Question

Predict the chemical formula for each of the following ternary ionic compounds given the formula of barium chlorate, \(\mathrm{Ba}\left(\mathrm{ClO}_{3}\right)_{2}:\) (a) radium chlorate (b) barium bromate

Short answer

(a) Radium chlorate: \( \text{Ra}(\text{ClO}_3)_2 \); (b) Barium bromate: \( \text{Ba}(\text{BrO}_3)_2 \).

Step-by-step solution

Understand the ternary ionic compound

A ternary ionic compound is made up of three different elements. Here, you are dealing with chlorate compounds, which include a metal cation and the polyatomic ion chlorate,  ext{ClO}_3^- . The same approach is used for bromate  ext{BrO}_3^-  in part (b).

Analyze the structure of Barium Chlorate

Observe that in  ext{Ba}( ext{ClO}_3)_2, a barium ion  ext{Ba}^{2+} balances with two chlorate ions  ext{ClO}_3^-. Barium has a 2+ charge, so two 1- charged chlorates are required for charge neutrality.

Formulate Radium Chlorate

Since radium  ext{Ra} is in the same group as barium in the periodic table, it also carries a 2+ charge like barium. Thus, the structure of radium chlorate is analogous to barium chlorate:  ext{Ra}( ext{ClO}_3)_2. Radium ions  ext{Ra}^{2+} balance with two chlorate ions for neutrality.

Formulate Barium Bromate

Instead of changing the metal cation, we're now substituting the polyatomic anion from chlorate to bromate. Barium still carries a 2+ charge, and the bromate ion  ext{BrO}_3^- has a 1- charge. Therefore, two bromate ions balance with one barium ion, resulting in the formula  ext{Ba}( ext{BrO}_3)_2.

Key concepts

Chemical Formula

A chemical formula is a concise way of expressing the number and type of atoms present in a compound. It reveals the elements in the compound and how many atoms of each element are present. For ionic compounds, such as in the case of the discussed ternary ionic compounds, the chemical formula also reflects the charge balance between ions.
To write a chemical formula for a compound like barium chlorate, we identify the elements involved and their respective charges. This ensures the compound is electrically neutral. For example, barium has a charge of +2, and each chlorate ion carries a charge of -1. Thus, it takes two chlorate ions to balance one barium ion, giving us the chemical formula:

• Barium: Ba²⁺
• Chlorate: \[ \text{ClO}_3^-\]

Combined, this results in the formula \[ \mathrm{Ba} (\mathrm{ClO}_3)_2\]. The subscript indicates that two chlorate ions are needed.

Barium Chlorate

Barium chlorate is a crystalline solid represented by the chemical formula \[ \mathrm{Ba}(\mathrm{ClO}_3)_2\]. This formula reveals that each formula unit is comprised of one barium ion and two chlorate ions.
The barium ion (Ba) is a metal cation that has a +2 charge. Since barium belongs to Group 2 of the periodic table, it consistently exhibits this +2 oxidation state.
To maintain charge neutrality in barium chlorate, each barium ion is paired with two chlorate ions. Each chlorate has a -1 charge, so two are needed to equal the +2 charge of the barium ion:

• Barium ion: Ba²⁺
• Chlorate ion: \[ \text{ClO}_3^-\]

The arrangement ensures that the positive and negative charges cancel out, creating a stable ionic compound.

Radium Chlorate

Radium chlorate, similar to barium chlorate, is a ternary ionic compound. Its chemical formula is \[ \mathrm{Ra}(\mathrm{ClO}_3)_2\]. In this compound, radium replaces barium as the metal cation. Like barium, radium also carries a +2 charge, since they are both in Group 2 of the periodic table.
Radium ions are balanced by two chlorate ions in this compound, ensuring electrical neutrality. The steps to derive the formula are identical to those used for barium chlorate:

• Radium ion: Ra²⁺
• Chlorate ion: \[ \text{ClO}_3^-\]

Two chlorate ions, each with a -1 charge, are needed to balance the +2 charge of one radium ion. This results in the balanced chemical formula mentioned above.

Barium Bromate

Barium bromate involves the substitution of bromate ions into a similar structure as barium chlorate. The chemical formula for barium bromate is \[ \mathrm{Ba}(\mathrm{BrO}_3)_2\]. Here, the chlorate ion is replaced by the bromate ion.
Both the bromate ion and the chlorate ion function similarly in terms of charge, each carrying a -1 charge. This means that the formula creation process is quite similar:

• Barium ion: Ba²⁺
• Bromate ion: \[ \text{BrO}_3^-\]

Two bromate ions are required to balance the +2 charge of one barium ion. Therefore, the neutral compound formula is stated as \[ \mathrm{Ba}(\mathrm{BrO}_3)_2\], with the subscript indicating how many bromate ions are involved.