Question

Write the formulas for the four ionic compounds that can be made by combining the cations \(\mathrm{Mg}^{2+}\) and \(\mathrm{Fe}^{3+}\) with the anions \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{NO}_{3}^{-} .\) Name each compound formed.

Short answer

Magnesium phosphate (\(\mathrm{Mg}_3(\mathrm{PO}_4)_2\)), magnesium nitrate (\(\mathrm{Mg}(\mathrm{NO}_3)_2\)), iron(III) phosphate (\(\mathrm{FePO}_4\)), iron(III) nitrate (\(\mathrm{Fe}(\mathrm{NO}_3)_3\)).

Step-by-step solution

Identifying Possible Combinations

To find all possible ionic compounds, we must combine each cation with each anion. This means combining \(\mathrm{Mg}^{2+}\) with \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{NO}_{3}^{-}\), and \(\mathrm{Fe}^{3+}\) with \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{NO}_{3}^{-}\).

Writing the Formula for \(\mathrm{Mg}^{2+}\) and \(\mathrm{PO}_{4}^{3-}\)

To create a neutral compound, balance the positive and negative charges. One \(\mathrm{Mg}^{2+}\) cation and one \(\mathrm{PO}_{4}^{3-}\) anion are combined, resulting in \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\).

Naming the Compound \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\)

This compound is named magnesium phosphate because it consists of magnesium ions and phosphate ions.

Writing the Formula for \(\mathrm{Mg}^{2+}\) and \(\mathrm{NO}_{3}^{-}\)

Each \(\mathrm{Mg}^{2+}\) cation pairs with two \(\mathrm{NO}_{3}^{-}\) anions to balance the charges, giving us \(\mathrm{Mg}(\mathrm{NO}_3)_2\).

Naming the Compound \(\mathrm{Mg}(\mathrm{NO}_3)_2\)

This compound is named magnesium nitrate because it consists of magnesium ions and nitrate ions.

Writing the Formula for \(\mathrm{Fe}^{3+}\) and \(\mathrm{PO}_{4}^{3-}\)

For this combination, one \(\mathrm{Fe}^{3+}\) cation matches with one \(\mathrm{PO}_{4}^{3-}\) anion to form \(\mathrm{FePO}_4\).

Naming the Compound \(\mathrm{FePO}_4\)

This compound is named iron(III) phosphate to reflect the iron's charge and the phosphate anion.

Writing the Formula for \(\mathrm{Fe}^{3+}\) and \(\mathrm{NO}_{3}^{-}\)

To balance the charges with the \(\mathrm{Fe}^{3+}\) cation, three \(\mathrm{NO}_{3}^{-}\) anions are needed, resulting in \(\mathrm{Fe}(\mathrm{NO}_3)_3\).

Naming the Compound \(\mathrm{Fe}(\mathrm{NO}_3)_3\)

This compound is named iron(III) nitrate because it consists of iron ions with a +3 charge and nitrate ions.

Key concepts

Cation-anion combinations

When creating ionic compounds, it's essential to understand the concept of cation-anion combinations. Ions are charged particles—the cations being positively charged and the anions negatively charged. In any ionic compound, the goal is to combine a cation and an anion to form a neutral compound.

For instance, with the cations \(\mathrm{Mg}^{2+}\)and \(\mathrm{Fe}^{3+}\), they can combine with anions such as \(\mathrm{PO}_4^{3-}\)and \(\mathrm{NO}_3^-\). Each cation can pair with each anion, creating different compounds. This is how we form the four different ionic compounds:

• \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\)
• \(\mathrm{Mg}(\mathrm{NO}_3)_2\)
• \(\mathrm{FePO}_4\)
• \(\mathrm{Fe}(\mathrm{NO}_3)_3\)

These combinations result from the need to balance the charges between the cations and anions effectively.

Chemical formula writing

Writing a chemical formula for an ionic compound involves listing the symbols of the cations and anions, with subscripts to indicate the number of each ion needed for charge neutrality.

To write the chemical formula, you need to ensure that the total positive charge equals the total negative charge. This involves calculating the least common multiple (LCM) of the cation and anion charges. For \(\mathrm{Mg}^{2+}\) and \(\mathrm{PO}_4^{3-}\), the LCM is 6. This means you will need three \(\mathrm{Mg}^{2+}\) ions and two \(\mathrm{PO}_4^{3-}\) ions, resulting in the formula \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\).

Similarly, for \(\mathrm{Fe}^{3+}\) and \(\mathrm{NO}_3^-\), the LCM is 9. Thus, you need one \(\mathrm{Fe}^{3+}\) ion and three \(\mathrm{NO}_3^-\) ions, leading to the formula \(\mathrm{Fe}(\mathrm{NO}_3)_3\). Ensuring the smallest set of whole numbers while keeping the compound neutral is key.

Naming ionic compounds

Naming ionic compounds follows specific rules to reflect the nature of the cations and anions involved. The name usually starts with the name of the cation followed by the base name of the anion.

For a compound like \(\mathrm{Mg}_3(\mathrm{PO}_4)_2\), magnesium is the cation and phosphate is the anion, hence it is named magnesium phosphate.

For elements with multiple possible charges, like iron, the charge of the iron must be specified in parentheses using Roman numerals. In \(\mathrm{Fe}(\mathrm{NO}_3)_3\), iron has a charge of +3, so this compound is named iron(III) nitrate. Precision in naming helps ensure we can communicate the exact compounds and their compositions.

Charge balancing in compounds

A critical step in forming ionic compounds is ensuring that the overall charge of the compound is neutral. This is known as charge balancing.

To achieve charge balance, the total positive charge from cations must equal the total negative charge from anions. For example, in \(\mathrm{Mg}(\mathrm{NO}_3)_2\), magnesium has a 2+ charge while each nitrate has a 1- charge. Two nitrate ions will balance one magnesium ion for neutral \(\mathrm{Mg}(\mathrm{NO}_3)_2\).

This process requires a consistent approach, often involving trial and error, by adjusting the subscripts in the chemical formula until a balance is achieved. This ensures that no excess positive or negative charges remain in the compound. Understanding this principle is fundamental for accurately writing and naming ionic compounds.