3.2, lithium and the sulfate ion will combine to form an ionic compound, because lithium, a metal, ionizes to form a cation (Li⁺¹), and the sulfate ion (SO₄^–2) is classified as a polyatomic anion. The ion symbol for the cation is currently written first, as is required in an ionic chemical formula, so the order in which the ions are written should not change. Removing the "+" and "–" signs yields Li¹ and SO₄², respectively.

The subscripts for the base formula can be determined using either of the methods described above.

The "Ratio" Method
To determine the correct cation-to-anion ratio, a mini-equation, in which the larger superscript value is multiplied by 1, and the smaller superscript value is multiplied by a variable, such as x, is solved. In the current example, the larger superscript value is "2," and the smaller superscript value is "1." Therefore,

2(1) = 1(x)
2 = x

This result indicates that for every 1 of the ions with the larger superscript value, in this case, SO₄², 2 of the other ions, Li¹, are required to achieve charge-balance between them. To apply this information, the numerical superscripts are removed from each symbol, and subscripts are utilized to indicate the ratio established above. Completion of this step results in a base formula of Li₂SO₄₁. However, this formula does not accurately reflect the intended meaning of the second subscript. As written, the "41" subscript indicates that 41 oxygens are present, but the base formula should actually contain 1 sulfate ion. Because a polyatomic ion is an indivisible unit, its chemical formula must be enclosed inside of two parentheses when incorporated into an ionic chemical formula. The subscript that specifies how many of that ion are present within a compound must be written after the closing parenthesis. A subscript in this position refers to the entire polyatomic ion, not simply the last element that it contains, which accurately reflects its intended meaning. Additionally, a subscript that is written outside of a parenthetical unit does not impact the identity of the polyatomic ion, which cannot be modified, by definition. Therefore, the true base formula for this ionic compound is Li₂(SO₄)₁.

The "Criss-Cross" Method
In this system, the superscript on the first symbol becomes the subscript on the second symbol, and the superscript on the second symbol is repositioned as the subscript on the first symbol, as shown below.

Completion of this step results in a base formula of Li₂SO₄₁. However, this formula does not accurately reflect the intended meaning of the second subscript. As written, the "41" subscript indicates that 41 oxygens are present, but the base formula should actually contain 1 sulfate ion. Because a polyatomic ion is an indivisible unit, its chemical formula must be enclosed inside of two parentheses when incorporated into an ionic chemical formula. The subscript that specifies how many of that ion are present within a compound must be written after the closing parenthesis. A subscript in this position refers to the entire polyatomic ion, not simply the last element that it contains, which accurately reflects its intended meaning. Additionally, a subscript that is written outside of a parenthetical unit does not impact the identity of the polyatomic ion, which cannot be modified, by definition. Therefore, the true base formula for this ionic compound is Li₂(SO₄)₁.

The final step in this process is to ensure that the subscripts in the base formula are mathematically-appropriate for inclusion in an ionic compound. If possible, the subscripts that are written outside of the parentheses must be reduced to the lowest-common ratio of whole numbers. Any subscripts that are written inside of the parentheses may not be modified in any way, as those subscripts are defined by and, therefore, are integral to, the identity of the polyatomic ion. In the current example, these subscripts are already the lowest-common ratio of whole numbers, so should not be further divided.

This formula does include an explicitly-written "1" and, therefore, should be revised to Li₂(SO₄). However, after removing this "1," there is no longer an explicitly-written subscript after the closing parentheses in the base chemical formula. As a result, removing the parentheses will not change the meaning of the base chemical formula in any way, as both Li₂(SO₄) and Li₂SO₄ should be interpreted to contain 2 lithium ions and a (1) sulfate ion. While both chemical formulas have equivalent meanings, the latter notation, in which the parentheses have been removed, is considered to be more chemically-correct, as it does not contain any non-essential symbols.

Therefore, Li₂SO₄ is the chemically-correct formula for the compound formed when lithium and the sulfate ion bond with one another.

Exercise \(\PageIndex{1}\)

Write the chemical formula for the compound that is formed when each of the following combinations of elements and/or polyatomic ions bond with one another.

1. The ammonium ion and the phosphite ion
2. The carbonate ion and a mercury (II) ion

Answer a

Based on the combinations listed in Section 3.2, the ammonium ion (NH₄⁺¹), which is classified as a polyatomic cation, and the phosphite ion (PO₃^–3), which is classified as a polyatomic anion, will combine to form an ionic compound. The ion symbol for the cation is currently written first, as is required in an ionic chemical formula, so the order in which the ions are written should not change. Removing the "+" and "–" signs yields NH₄¹ and PO₃³, respectively.

The subscripts for the base formula for this chemical combination can be determined using either of the methods described above.

The "Ratio" Method
To determine the correct cation-to-anion ratio, a mini-equation, in which the larger superscript value is multiplied by 1, and the smaller superscript value is multiplied by a variable, such as x, is solved. In the current example, the larger superscript value is "3," and the smaller superscript value is "1." Therefore,

3(1) = 1(x)
3 = x

This result indicates that for every 1 of the ions with the larger superscript value, in this case, PO₃³, 3 of the other ions, NH₄¹, are required to achieve charge-balance between them. To apply this information, the numerical superscripts are removed from each symbol, and subscripts are utilized to indicate the ratio established above. Completion of this step results in a base formula of NH₄₃PO₃₁. However, this formula does not accurately reflect the intended meaning of either subscript. As written, the "43" subscript indicates that 43 hydrogens are present, but the base formula should actually contain 3 ammonium ions. Furthermore, the "31" subscript indicates that 31 oxygens are present, but the base formula should actually contain 1 phosphite ion. Because a polyatomic ion is an indivisible unit, its chemical formula must be enclosed inside of two parentheses when incorporated into an ionic chemical formula. The subscript that specifies how many of that ion are present within a compound must be written after the closing parenthesis. A subscript in this position refers to the entire polyatomic ion, not simply the last element that it contains, which accurately reflects its intended meaning. Additionally, a subscript that is written outside of a parenthetical unit does not impact the identity of the polyatomic ion, which cannot be modified, by definition. Therefore, the true base formula for this ionic compound is (NH₄)₃(PO₃)₁.

The "Criss-Cross" Method
In this system, the superscript on the first symbol becomes the subscript on the second symbol, and the superscript on the second symbol is repositioned as the subscript on the first symbol, as shown below.

Completion of this step results in a base formula of NH₄₃PO₃₁. However, this formula does not accurately reflect the intended meaning of either subscript. As written, the "43" subscript indicates that 43 hydrogens are present, but the base formula should actually contain 3 ammonium ions. Furthermore, the "31" subscript indicates that 31 oxygens are present, but the base formula should actually contain 1 phosphite ion. Because a polyatomic ion is an indivisible unit, its chemical formula must be enclosed inside of two parentheses when incorporated into an ionic chemical formula. The subscript that specifies how many of that ion are present within a compound must be written after the closing parenthesis. A subscript in this position refers to the entire polyatomic ion, not simply the last element that it contains, which accurately reflects its intended meaning. Additionally, a subscript that is written outside of a parenthetical unit does not impact the identity of the polyatomic ion, which cannot be modified, by definition. Therefore, the true base formula for this ionic compound is (NH₄)₃(PO₃)₁.

The final step in this process is to ensure that the subscripts in the base formula are mathematically-appropriate for inclusion in an ionic compound. If possible, the subscripts that are written outside of the parentheses must be reduced to the lowest-common ratio of whole numbers. Any subscripts that are written inside of the parentheses may not be modified in any way, as those subscripts are defined by and, therefore, are integral to, the identity of the polyatomic ion. In the current example, these subscripts are already the lowest-common ratio of whole numbers, so should not be further divided.

This formula does include an explicitly-written "1" and, therefore, should be revised to (NH₄)₃(PO₃). However, after removing this "1," there is no longer an explicitly-written subscript after the final closing parentheses in the base chemical formula. As a result, removing the second set of parentheses will not change the meaning of the base chemical formula in any way,as both (NH₄)₃(PO₃) and (NH₄)₃PO₃ should be interpreted to contain 3 ammonium ions and a (1) phosphite ion. While both chemical formulas have equivalent meanings, the latter notation, in which the parentheses have been removed, is considered to be more chemically-correct, as it does not contain any non-essential symbols. Since removing the first set of parentheses would change the meaning of the base chemical formula, these parentheses must remain explicitly-written.

Therefore, (NH₄)₃PO₃ is the chemically-correct formula for the compound formed when the ammonium ion and the phosphite ion bond with one another.

Answer b

Based on the combinations listed in Section 3.2, these elements will combine to form an ionic compound, because the carbonate ion (CO₃^–2) is classified as a polyatomic anion, and mercury (Hg), a metal, ionizes to form a cation. Since mercury is able to achieve a stable electron configuration through multiple ionization pathways, a Roman numeral must be included in the given ion name to specify the charge of the particular cation that is formed. In this example, the Roman numeral (II) in the given ion name indicates that this ion of mercury has a charge of +2 and, therefore, is symbolized as Hg⁺². Ionic chemical formulas require that the symbol for the cation should be written first; therefore, the order in which the ions are written should be reversed. As a result, Hg⁺² will be written before CO₃^–2 in the final chemical formula. Removing the "+" and "–" signs yields Hg² and CO₃², respectively.

The subscripts for the base formula for this chemical combination can be determined using either of the methods described above.

The "Ratio" Method
To determine the correct cation-to-anion ratio, a mini-equation, in which the larger superscript value is multiplied by 1, and the smaller superscript value is multiplied by a variable, such as x, is solved. In the current example, the superscript values are equal. Therefore,

2(1) = 2(x)
1 = x

This result indicates that these ions must be combined in a 1 to 1 ratio, in order to achieve charge-balance between them. To apply this information, the numerical superscripts are removed from each symbol, the chemical formula for the polyatomic ion is enclosed inside of two parentheses, and subscripts are written outside of the parentheses to indicate the ratio established above. The resultant base formula is Hg₁(CO₃)₁.

The "Criss-Cross" Method
In this system, the superscript on the first symbol becomes the subscript on the second symbol, and the superscript on the second symbol is repositioned as the subscript on the first symbol, as shown below. When "criss-crossing," the chemical formula for the polyatomic ion is enclosed inside of two parentheses, and the subscripts are written outside of the parentheses.

The resultant base formula, Hg₂(CO₃)₂, is not identical to what was derived using the first method.

The final step in this process is to ensure that the subscripts in the base formula are mathematically-appropriate for inclusion in an ionic compound. However, as the base formula derived from the "Ratio Method" is different from the result of the "Criss-Cross Method," both will be investigated further in this step.

First, consider the base formula derived using the "Ratio Method", Hg₁(CO₃)₁. In this chemical formula, the subscripts that are written outside of the parentheses are already the lowest-common ratio of whole numbers, so should not be further divided. However, this formula does include two explicitly-written "1"s and, therefore, should be revised to Hg(CO₃). As there is no longer an explicitly-written subscript after the closing parentheses in the base chemical formula, removing the parentheses will not change the meaning of the formula in any way. The resultant chemical formula, HgCO₃, is considered chemically-correct, as it does not contain any non-essential symbols.

Next, analyze the base formula that resulted from using the "Criss-Cross Method," Hg₂(CO₃)₂. In this chemical formula, both of the subscripts that are written outside of the parentheses must be divided by 2, in order to reduce them to the lowest-common ratio of whole numbers. This division results in a revised base formula of Hg₁(CO₃)₁. Note that this formula is identical to the base formula that was initially derived from the "Ratio Method." This formula does include two explicitly-written "1"s and, therefore, should be revised to Hg(CO₃). As there is no longer an explicitly-written subscript after the closing parentheses in the base chemical formula, removing the parentheses will not change the meaning of the formula in any way. The resultant chemical formula, HgCO₃, is considered chemically-correct, as it does not contain any non-essential symbols.

Therefore, while the base formulas were not immediately identical, both resulted in the conclusion that HgCO₃ is the chemically-correct formula for the compound formed when the carbonate ion and a mercury (II) ion bond with one another.