Problem 18 - Chemistry A Molecular Approach

Question

In the pyroxene kanoite, the formula unit has two \(\mathrm{SiO}_{3}^{2-}\) units and is balanced by manganese and magnesium ions. Determine the formula unit of kanoite. Assume that the oxidation state of Mn is +2 .

Step-by-Step Solution

Answer

\(\mathrm{Mn}_{2}\mathrm{Mg}_{2}\mathrm{Si}_{2}\mathrm{O}_{6}\)

Step 1: Calculate the Total Negative Charge

Calculate the total negative charge contributed by the silicate anions. Since we have two \(\mathrm{SiO}_{3}^{2-}\) units, the total negative charge can be determined by multiplying the charge of one silicate ion (2-) by the number of silicate ions (2): \[(-2) \times 2 = -4\].

Step 2: Determine the Total Positive Charge Needed

To balance the total negative charge, the sum of the positive charges from the manganese (Mn) and magnesium (Mg) ions should equal +4. Since manganese is in the +2 oxidation state: \[2(Mn^{+2}) + 2(Mg^{+2}) = +4\]. Therefore, we need two Mn ions and two Mg ions to balance the charge.

Step 3: Write the Formula Unit for Kanoite

Combine the silicate units with the manganese and magnesium ions in their correct proportions to write the formula unit of kanoite: \[\mathrm{Mn}_{2} \mathrm{Mg}_{2}\mathrm{Si}_{2}\mathrm{O}_{6}\].

Key Concepts

Silicate Anions and Their Role in Minerals

Understanding silicate anions is crucial in the study of mineralogy and geology. Silicate anions form the backbone of silicate minerals, which make up the vast majority of Earth's crust. In the context of the pyroxene mineral kanoite, the chemical formula unit reveals the presence of silicate anions represented as \(\mathrm{SiO}_{3}^{2-}\). These units are fundamental building blocks of the mineral's structure.

Each \(\mathrm{SiO}_{3}^{2-}\) unit contains a silicon atom surrounded by three oxygen atoms, forming a pyramid-like shape known as a silicate tetrahedron. In the tetrahedron, silicon is centrally located, and the negative charge is due to the excess of electrons from oxygen atoms. The charge of -2 on each \(\mathrm{SiO}_{3}^{2-}\) anion highlights its ability to bond with positively charged metal ions, such as manganese (Mn) and magnesium (Mg), to form a stable, neutral mineral structure.

Oxidation States in Ionic Compounds

The oxidation state, often known as the oxidation number, is a fundamental concept in chemistry that indicates the degree of oxidation (loss of electrons) of an atom in a chemical compound. Recognizing oxidation states is crucial for determining the formula of compounds, especially when dealing with transition metals like manganese (Mn) which can exhibit multiple oxidation states.

In the exercise, manganese is assumed to be in the +2 oxidation state, denoted as Mn\(^{+2}\). This indicates that the manganese ion has lost two electrons, acquiring a positive charge. Magnesium (Mg) also commonly exists in the +2 state as Mg\(^{+2}\). The oxidation states enable chemists to deduce how these metal ions will combine with the silicate anions to form a stable, electrically neutral compound. It's the balance between the negative charges of the silicate anions and the positive charges of the metal ions that ultimately dictates the composition of the mineral.

Ionic Charge Balance in Minerals

Ionic charge balance is the principle where the total positive charge in a compound equals the total negative charge, resulting in an electrically neutral substance. It's particularly relevant in the context of minerals, as their stability is linked to this electrostatic balance.

For kanoite, the total negative charge from the two silicate anions is calculated as -4. According to the ionic charge balance principle, this charge must be counteracted by an equal and opposite positive charge. With manganese and magnesium both having an oxidation state of +2, we find that two Mn\(^{+2}\) ions and two Mg\(^{+2}\) ions provide the required +4 charge to achieve neutrality. By combining these with the silicate anions, we can deduce the chemical formula unit of kanoite as Mn\(_{2}\)Mg\(_{2}\)Si\(_{2}\)O\(_{6}\).

The exercise in composing the formula unit of kanoite illustrates how by understanding oxidation states and employing the principle of ionic charge balance, one can rationalize the composition of complex minerals.