Question

Fill in the missing information to give the correct formula for each compound: (a) \(\mathrm{Al}_{?}\left(\mathrm{SO}_{4}\right)_{?}\) (b) \(\left(\mathrm{NH}_{4}\right)_{2}\left(\mathrm{PO}_{4}\right)_{2}\) (c) \(\mathrm{Rb}_{2}\left(\mathrm{SO}_{4}\right)_{?}\)

Short answer

(a) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) , (b) correct as given, (c) \(\mathrm{Rb}_{2}\left(\mathrm{SO}_{4}\right)\).

Step-by-step solution

Determine the charge of each ion in the compounds

For (a) Aluminum ion (\(\mathrm{Al}^{3+}\) ) and sulfate ion (\(\mathrm{SO}_{4}^{2-}\)) - we need to balance the overall charge.(b) Ammonium ion (\(\mathrm{NH}_{4}^{+}\)) and phosphate ion (\(\mathrm{PO}_{4}^{3-}\)) -- ensure the compound charge balance is correct.(c) Rubidium ion (\(\mathrm{Rb}^{+}\)) and sulfate ion (\(\mathrm{SO}_{4}^{2-}\)) - find the number of sulfate ions needed to balance the charge.

Balance the charges to find the subscript values

(a) To balance \(\mathrm{Al}^{3+}\) with \(\mathrm{SO}_{4}^{2-}\), use the least common multiple of the charges: 6. This implies the formula is \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\).(b) The compound given is \(\left(\mathrm{NH}_{4}\right)_{2}\left(\mathrm{PO}_{4}\right)_{2}\), there's no need to change since it already describes formation between two di-ammonium units and two phosphate units.(c) For \(\mathrm{Rb}^{+}\) and \(\mathrm{SO}_{4}^{2-}\),two rubidium ions will be needed to balance one sulfate ion, hence the formula is \(\mathrm{Rb}_{2}\left(\mathrm{SO}_{4}\right)_{1}\).

Key concepts

Ion Charges

Atoms can gain or lose electrons to form ions, which are charged particles. When an atom loses electrons, it becomes a positively charged ion, or cation. Conversely, when an atom gains electrons, it forms a negatively charged ion, or anion. The charge on an ion plays a critical role in the formation of chemical compounds.

• Cations: Metals frequently lose electrons, forming cations. For example, an aluminum atom loses three electrons to become \( ext{Al}^{3+} \).
• Anions: Non-metals typically gain electrons, developing into anions. A sulfate ion, \( ext{SO}_{4}^{2-} \), is formed when the sulfur atom gains two electrons.

Identifying the charges of the ions is essential as it aids in determining how the ions will combine to form a neutral compound. This charge information is the starting point for understanding how to achieve charge balance in compounds.

Charge Balance

The next step in forming a chemical compound is ensuring that the total charge of the compound is balanced. This means that the sum of positive charges (from cations) must equal the sum of negative charges (from anions).

Balancing the charges necessitates finding the least common multiple of the ions' charges. For instance, in aluminum sulfate, the charges are \( ext{Al}^{3+} \) and \( ext{SO}_{4}^{2-} \). The least common multiple of the charges 3 and 2 is 6. Therefore, you will need two aluminum ions (each with a charge of +3) and three sulfate ions (each with a charge of -2) to balance the charges, resulting in the neutral compound formula \( ext{Al}_2( ext{SO}_4)_3 \).

Understanding charge balance is crucial because compounds existing as neutral entities ensure that chemical reactions can proceed efficiently and predictably.

Compound Formation

Once ion charges are understood and balanced, ions combine in specific ratios to form compounds. The subscripts in a chemical formula indicate the number of each type of ion required to achieve electrical neutrality in the compound.

In the process of forming ammonium phosphate, ions \( ext{NH}_4^{+} \) and \( ext{PO}_4^{3-} \) are involved. The compound formula \( ( ext{NH}_4)_3( ext{PO}_4) \) sets three positive ammonium ions against one negative phosphate ion, balancing the overall charge.

For rubidium sulfate, the addition of two \( ext{Rb}^{+} \) ions to one \( ext{SO}_4^{2-} \) ion results in the compound \( ext{Rb}_2( ext{SO}_4) \). Compound formation, therefore, is the culmination of understanding ion charges and attaining charge balance, fundamentally depicted in the chemical formula. This atomic choreography provides the structure that helps predict compound behavior during chemical reactions.