Question

Write the correct ionic formula for the compound formed between each of the following pairs of ions: a. \(\mathrm{Na}^{+}\) and \(\mathrm{O}^{2}\) b. \(\mathrm{Al}^{3+}\) and \(\mathrm{Br}^{-}\) c. \(\mathrm{Ba}^{2+}\) and \(\mathrm{N}^{3-}\) d. \(\mathrm{Mg}^{2+}\) and \(\mathrm{F}^{-}\) e. \(\mathrm{Al}^{3+}\) and \(\mathrm{S}^{2-}\)

Short answer

(a) \(\text{Na}_2\text{O}\) (b) \(\text{AlBr}_3\) (c) \(\text{Ba}_3\text{N}_2\) (d) \(\text{MgF}_2\) (e) \(\text{Al}_2\text{S}_3\)

Step-by-step solution

Identify the charges of each ion

Look at the given pairs of ions and note their charges: (a) \(\text{Na}^+\) and \(\text{O}^{2-}\) (b) \(\text{Al}^{3+}\) and \(\text{Br}^-\) (c) \(\text{Ba}^{2+}\) and \(\text{N}^{3-}\) (d) \(\text{Mg}^{2+}\) and \(\text{F}^-\) (e) \(\text{Al}^{3+}\) and \(\text{S}^{2-}\)

Determine the ratio of ions

To balance the overall charge of the compound, the total positive charge should equal the total negative charge for each pair: (a) Two \(\text{Na}^+\) ions for every one \(\text{O}^{2-}\) ion (b) Three \(\text{Br}^-\) ions for every one \(\text{Al}^{3+}\) ion (c) Three \(\text{Ba}^{2+}\) ions for every two \(\text{N}^{3-}\) ions (d) Two \(\text{F}^-\) ions for every one \(\text{Mg}^{2+}\) ion (e) Two \(\text{Al}^{3+}\) ions for every three \(\text{S}^{2-}\) ions

Write the chemical formula

Form the chemical formula using the determined ratios, ensuring the total charge balance: (a) \(\text{Na}_2\text{O}\) (b) \(\text{AlBr}_3\) (c) \(\text{Ba}_3\text{N}_2\) (d) \(\text{MgF}_2\) (e) \(\text{Al}_2\text{S}_3\)

Key concepts

ion charges

In any ionic compound, the charges on the ions are crucial because they determine how these ions combine. Atoms can lose or gain electrons to form ions, resulting in a positive (cation) or a negative (anion) charge.
For instance, \(\text{Na}^{+}\) is a cation because it has lost one electron, while \(\text{O}^{2-}\) is an anion because it has gained two electrons.Recognizing these charges helps us figure out how many of each ion are needed to form a neutral compound.
To balance the charges in an ionic compound, we adjust the number of cations and anions so that the total positive charge equals the total negative charge.
This concept is fundamental in correctly writing ionic formulas.

ratio of ions

Once we know the charges of the ions, the next step is to determine the correct ratio of ions in the compound.
The goal is to balance the overall charge. Let's take some examples to understand better:

• For \(\text{Na}^{+}\) and \(\text{O}^{2-}\), to balance two positive charges from \(\text{Na}^{+}\) with one negative charge from \(\text{O}^{2-}\), we need two \(\text{Na}^{+}\) ions. Thus, the ratio is 2:1, forming \(\text{Na}_{2}\text{O}\).
• For \(\text{Al}^{3+}\) and \(\text{Br}^{-}\), three \(\text{Br}^{-}\) ions (each bringing one negative charge) are needed to balance one \(\text{Al}^{3+}\) ion (bringing three positive charges), making the ratio 1:3 and forming \(\text{AlBr}_3\).
• For \(\text{Ba}^{2+}\) and \(\text{N}^{3-}\), we need three \(\text{Ba}^{2+}\) ions to balance two \(\text{N}^{3-}\) ions, bringing the ratio to 3:2 and yielding \(\text{Ba}_3\text{N}_2\).

Understanding the ratio of ions ensures the compound remains electrically neutral.

chemical formula

The chemical formula of an ionic compound is a concise way of expressing the ratios of ions within that compound.
Let's look at the finalized formulas from our examples:

• \(\text{Na}_2\text{O}\) reflects two sodium ions (each +1 charge) balancing one oxide ion (with a -2 charge).
• \(\text{AlBr}_3\) shows one aluminum ion (+3 charge) balanced by three bromide ions (each -1 charge).
• \(\text{Ba}_3\text{N}_2\) indicates three barium ions (each +2 charge) balanced by two nitride ions (each -3 charge).

In each case, we are ensuring that the total number of positive charges equals the total number of negative charges.
This is how we maintain electrical neutrality in the compound.
Writing the correct chemical formula is essentially about showing these balanced ratios in a compact form.