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Chapter 21: Problem 69

Iron is present in the earth's crust in many types of minerals. The iron oxide minerals are hematite \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\) and magnetite \(\left(\mathrm{Fe}_{3} \mathrm{O}_{4}\right) .\) What is the oxidation state of iron in each mineral? The iron ions in magnetite are a mixture of \(\mathrm{Fe}^{2+}\) and Fe \(^{3+}\) ions. What is the ratio of \(\mathrm{Fe}^{3+}\) to \(\mathrm{Fe}^{2+}\) ions in magnetite? The formula for magnetite is often written as $\mathrm{FeO} \cdot \mathrm{Fe}_{2} \mathrm{O}_{3} .$ Does this make sense? Explain.

Short Answer

Expert verified
The oxidation state of iron in hematite (Fe2O3) is +3. In magnetite (Fe3O4), the ratio of Fe³⁺ to Fe²⁺ ions is 2:1, and the formula FeO · Fe2O3 makes sense as it represents the balanced cationic and anionic charges in the compound, with FeO representing the part with Fe²⁺ ions and Fe2O3 representing the part with Fe³⁺ ions.

Step by step solution

01

Determine the oxidation state of oxygen in the minerals

In general, the oxidation state of oxygen in oxide compounds is -2. This means that in both hematite (Fe2O3) and magnetite (Fe3O4), oxygen atoms have an oxidation state of -2.
02

Determine the oxidation state of iron in hematite (Fe2O3)

We have 2 iron (Fe) atoms and 3 oxygen (O) atoms in hematite (Fe2O3). As we know that the oxidation state of oxygen is -2, the total negative charge from the oxygen atoms is -6. Since the compound is neutral, the total positive charge from the iron atoms must be +6. As there are 2 iron atoms, each iron atom must have an oxidation state of +3. Therefore, the oxidation state of iron in hematite is +3.
03

Determine the overall oxidation state of iron in magnetite (Fe3O4)

We have 3 iron (Fe) atoms and 4 oxygen (O) atoms in magnetite (Fe3O4). As we know that the oxidation state of oxygen is -2, the total negative charge from the oxygen atoms is -8. Since the compound is neutral, the total positive charge from the iron atoms must be +8.
04

Determine the ratio of Fe³⁺ to Fe²⁺ ions in magnetite

In magnetite, the iron ions are a mixture of Fe²⁺ and Fe³⁺ ions. Since the total positive charge from the iron atoms in magnetite is +8: Let x = number of Fe³⁺ ions Then, (3-x) = number of Fe²⁺ ions The total charge of Fe³⁺ ions = x * (+3) The total charge of Fe²⁺ ions = (3 - x) * (+2) Now, the sum of their charges should be equal to the total (+8) charge: x * (+3) + (3 - x) * (+2) = +8 By solving this equation for x, we get x = 2. This means that there are 2 Fe³⁺ ions and (3 - 2) = 1 Fe²⁺ ion in magnetite. Therefore, the ratio of Fe³⁺ to Fe²⁺ ions in magnetite is 2:1.
05

Check if the formula FeO · Fe2O3 makes sense for magnetite

We can rewrite this formula as: FeO · Fe2O3 = Fe(II)O + Fe(III)2O3 = Fe²⁺O²⁻ + 2Fe³⁺O²⁻*1.5 Both the cationic and anionic charges on both sides of the equation are balanced. Therefore, this formula makes sense for magnetite: - FeO represents the portion with Fe²⁺ ions (1 Fe²⁺ ion per formula unit). - Fe2O3 represents the portion with Fe³⁺ ions (2 Fe³⁺ ions per formula unit). This confirms that the formula FeO · Fe2O3 is consistent with the composition of magnetite.

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