3.9: Ionic Bonding: Writing Chemical Formulas of Ionic Compounds Containing Transition Metals

Learning Objectives

• Write the chemical formulas of ionic compounds containing transition metal elements.

The previous section of this chapter outlined the complications that arise when transition metal elements ionize. As most transition metals are able to achieve stable electron configurations through multiple ionization pathways, a single transition metal can ionize to form several unique cations. In order to unambiguously distinguish these ions from one another, their corresponding ion names must be modified using either a Roman numeral or a distinctive suffix. However, the suffixes employed in the common system still limit the variety of transition metal cations that can be clearly named. In contrast, the IUPAC system indicates the charge of a transition metal cation by writing a corresponding Roman numeral in parentheses after the element name, but before the word "ion," in an ion name. As the Roman numeral is directly tied to the charge of the cation, the IUPAC system is both less restrictive and less ambiguous than the common system. Therefore, this method for naming transition metal cations will be used exclusively in the remaining sections of this text.

Writing Chemical Formulas of Ionic Compounds Containing Transition Metals

Section 3.6 presented the procedure for determining the chemical formula of an ionic compound containing main group elements. These steps can also be utilized to establish the chemical formula of an ionic compound that contains a transition metal.

For example, consider phosphorus and a tin (IV) ion.

Based on the combinations listed in Section 3.2, these elements 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, phosphorus, a non-metal, ionizes to form an anion, and tin (Sn), 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 symbol for the ion that results upon the ionization of each of the given elements. Based on the information presented in the previous sections of this chapter, phosphorus ionizes to form P^–3. Tin is able to achieve a stable electron configuration through multiple ionization pathways. For elements that can ionize to form more than one cation, 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 (IV) in the given ion name indicates that this ion of tin has a charge of +4 and, therefore, is symbolized as Sn⁺⁴.
   
2. In order to ensure consistent formatting in all ionic chemical formulas, the symbol for the cation is written first. In this example, Sn⁺⁴ will be written before P^–3 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 Sn⁺⁴ and the "–" sign is removed from P^–3. The revised symbols are written as Sn⁴ and P³, 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 "4," and the smaller superscript value is "3." Therefore,

      4(1) = 3(x)
      ⁴⁄₃ = x (or, x = 1.333...)

      This result indicates that for every 1 of the ions with the larger superscript value, in this case, Sn⁴, ⁴⁄₃ of the other ions, P³, are required to achieve charge-balance between them. However, subscripts must be written as whole-number values, as it is physically-impossible for a fraction of an ion to exist. Therefore, the third-fraction is cleared by tripling both of the numbers in the ratio indicated above. Therefore, for every 3 of the ions with the larger superscript value, in this case, Sn⁴, 4 of the other ions, P³, 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. Therefore, the resultant chemical formula, which is called a base formula, is Sn₃P₄.
      
   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. The resultant base formula is identical to what was derived using the first method: Sn₃P₄.
      
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 must be reduced to the lowest-common ratio of whole numbers by dividing both of the subscripts by the same numerical value. 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: Sn₃P₄.
   
   
   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, no explicitly-written "1"s are present, and the chemical formula again remains unchanged: Sn₃P₄.

The chemical formula that results upon the completion of this final step is a chemically-correct formula for an ionic compound. Therefore, Sn₃P₄ is the chemical formula for the compound formed when phosphorus and a tin (IV) ion bond with one another.

Example \(\PageIndex{1}\)

Write the chemical formula for the compound that is formed when a nickel (III) ion and iodine bond with one another.

Solution

Based on the combinations listed in Section 3.2, these elements will combine to form an ionic compound, because nickel (Ni), a metal, ionizes to form a cation, and iodine, a non-metal, ionizes to form an anion (I^–1). Since nickel 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 (III) in the given ion name indicates that this ion of nickel has a charge of +3 and, therefore, is symbolized as Ni⁺³. 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 Ni³ and I¹, 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 "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, Ni³, 3 of the other ions, I¹, 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. The resultant base formula is Ni₁I₃.

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.

The resultant base formula is identical to what was derived using the first method: Ni₁I₃.

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. In the current example, the subscripts are already the lowest-common ratio of whole numbers, so should not be further divided. However, this formula does include an explicitly-written "1" and, therefore, should be revised to NiI₃.

Therefore, NiI₃ is the chemically-correct formula for the compound formed when a nickel (III) ion and iodine 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 bond with one another.

1. A lead (II) ion and oxygen
2. Nitrogen and a copper (I) ion

Answer a

Based on the combinations listed in Section 3.2, these elements will combine to form an ionic compound, because lead (Pb), a metal, ionizes to form a cation, and oxygen, a non-metal, ionizes to form an anion (O^–2). Since lead 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 lead has a charge of +2 and, therefore, is symbolized as Pb⁺². 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 Pb² and O², 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, and subscripts are utilized to indicate the ratio established above. The resultant base formula is Pb₁O₁.

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.

The resultant base formula, Pb₂O₂, 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", Pb₁O₁. In this chemical formula, the subscripts 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 PbO.

Next, analyze the base formula that resulted from using the "Criss-Cross Method," Pb₂O₂. In this chemical formula, both of the subscripts 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 Pb₁O₁. 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 PbO.

Therefore, while the base formulas were not immediately identical, both resulted in the conclusion that PbO is the chemically-correct formula for the compound formed when a lead (II) ion and oxygen 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 nitrogen, a non-metal, ionizes to form an anion (N^–3), and copper (Cu), a metal, ionizes to form a cation. Since copper is able to achieve a stable electron configuration through multiple ionization pathways, the Roman numeral (I) in the given ion name indicates that this ion of copper has a charge of +1 and, therefore, is symbolized as Cu⁺¹. The ion symbol for the cation is currently written second. 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, Cu⁺¹ will be written before N^–3 in the final chemical formula. Removing the "+" and "–" signs yields Cu¹ and N³, 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, N³, 3 of the other ions, Cu¹, 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. The resultant base formula is Cu₃N₁.

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.

The resultant base formula is identical to what was derived using the first method: Cu₃N₁.

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. In this example, the subscripts are already the lowest-common ratio of whole numbers, so should not be further divided. However, this formula does include an explicitly-written "1" and, therefore, should be revised to Cu₃N.

Therefore, Cu₃N is the chemically-correct formula for the compound formed when nitrogen and a copper (I) ion bond with one another.