Problem 122 - Chemistry Matter and Change

Question

Ionic Compounds Chrysoberyl is a transparent or translucent mineral that is sometimes opalescent. It is composed of beryllium aluminum oxide, \(\mathrm{BeAl}_{2} \mathrm{O}_{4}\) Identify the oxidation numbers of each of the ions found in this compound. Explain the formation of this ionic compound.

Step-by-Step Solution

Answer

In Chrysoberyl (\(\mathrm{BeAl}_{2} \mathrm{O}_{4}\)), the oxidation numbers of the constituent elements are +2 for beryllium (Be), +3 for aluminum (Al), and -2 for oxygen (O). The formation of this ionic compound occurs due to the electrostatic attraction between the beryllium cation (\(\mathrm{Be}^{2+}\)), the aluminum cation (\(\mathrm{Al}^{3+}\)), and the oxygen anion (\(\mathrm{O}^{2-}\)). The ratio of these ions in Chrysoberyl is 1:2:4, resulting in the neutral compound \(\mathrm{BeAl}_{2} \mathrm{O}_{4}\).

Step 1: Identifying the Oxidation Numbers of Elements

To find the oxidation numbers of the elements in the given compound, let's recall the general guidelines for assigning oxidation numbers: 1. The oxidation number of an element in its free state is 0. 2. The oxidation number of a monoatomic ion is equal to its charge. 3. The sum of oxidation numbers of all atoms in a molecule or ion is equal to its overall charge. Given the formula of Chrysoberyl, \(\mathrm{BeAl}_{2} \mathrm{O}_{4}\), we can see that it is a neutral compound with no overall charge. Now, let's assign oxidation numbers for each element: - Beryllium (Be) has an oxidation number of +2 as it tends to lose 2 electrons to achieve a stable electronic configuration. - Aluminum (Al) has an oxidation number of +3, as it usually loses three electrons to form a stable ion. - Oxygen (O) has an oxidation number of -2, as it gains two electrons to achieve a stable electronic configuration. Now, we'll verify the oxidation numbers using the compound's formula.

Step 2: Verifying Oxidation Numbers Using Formula

Using the oxidation numbers obtained from the previous step, we can verify if they add up to the overall charge of the compound, which in this case is neutral or zero charge. The compound formula is \(\mathrm{BeAl}_{2} \mathrm{O}_{4}\), so we have: 1 Be atom: oxidation number +2 2 Al atoms: oxidation number +3 each 4 O atoms: oxidation number -2 each Plugging in the oxidation numbers and the number of atoms present in the compound: (+2) + 2(+3) + 4(-2) = 0 This verifies that the oxidation numbers are correct.

Step 3: Explaining the Formation of Chrysoberyl

With the oxidation numbers identified, we can now explain the formation of Chrysoberyl, \(\mathrm{BeAl}_{2} \mathrm{O}_{4}\). The ionic compound forms due to the electrostatic attraction between positively charged ions (cations) and negatively charged ions (anions). In this compound: 1. A beryllium atom (Be) loses two electrons to form a beryllium cation, \(\mathrm{Be}^{2+}\). 2. Two aluminum atoms (Al) each lose three electrons to form two aluminum cations, \(\mathrm{Al}^{3+}\). 3. Four oxygen atoms (O) each gain two electrons to form four oxygen anions, \(\mathrm{O}^{2-}\). These cations and anions combine in a ratio that satisfies the electrostatic attraction between them, resulting in a neutral compound. In Chrysoberyl, the ratio is 1:2:4 for \(\mathrm{Be}^{2+}\), \(\mathrm{Al}^{3+}\), and \(\mathrm{O}^{2-}\), respectively, leading to the formula \(\mathrm{BeAl}_{2} \mathrm{O}_{4}\). To sum up, Chrysoberyl (\(\mathrm{BeAl}_{2} \mathrm{O}_{4}\)) is formed as a result of the electrostatic attraction between beryllium, aluminum, and oxygen ions with the respective oxidation numbers +2, +3, and -2.

Key Concepts

Oxidation Numbers

Oxidation numbers are a handy tool to understand how electrons are distributed in a chemical compound. They represent the charge an atom would have if all bonds were ionic. Here are the basic rules:

• The oxidation number of a pure element is always 0.
• For monatomic ions, the oxidation number equals the ion's charge.
• The sum of oxidation numbers for all atoms in a neutral compound is zero, while for a polyatomic ion, it equals the ion's charge.

In Chrysoberyl, \( \mathrm{BeAl}_{2} \mathrm{O}_{4} \), the oxidation number of beryllium (Be) is +2. Beryllium loses two electrons to stabilize. Aluminum (Al) is +3 because it loses three electrons. Finally, oxygen (O) is -2, since it gains two electrons. Together these values balance out to zero, confirming a neutral compound.

Electrostatic Attraction

Electrostatic attraction is the glue that holds ionic compounds together. It's the force of attraction between positively charged ions (cations) and negatively charged ions (anions), key for substances like Chrysoberyl. In ionic structures:

• Cations, with their positive charge, naturally attract anions, which have a negative charge.
• This attraction leads to the formation of a crystal lattice structure, a stable arrangement of ions.

For Chrysoberyl, the beryllium and aluminum atoms become positive ions, while oxygen atoms become negative ions. Their electrostatic attractions result in a solid compound, with each ion contributing to the stability of the overall structure.

Cations and Anions

Cations and anions are the charged particles that result from atoms losing or gaining electrons. They play a crucial role in forming ionic compounds like Chrysoberyl:

• Cations are positively charged ions, formed when atoms lose electrons. In Chrysoberyl, these include beryllium \((\mathrm{Be}^{2+})\) and aluminum \((\mathrm{Al}^{3+})\).
• Anions are negatively charged ions, formed when atoms gain electrons. Oxygen \((\mathrm{O}^{2-})\) is the anion in this compound.

The interaction between cations and anions is foundational in the formation of ionic bonds. Their opposite charges attract, which is why ions stick together to form a stable compound.

Stable Electronic Configuration

At the heart of many chemical reactions is the quest for a stable electronic configuration. Atoms strive to achieve a stable arrangement of electrons, often resembling the nearest noble gas:

• For metals like beryllium and aluminum, stability is achieved by losing electrons to form cations, resulting in a filled outer shell.
• Nonmetals like oxygen gain electrons to become anions, filling their outermost shell to reach a stable state.

In the structure of Chrysoberyl, beryllium loses two electrons, aluminum loses three, and oxygen gains two. This transfer leads to a stable electronic configuration for each ion involved, achieving the balance that stabilizes the compound.