Problem 42 - Chemistry and Chemical Reactivity

Question

What are the charges of the ions in an ionic compound containing cobalt(III) and fluoride ions? Write the formula for the compound.

Step-by-Step Solution

Answer

The charges are +3 for cobalt(III) and -1 for fluoride. The formula is \( \text{CoF}_3 \).

Step 1: Identify the Ions

Cobalt(III) indicates that the cobalt ion has a charge of +3, written as \( \text{Co}^{3+} \).Fluoride ion is the ion of fluorine, with a charge of -1, written as \( \text{F}^{-} \).

Step 2: Balance the Charges

To write a neutral compound, the total positive charge must balance the total negative charge. Cobalt(III) has a charge of +3, and each fluoride ion has a charge of -1. To balance the charges, three fluoride ions are needed to balance one cobalt ion: \( \text{Co}^{3+} + 3 \times \text{F}^{-} \).

Step 3: Write the Formula

Combine the ions to form the neutral ionic compound. The formula is determined by the ratio of ions needed to balance the charges. The formula for the compound is \( \text{CoF}_3 \).

Key Concepts

Ion Charges

In ionic compounds, ions are atoms or molecules that have gained or lost electrons, resulting in a net charge. For example, in the compound involving cobalt(III) and fluoride, we have two kinds of ions.

• Cobalt(III) Ion: The Roman numeral "III" indicates that the cobalt ion has lost three electrons, giving it a charge of +3, expressed as \( \text{Co}^{3+} \).
• Fluoride Ion: This ion originates from fluorine, which gains one electron, resulting in a charge of -1, expressed as \( \text{F}^{-} \).

Understanding the charges of ions is crucial because they determine how ions will interact and combine in an ionic compound. Knowing that cobalt is \( +3 \) and fluoride is \( -1 \), allows us to balance these charges in a compound to achieve neutrality.

Chemical Formula

The chemical formula of an ionic compound represents the simplest ratio of the ions involved. This ratio ensures the compound is electrically neutral. To find the formula, observe the charges for each type of ion. Since cobalt has a +3 charge and fluoride has a -1 charge, the formula must reflect a charge-neutral arrangement.

• Add the ions in such ratios that the positive and negative charges sum to zero. In our case, one cobalt(III) ion \( \text{Co}^{3+} \) balances out three fluoride ions \( \text{F}^{-} \).
• Write the formula by placing the cation (positive ion) first, followed by the anion (negative ion). The chemical formula for our compound is \( \text{CoF}_3 \).

In essence, the chemical formula provides a snapshot of the compound's composition, showing how the ions fit together to maintain charge neutrality.

Charge Balance

Charge balance is a fundamental principle in forming ionic compounds. It ensures that the total positive and negative charges in the compound are equal, resulting in a neutral compound. For cobalt(III) fluoride, the charge balance can be explained as follows:

• Calculate the Total Positive Charge: The cobalt ion contributes a +3 charge.
• Calculate the Total Negative Charge: With three fluoride ions, each contributing a -1 charge, the total negative charge is \( 3 \times (-1) = -3 \).
• Balance the Charges: To have a balanced compound, the +3 from cobalt and the -3 from three fluoride ions must equal zero.

This balancing act is crucial; it dictates the precise proportions of ions in the chemical formula \( \text{CoF}_3 \), ensuring the compound is neutral overall.