Problem 80 - Chemistry Matter and Change

Question

Explain what the name scandium(III) oxide means in terms of electrons lost and gained, and identify the correct formula.

Step-by-Step Solution

Answer

Scandium(III) oxide implies Sc loses 3 electrons and forms \( \text{Sc}^{3+} \) ions; Oxygen gains 2 electrons forming \( \text{O}^{2-} \) ions; formula: \( \text{Sc}_2\text{O}_3 \).

Step 1: Understand the Metal Cation

Scandium(III) indicates that scandium has a positive charge of +3. This means that it has lost three electrons. In its neutral state, scandium has an atomic number of 21, so initially, it has 21 electrons. Losing 3 electrons results in a Scandium ion with 18 electrons.

Step 2: Identify the Oxide Anion

The oxide refers to the oxygen ion, which is known to have a charge of -2 because it gains two electrons to achieve a full outer electron shell, resembling the noble gas configuration. In its neutral state, oxygen has 8 electrons and gains 2 to have a total of 10 electrons in the oxide ion.

Step 3: Determine the Formula

To maintain electrical neutrality in scandium(III) oxide, the total positive charge must equal the total negative charge. The scandium ion has a +3 charge, and the oxide ion has a -2 charge. The smallest combination of ions where the charges balance is two scandium ions (+6 total) with three oxide ions (-6 total). This results in the formula for scandium(III) oxide: \( \text{Sc}_2\text{O}_3 \).

Key Concepts

Scandium(III) oxide

Scandium(III) oxide is a chemical compound consisting of scandium and oxygen. It is an example of an ionic compound, which is formed through the transfer of electrons between a metal and a nonmetal. In this case, scandium, a metal, donates electrons while oxygen, a nonmetal, gains electrons. The term "Scandium(III)" refers to the oxidation state of the scandium ion in the compound, which is +3. This indicates that each scandium atom loses three electrons. This loss is because scandium needs to achieve a stable electron configuration by emptying its valence shell. Once these electrons are lost, they are taken up by oxygen atoms, forming oxide ions. The result is a stable ionic compound, Scandium(III) oxide, with a specific crystal structure and distinct chemical properties.

Electrostatic charge balance

In ionic compounds like scandium(III) oxide, maintaining an electrostatic charge balance is crucial. Each compound must be electrically neutral overall, meaning the total positive charge must equal the total negative charge.

• Scandium ions carry a charge of +3 because they lose three electrons.
• Oxide ions, formed from oxygen, carry a charge of -2 because they gain two electrons.

To balance the charges in scandium(III) oxide, we need a certain ratio of scandium ions to oxide ions. The correct balance occurs when the total positive charge from the scandium ions equals the total negative charge from the oxide ions. In scandium(III) oxide, the balance is achieved with two scandium ions (total charge of +6) and three oxide ions (total charge of -6), ensuring the compound is neutral.

Chemical formula determination

The formula of an ionic compound like scandium(III) oxide comes from the need to balance the overall charges between the ions involved. The process involves determining the smallest whole number ratio of ions that results in no net charge. For scandium(III) oxide:

• Each scandium ion has a +3 charge.
• Each oxide ion has a -2 charge.

To balance, we look for the least common multiple of these charges. By choosing two scandium ions (2 x +3 = +6) and three oxide ions (3 x -2 = -6), we achieve a balance where the positive and negative charges cancel out. This results in the chemical formula for scandium(III) oxide: \[ \text{Sc}_2\text{O}_3 \]This formula shows the smallest ratio of scandium to oxide ions needed to maintain charge neutrality, which is a fundamental principle in the formation of ionic compounds.