Question

Write the chemical formula for the following ternary compounds given their constituent ions: (a) iron(III) hydrogen carbonate, \(\mathrm{Fe}^{3+}\) and \(\mathrm{HCO}_{3}^{-}\) (b) cuprous carbonate, \(\mathrm{Cu}^{+}\) and \(\mathrm{CO}_{3}^{2-}\) (c) mercury(II) cyanide, \(\mathrm{Hg}^{2+}\) and \(\mathrm{CN}\) (d) stannic acetate, \(\mathrm{Sn}^{4+}\) and \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\)

Short answer

(a) Fe(HCO_{3})_{3} , (b) Cu_{2}CO_{3} , (c) Hg(CN)_{2} , (d) Sn(C_{2}H_{3}O_{2})_{4}

Step-by-step solution

Understanding the Problem

To form the chemical formulas for ternary compounds, we need to ensure that the total positive charge from the metal ion balances with the total negative charge from the polyatomic ions. We will find the smallest ratio of metal ions to polyatomic ions needed to achieve this balance.

Determine Formula for Iron(III) Hydrogen Carbonate

Iron(III) has a charge of +3 ( Fe^{3+} ), while hydrogen carbonate has a charge of -1 ( HCO_{3}^{-} ). To balance the charges, we need three hydrogen carbonate ions for every one iron(III) ion. Hence, the formula is Fe(HCO_{3})_{3} .

Determine Formula for Cuprous Carbonate

Cuprous (copper I) has a charge of +1 ( Cu^{+} ) and carbonate has a charge of -2 ( CO_{3}^{2-} ). Thus, two cuprous ions are needed per carbonate ion to balance the charges. The chemical formula is Cu_{2}CO_{3} .

Determine Formula for Mercury(II) Cyanide

Mercury(II) has a charge of +2 ( Hg^{2+} ) and cyanide has a charge of -1 ( CN^{-} ). Therefore, two cyanide ions are required to balance the charge of one mercury(II) ion, resulting in the formula Hg(CN)_{2} .

Determine Formula for Stannic Acetate

Stannic (tin IV) has a charge of +4 ( Sn^{4+} ) and acetate has a charge of -1 ( C_{2}H_{3}O_{2}^{-} ). We need four acetate ions to balance the charge of one stannic ion. Thus, the compound's formula is Sn(C_{2}H_{3}O_{2})_{4} .

Key concepts

Ternary Compounds

Ternary compounds involve three different elements coming together to form a compound. Often, the combination includes a metal along with two non-metals. Usually, one of these non-metals forms a polyatomic ion, such as carbonate or acetate.
These compounds are diverse and can include elements from several groups on the periodic table.

• For example, in iron(III) hydrogen carbonate, you have iron as the metal and carbonate as the polyatomic ion combined with hydrogen.
• These ternary compounds are a bit more complex than binary compounds, which only consist of two elements.

To form ternary compounds, understanding and balancing the charges of their constituent ions is crucial.

Ions and Charges

Ions are atoms or molecules that have gained or lost one or more electrons, resulting in a positive or negative charge. This charge is critical when writing chemical formulas, especially for compounds involving multiple ions.
Ions can be either cations, which are positively charged, or anions, which are negatively charged:

• Cations: Formed by losing electrons, leading to a positive charge. For example, \(\mathrm{Fe}^{3+}\) indicates iron has lost three electrons.
• Anions: Formed by gaining electrons, resulting in a negative charge. For instance, \(\mathrm{HCO}_{3}^{-}\) means the hydrogen carbonate ion has gained an electron.

The charges on the ions must be balanced when forming chemical compounds, an essential step in writing chemical formulas.

Balancing Charges

Balancing charges is a vital step in forming chemical formulas for compounds, especially ternary compounds. Each compound's neutrality means the total positive charge must equal the total negative charge.
This step often involves determining the smallest ratio of cations to anions required to achieve a net charge of zero.

• Take, for example, mercury(II) cyanide. Mercury's charge is \(\mathrm{Hg}^{2+}\), while cyanide is \(\mathrm{CN}^{-}\). You need two cyanide ions to balance one mercury ion, leading to the formula \(\mathrm{Hg(CN)_{2}}\).
• Similarly, cuprous carbonate, with \(\mathrm{Cu}^{+}\) and \(\mathrm{CO}_{3}^{2-}\), requires two copper ions per carbonate ion for charge balance. Thus, it forms \(\mathrm{Cu_{2}CO_{3}}\).

Polyatomic Ions

Polyatomic ions are ions that consist of more than one atom. Unlike monatomic ions, which are composed of a single atom, polyatomic ions have multiple atoms bonded together, often with an overall charge.
These ions are stable groups of atoms that maintain their identity in chemical reactions.

• Common examples include bicarbonate \(\mathrm{HCO}_{3}^{-}\), carbonate \(\mathrm{CO}_{3}^{2-}\), and acetate \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\).
• They play a crucial role in forming ternary compounds by complementing metal ions to balance charges.

Polyatomic ions require special consideration when balancing charges due to their collective charge and complex structure.