Question

For the following pairs of ions, use the principle of electrical neutrality to predict the formula of the binary compound that the ions are most likely to form. a. \(\mathrm{Na}^{+}\) and \(\mathrm{S}^{2-}\) b. \(\mathrm{K}^{+}\) and \(\mathrm{Cl}^{-}\) c. \(\mathrm{Ba}^{2+}\) and \(\mathrm{O}^{2-}\) d. \(\mathrm{Mg}^{2+}\) and \(\mathrm{Se}^{2-}\) e. \(\mathrm{Cu}^{2+}\) and \(\mathrm{Br}^{-}\) f. \(\mathrm{Al}^{3+}\) and \(\mathrm{I}^{-}\) g. \(\mathrm{Al}^{3+}\) and \(\mathrm{O}^{2-}\) h. \(\mathrm{Ca}^{2+}\) and \(\mathrm{N}^{3-}\)

Short answer

The formulas for the binary compounds are: a. \(\mathrm{Na_{2}S}\) b. \(\mathrm{KCl}\) c. \(\mathrm{BaO}\) d. \(\mathrm{MgSe}\) e. \(\mathrm{CuBr_{2}}\) f. \(\mathrm{AlI_{3}}\) g. \(\mathrm{Al_{2}O_{3}}\) h. \(\mathrm{Ca_{3}N_{2}}\)

Step-by-step solution

Understand Electrical Neutrality

The principle of electrical neutrality states that in a compound, the total positive charges from the cations (positively charged ions) must equal the total negative charges from the anions (negatively charged ions) to achieve a neutral compound.

Predict the formulas for each pair of ions

For each pair of ions, find the least common multiple of their charges and determine the ratio of the ions in the compound so that the charges neutralize. a. \(\mathrm{Na}^{+}\), \(\mathrm{S}^{2-}\): Since \(\mathrm{Na}\) has a charge of +1 and \(\mathrm{S}\) has a charge of -2, their least common multiple is 2. Hence, the formula is \(\mathrm{Na_{2}S}\). b. \(\mathrm{K}^{+}\), \(\mathrm{Cl}^{-}\): Since \(\mathrm{K}\) has a charge of +1 and \(\mathrm{Cl}\) has a charge of -1, their least common multiple is 1. Hence, the formula is \(\mathrm{KCl}\). c. \(\mathrm{Ba}^{2+}\), \(\mathrm{O}^{2-}\): Since \(\mathrm{Ba}\) has a charge of +2 and \(\mathrm{O}\) has a charge of -2, their least common multiple is 2. Hence, the formula is \(\mathrm{BaO}\). d. \(\mathrm{Mg}^{2+}\), \(\mathrm{Se}^{2-}\): Since \(\mathrm{Mg}\) has a charge of +2 and \(\mathrm{Se}\) has a charge of -2, their least common multiple is 2. Hence, the formula is \(\mathrm{MgSe}\). e. \(\mathrm{Cu}^{2+}\), \(\mathrm{Br}^{-}\): Since \(\mathrm{Cu}\) has a charge of +2 and \(\mathrm{Br}\) has a charge of -1, their least common multiple is 2. Hence, the formula is \(\mathrm{CuBr_{2}}\). f. \(\mathrm{Al}^{3+}\), \(\mathrm{I}^{-}\): Since \(\mathrm{Al}\) has a charge of +3 and \(\mathrm{I}\) has a charge of -1, their least common multiple is 3. Hence, the formula is \(\mathrm{AlI_{3}}\). g. \(\mathrm{Al}^{3+}\), \(\mathrm{O}^{2-}\): Since \(\mathrm{Al}\) has a charge of +3 and \(\mathrm{O}\) has a charge of -2, their least common multiple is 6. To achieve electrical neutrality, we need 2 \(\mathrm{Al}\) ions (+6 total charge) and 3 \(\mathrm{O}\) ions (-6 total charge). Hence, the formula is \(\mathrm{Al_{2}O_{3}}\). h. \(\mathrm{Ca}^{2+}\), \(\mathrm{N}^{3-}\): Since \(\mathrm{Ca}\) has a charge of +2 and \(\mathrm{N}\) has a charge of -3, their least common multiple is 6. To achieve electrical neutrality, we need 3 \(\mathrm{Ca}\) ions (+6 total charge) and 2 \(\mathrm{N}\) ions (-6 total charge). Hence, the formula is \(\mathrm{Ca_{3}N_{2}}\).

Key concepts

Ionic Bonding

When atoms come together to form compounds, they often either lose or gain electrons in pursuit of more stable electron configurations. This can lead to the formation of ions: positively charged cations and negatively charged anions. Ionic bonding occurs when these oppositely charged ions are strongly attracted to each other. This attraction creates a stable compound.

In ionic bonding:

• Cations, like \( ext{Na}^+\), lose electrons and thus carry a positive charge.
• Anions, like \( ext{S}^{2-}\), gain electrons and carry a negative charge.
• The strength of ionic bonding is influenced by the charge and size of the ions involved.

For example, when \( ext{Na}^+\) and \( ext{S}^{2-}\) form a compound, they combine to neutralize their charges through ionic bonds, creating sodium sulfide \( ext{Na}_{2} ext{S}\).

This type of bonding is common in compounds formed between metals (which form cations) and non-metals (which form anions). Understanding ionic bonding is fundamental to predicting the structure and properties of ionic compounds.

Electrical Neutrality

Chemical compounds, to be stable, need to be electrically neutral. This means that the total positive charges from cations must equal the total negative charges from anions within the compound. Without this balance, the compound would have a net charge, which is generally not stable in natural conditions.

The principle of electrical neutrality dictates that:

• The sum of all charges should equal zero.
• Each compound has a specific formula that reflects this balance.

To find the formula of a compound, you can use the charges from the ions to determine how many of each ion you need. Take, for instance, the ions \( ext{K}^+\) and \( ext{Cl}^-\). Each potassium ion has a +1 charge and each chloride ion has a -1 charge. Therefore, one \( ext{K}^+\) ion pairs with one \( ext{Cl}^-\) ion to form potassium chloride \( ext{KCl}\), achieving electrical neutrality.

Charge Balancing

Predicting the formula of an ionic compound involves understanding charge balancing. This means figuring out the right ratio of cations to anions such that their charges neutralize each other.

Here's how you can achieve charge balancing:

• Identify the charge of each ion involved.
• Find the least common multiple (LCM) of the charges if they differ.
• Determine how many ions are needed from each to achieve a total charge of zero.

For example, in the case of \( ext{Ca}^{2+}\) and \( ext{N}^{3-}\), the LCM of 2 and 3 is 6. To balance charges, you need three \( ext{Ca}^{2+}\) ions (totaling +6 charge) and two \( ext{N}^{3-}\) ions (totaling -6 charge). This balance gives the formula \( ext{Ca}_{3} ext{N}_{2}\).

Mastering charge balancing is crucial for correctly writing formulas and understanding the structures of ionic compounds. It ensures that we adhere to the universal principle that compounds strive for electrical neutrality.