Question

Predict the chemical formulas of the compounds formed by the following pairs of ions: (a) \(\mathrm{Cr}^{3+}\) and \(\mathrm{Br}^{-}\), (b) \(\mathrm{Fe}^{3+}\) and \(\mathrm{O}^{2-}\), (c) \(\mathrm{Hg}_{2}{ }^{2+}\) and \(\mathrm{CO}_{3}{ }^{2-}\), (d) \(\mathrm{Ca}^{2+}\) and \(\mathrm{ClO}_{3}^{-}\), (e) \(\mathrm{NH}_{4}^{+}\)and \(\mathrm{PO}_{4}{ }^{3-}\).

Short answer

The chemical formulas of the compounds formed by the given pairs of ions are: (a) \(\mathrm{CrBr}_{3}\) (b) \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) (c) \(\mathrm{Hg}_{2}\mathrm{CO}_{3}\) (d) \(\mathrm{Ca}(\mathrm{ClO}_{3})_{2}\) (e) \(\mathrm{(NH}_{4}\mathrm{)_{3}PO}_{4}\)

Step-by-step solution

(a) \(\mathrm{Cr}^{3+}\) and \(\mathrm{Br}^{-}\)

To balance the charges, we need to find the least common multiple (LCM) of the two charges which in our case is 3. This means we need 3 \(\mathrm{Br}^-\) ions to balance the charge of one \(\mathrm{Cr}^{3+}\) ion. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{CrBr}_{3}\).

(b) \(\mathrm{Fe}^{3+}\) and \(\mathrm{O}^{2-}\)

To balance the charges, we need to find the least common multiple (LCM) of the two charges which in our case is 6. This means we need 2 \(\mathrm{O}^{2-}\) ions to balance the charge of 3 \(\mathrm{Fe}^{3+}\) ions. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{Fe}_{2}\mathrm{O}_{3}\).

(c) \(\mathrm{Hg}_{2}{ }^{2+}\) and \(\mathrm{CO}_{3}{ }^{2-}\)

In this case, the charges are already balanced as the positive charge is +2 and the negative charge is -2. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{Hg}_{2}\mathrm{CO}_{3}\).

(d) \(\mathrm{Ca}^{2+}\) and \(\mathrm{ClO}_{3}^{-}\)

To balance the charges, we need to find the least common multiple (LCM) of the two charges which in our case is 2. This means we need 2 \(\mathrm{ClO}_3^-\) ions to balance the charge of one \(\mathrm{Ca}^{2+}\) ion. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{Ca}(\mathrm{ClO}_{3})_{2}\).

(e) \(\mathrm{NH}_{4}^{+}\) and \(\mathrm{PO}_4^{3-}\)

To balance the charges, we need to find the least common multiple (LCM) of the two charges which in our case is 3. This means we need 3 \(\mathrm{NH}_4^+\) ions to balance the charge of one \(\mathrm{PO}_4^{3-}\) ion. Therefore, the chemical formula of the compound formed by these ions is \(\mathrm{(NH}_{4}\mathrm{)_{3}PO}_{4}\).

Key concepts

Understanding Ions

Ions are atoms or molecules that have gained or lost electrons, leading them to have a charge. This charge can be positive or negative:

• Cations: Positively charged ions created when an atom loses electrons. For example, \( \mathrm{Cr}^{3+} \) is a cation because it has lost three electrons.
• Anions: Negatively charged ions formed when an atom gains electrons. \( \mathrm{Br}^{-} \) is an anion, having gained one electron.

These ions combine to form compounds, balancing out their charges in the process.

Forming Compounds

Compounds are created when ions of opposite charges attract and bond. The key is to balance the charges so that the overall charge of the compound equals zero.
- **Example:** When \( \mathrm{Cr}^{3+} \) combines with \( \mathrm{Br}^{-} \), three \( \mathrm{Br}^{-} \) ions are needed to balance the charge of one \( \mathrm{Cr}^{3+} \), resulting in the formula \( \mathrm{CrBr}_{3} \).
This principle applies to all ionic compounds, ensuring that the total positive charges equal the total negative charges.

The Importance of Charge Balancing

Charge balancing is essential when predicting chemical formulas because it ensures stability in compounds. When unbalanced, compounds would have surplus charges, making them unstable.
- **How to Balance Charges:**

• Determine the charge of each ion.
• Find the least common multiple (LCM) of the charges.
• Adjust the number of ions needed to balance the charges.

For example, with \( \mathrm{Fe}^{3+} \) and \( \mathrm{O}^{2-} \), the LCM is 6, meaning you require two \( \mathrm{O}^{2-} \) ions and three \( \mathrm{Fe}^{3+} \) ions to form \( \mathrm{Fe}_{2}\mathrm{O}_{3} \). This ensures the compound is neutral and stable.