Question

Predict the chemical formulas of the compounds formed by the following paire of ions: (a) \(\mathrm{Cu}^{2+}\) 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 \(\mathrm{AsO}_{4}{ }^{3-}\), (e) \(\mathrm{NH}_{4}{ }^{+}\) and \(\mathrm{CO}_{3}{ }^{2-}\)

Short answer

The chemical formulas of the compounds formed by the given pairs of ions are: (a) \(\mathrm{CuBr}\) (b) \(\mathrm{Fe}_2\mathrm{O}_3\) (c) \(\mathrm{Hg}_{2}\mathrm{CO}_3\) (d) \(\mathrm{Ca}_3(\mathrm{AsO}_4)_2\) (e) \((\mathrm{NH}_4)_2\mathrm{CO}_{3}\)

Step-by-step solution

Understanding the rules for writing chemical formulas

To determine the correct ratio of the ions in the ionic compound, we can use the "cross-over rule." This rule states that the numerical values of the charges on the positive and negatively charged ions should be switched to determine the correct ratio for the neutral compound. For example, if one ion has a charge of +2 and the other has a charge of -3, the compound's formula would have three of the +2 ion and two of the -3 ion to create a neutral compound.

Applying the cross-over rule for ion pair (a)

The given ions are \(\mathrm{Cu}^{2+}\) and \(\mathrm{Br}^{-}\). Swap the charge numbers between the ions and write them as subscripts: \(\mathrm{CuBr}_2\). Since the ratio is 1:1, we can simplify and write the final formula as \(\mathrm{CuBr}\).

Applying the cross-over rule for ion pair (b)

The given ions are \(\mathrm{Fe}^{3+}\) and \(\mathrm{O}^{2-}\). Swap the charge numbers between the ions and write them as subscripts: \(\mathrm{Fe}_2\mathrm{O}_3\). The formula for this compound is \(\mathrm{Fe}_2\mathrm{O}_3\).

Applying the cross-over rule for ion pair (c)

The given ions are \(\mathrm{Hg}_{2}^{2+}\) and \(\mathrm{CO}_{3}^{2-}\). Since both ions have a charge of 2, the ratio is 1:1 and no subscripts are needed. The formula for this compound is \(\mathrm{Hg}_{2}\mathrm{CO}_3\).

Applying the cross-over rule for ion pair (d)

The given ions are \(\mathrm{Ca}^{2+}\) and \(\mathrm{AsO}_{4}^{3-}\). Swap the charge numbers between the ions and write them as subscripts: \(\mathrm{Ca}_3(\mathrm{AsO}_4)_2\). The formula for this compound is \(\mathrm{Ca}_3(\mathrm{AsO}_4)_2\).

Applying the cross-over rule for ion pair (e)

The given ions are \(\mathrm{NH}_{4}^{+}\) and \(\mathrm{CO}_{3}^{2-}\). Swap the charge numbers between the ions and write them as subscripts: \((\mathrm{NH}_4)_2\mathrm{CO}_{3}\). The formula for this compound is \((\mathrm{NH}_4)_2\mathrm{CO}_{3}\). In conclusion, the chemical formulas of the compounds formed by the given pairs of ions are: (a) \(\mathrm{CuBr}\) (b) \(\mathrm{Fe}_2\mathrm{O}_3\) (c) \(\mathrm{Hg}_{2}\mathrm{CO}_3\) (d) \(\mathrm{Ca}_3(\mathrm{AsO}_4)_2\) (e) \((\mathrm{NH}_4)_2\mathrm{CO}_{3}\)

Key concepts

Cross-Over Rule

The cross-over rule is a simple method used to determine the correct chemical formula of an ionic compound. It utilizes the idea of combining positive ions (cations) and negative ions (anions) to form a neutral compound. To use this rule, first identify the charges on the ions you wish to combine. Then, switch the numerical values of these charges from one ion to the other, and use them as subscripts in the chemical formula. This helps balance the total positive and negative charges, ensuring the compound is neutral.

For example, consider the ions \(\mathrm{Fe}^{3+}\) and \(\mathrm{O}^{2-}\):- The positive ion, \(\mathrm{Fe}^{3+}\), has a charge of \(+3\). - The negative ion, \(\mathrm{O}^{2-}\), has a charge of \(-2\). By applying the cross-over rule, the 3 from \(\mathrm{Fe}^{3+}\) becomes the subscript for \(\mathrm{O}\), and the 2 from \(\mathrm{O}^{2-}\) becomes the subscript for \(\mathrm{Fe}\). Thus, the chemical formula derived is \(\mathrm{Fe}_2\mathrm{O}_3\). This ensures an overall neutral charge in the compound.

Ionic Compounds

Ionic compounds are chemical compounds composed of ions held together by ionic bonds. These bonds form when atoms donate or accept electrons, resulting in a positive or negative charge. Cations are positively charged ions, whereas anions are negatively charged. The strong electrostatic attraction between oppositely charged ions leads to the formation of ionic compounds.

Some characteristics of ionic compounds include:

• They typically have high melting and boiling points because of the strong ionic bonds.
• Ionic compounds are usually soluble in water, facilitating the formation of solutions that conduct electricity.
• They often form crystalline solids, exhibiting a remarkable, repeating structure.

Consider the ionic compound \(\mathrm{Ca}_3(\mathrm{AsO}_4)_2\): This compound contains \(\mathrm{Ca}^{2+}\) cations and \(\mathrm{AsO}_4^{3-}\) anions. The compound's formula reflects a balanced charge, achieved by properly following the cross-over rule.

Ion Charges

Ion charges are crucial for understanding the nature of ionic compounds. When atoms lose or gain electrons, they become ions, possessing a net charge due to an imbalance of protons and electrons. The charge on an ion is determined by the number of electrons that are lost or gained.

For instance:- A \(\mathrm{Cu}^{2+}\) ion has lost two electrons, leading to a positive charge of 2.- A \(\mathrm{Br}^{-}\) ion has gained one electron, resulting in a negative charge of 1.
These charges play a vital role in forming stable ionic compounds as ions with opposite charges attract each other. The charges ensure the correct stoichiometry of the compounds, making them electrically neutral. When predicting chemical formulas, understanding and correctly applying ion charges is essential to ensure that the resulting compounds have balanced charges.