Question

Consider an anion and a cation joining to form a compound. (a) How does knowing the charge of the ions help to determine the formula? (b) What would be the formula of the compound formed from \(\mathrm{Ca}^{2+}\) cations and \(\mathrm{N}^{3-}\) anions?

Short answer

Knowing the charges of ions helps determine the formula of an ionic compound as it allows us to find the ratio of cations and anions required to achieve a neutral charge. To find the formula of the compound formed by Ca²⁺ cations and N³⁻ anions, balance their charges by finding their least common multiple, which is 6 in this case. The balanced ratio requires 3 Ca²⁺ ions and 2 N³⁻ ions, resulting in the compound formula Ca₃N₂.

Step-by-step solution

((a) Understanding Charge Role)

In an ionic compound, cations (positively charged ions) and anions (negatively charged ions) are held together by electrostatic forces. The overall charge of the compound must be neutral (meaning their charges cancel out each other). Knowing the charges of the ions helps in determining the ratio of the ions in the compound to achieve a neutral charge. The compound's formula can be determined by finding this balance between the charges of the cations and the anions.

(b) Finding the Compound Formula for Ca²⁺ and N³⁻)

In order to find the formula of the compound formed by Ca²⁺ cations and N³⁻ anions, we should first balance their charges: 1. The calcium ion, Ca²⁺, has a charge of +2. 2. The nitrogen ion, N³⁻, has a charge of -3. The goal is to find the ratio of Ca²⁺ and N³⁻ ions in the compound so that the total charge becomes zero. To do this, determine the smallest multiple of the charges that will make their sum zero. This can be done by finding the least common multiple (LCM) of the absolute values of charges. The LCM of 2 and 3 is 6. To make the sum of charges zero, we need: 1. 3 Ca²⁺ ions: total charge = 3 * (+2) = +6 2. 2 N³⁻ ions: total charge = 2 * (-3) = -6 Thus, the formula of the compound will have three calcium ions (Ca³) and two nitrogen ions (N²). The formula of the compound formed by Ca²⁺ and N³⁻ ions is Ca₃N₂.

Key concepts

Cation and Anion Charges

Understanding the charges on cations and anions is critical when studying ionic compounds. Cations are positively charged ions, usually metal atoms that have lost one or more electrons.
Anions, on the other hand, are negatively charged ions, typically non-metal atoms that have gained one or more electrons. The charge of an ion is usually indicated by a superscript number and sign, with positive for cations and negative for anions. For example, a calcium ion with a charge of +2 is denoted as \(\mathrm{Ca}^{2+}\), while a nitrogen ion with a charge of -3 is represented as \(\mathrm{N}^{3-}\).

The charge determines how ions will combine to form an ionic compound. Ions come together in a way that their total charge is neutralized, meaning the positive and negative charges balance out to zero. Consequently, knowing the charge of an ion can help predict with what and how it will bond to form a stable ionic compound.

Neutral Charge Balance

The principle of neutral charge balance is the cornerstone of forming ionic compounds. It states that the total positive charge must equal the total negative charge, resulting in a compound with no overall charge.
This is because in nature, substances tend to be electrically neutral. To achieve this balance, ions combine in ratios that make the sum of their charges equal to zero. For example, if we have a metal ion with a 2+ charge and a non-metal ion with a 3- charge, the metal ion will need to pair with one and a half non-metal ions to balance out. However, since we can't have half an ion, we find the least common multiple of their charges to determine the smallest whole number of ions we need for a neutral compound, which in our example leads to a formula of the compound as \(\mathrm{Ca}_3\mathrm{N}_2\).

By understanding the need for a neutral charge and how to balance charges, students can more confidently predict the formula of any ionic compound they encounter.

Least Common Multiple (LCM)

When figuring out the formula for an ionic compound, the least common multiple (LCM) of the charges is used to find the smallest ratios of ions that result in a neutral compound. The LCM is the smallest number that is a multiple of both charges.
Let's say we have a \(\mathrm{Ca}^{2+}\) ion and a \(\mathrm{N}^{3-}\) ion. To combine them into a compound where the charges cancel out, we find the LCM of 2 and 3, which is 6. This implies that we need three \(\mathrm{Ca}^{2+}\) ions (totaling a +6 charge) and two \(\mathrm{N}^{3-}\) ions (totaling a -6 charge) to create an electrically neutral compound \(\mathrm{Ca}_3\mathrm{N}_2\).

Understanding the concept of LCM is vital as it not only applies to chemistry but is also a fundamental mathematical principle used across various fields, reinforcing the importance of interdisciplinary knowledge in solving scientific problems.