Problem 53 - Chemistry and Chemical Reactivity

Question

Spinels are solids with the general formula \(\mathrm{AB}_{2} \mathrm{O}_{4}\) (where \(A^{2+}\) and \(B^{3+}\) are metal cations of the same or different metals). The best-known example is common magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) [which you can formulate as \(\left.\left(\mathrm{Fe}^{2+}\right)\left(\mathrm{Fe}^{3+}\right)_{2} \mathrm{O}_{4}\right] .\) Another example is the mineral often referred to as spinel, \(\mathrm{MgAl}_{2} \mathrm{O}_{4}\) (IMAGE CAN'T COPY)

Step-by-Step Solution

Answer

Magnesium aluminate spinel is \( \text{MgAl}_2\text{O}_4 \).

Step 1: Understand the Spinel Structure

Spinels have the general chemical formula \( \text{AB}_2\text{O}_4 \), where \( A^{2+} \) represents a divalent metal cation and \( B^{3+} \) represents a trivalent metal cation. It's important to remember that \( A \) and \( B \) can be different elements or the same element in different oxidation states.

Step 2: Identify Components of Magnetite

For common magnetite \( \text{Fe}_3\text{O}_4 \), the formula can be written out as \( (\text{Fe}^{2+})(\text{Fe}^{3+})_2\text{O}_4 \). Here, one Fe ion is divalent \( (Fe^{2+}) \) and the other two are trivalent \( (Fe^{3+}) \).

Step 3: Identify Components of Magnesium Aluminate Spinel

The spinel mineral \( \text{MgAl}_2\text{O}_4 \) is composed of \( Mg^{2+} \) as the \( A^{2+} \) cation and two \( Al^{3+} \) cations as the \( B^{3+} \) components. This confirms its structure as a spinel.

Step 4: Verify the Charge Balance

For \( \text{MgAl}_2\text{O}_4 \), the charges balance as follows: \( Mg^{2+} \) contributes \(+2\), two \( Al^{3+} \) each contribute \(+3\), totaling \(+8\) for the cations. The four oxygen atoms \( O^{2-} \) each contribute \(-2\) or \(-8\) in total, ensuring that the compound is electrically neutral overall.

Key Concepts

Crystal Structure

Spinel structures are a fascinating aspect of chemistry. They are characterized by their composition, denoted by the general formula \( \text{AB}_2\text{O}_4 \). In simple terms, this means that in each unit of the spinel, there is one divalent metal cation \( A^{2+} \) and two trivalent metal cations \( B^{3+} \). The oxygen forms the backbone, binding these metals together to create the crystal structure.
These structures occur naturally in various minerals. Many students might know the example of magnetite \( \text{Fe}_3\text{O}_4 \). Here, iron sits in different oxidation states, showcasing how these structures can easily adapt varying metal cations. The arrangement enhances unique properties, such as magnetism in magnetite.
Understanding crystal structures helps in appreciating how substances like spinels show varied and exceptional physical and chemical properties. They offer a window into how nature packs atoms efficiently.

Metal Cations

In a spinel structure, the metal cations play crucial roles in defining the compound's properties. When we talk about metal cations in spinels, we are referring to the \( A^{2+} \) and \( B^{3+} \) components.
- \( A^{2+} \) is a divalent metal cation, meaning it carries a charge of +2. In practice, this metal cation can be magnesium in \( \text{MgAl}_2\text{O}_4 \), or iron in magnetite \( \text{Fe}_3\text{O}_4 \).- \( B^{3+} \) is a trivalent metal cation with a charge of +3. In magnetite, iron fills the \( B^{3+} \) spot as well, but in other spinel examples like \( \text{MgAl}_2\text{O}_4 \), aluminum steps in.
The ability of these metal cations to vary in both identity and charge is what allows spinels to show such a wide range of characteristics. Each substitution or variation in the cations can result in distinct properties, making the study of metal cations in spinels essential to fields like material science and geology.

Oxidation States

Oxidation states in chemistry are a way to keep track of electrons in atoms during chemical reactions. In spinels, understanding oxidation states is crucial as they directly affect the formula and stability of the compound.
A core part of understanding spinel structures is recognizing the different oxidation states metal cations can possess. Take, for instance, magnetite \( \text{Fe}_3\text{O}_4 \): here, iron exists in two key oxidation states. There's the divalent \( Fe^{2+} \) and the trivalent \( Fe^{3+} \). This dual presence indicates that iron can donate different numbers of electrons depending on its role in the structure.
By understanding these oxidation states, we gain insights into how spinels maintain their structure and how they can be adapted or synthesized for various applications. This knowledge helps predict behavior in chemical reactions and determine physical properties like melting points or electrical conductivity.

Charge Balance

Maintaining a charge balance is essential in any chemical compound. For a spinel, whose formula is \( \text{AB}_2\text{O}_4 \), all the charges should add up to zero, resulting in a neutrally charged compound.
Let's break down the charge contributions in a mineral like \( \text{MgAl}_2\text{O}_4 \):

• \( Mg^{2+} \) contributes a charge of +2.
• Each \( Al^{3+} \) adds a +3 charge, totaling +6 for both aluminum ions.
• Oxygen, as \( O^{2-} \), contributes a -2 charge per atom, culminating in -8 for four oxygen atoms.

Balancing these, the positive and negative charges cancel each other out. This neutral state ensures the stability of the crystal structure. When designing or analyzing such compounds, mastering the concept of charge balance allows for accurate predictions of solubility, reactivity, and other chemical properties.