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Chapter 21: Problem 63

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 \(\mathrm{Fe}^{3+}\) 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 (Fe鈧侽鈧�) is +3, and the ratio of Fe鲁鈦� to Fe虏鈦� ions in magnetite (Fe鈧僌鈧�) is 2:1. The formula of magnetite can be written as FeO 路 Fe鈧侽鈧�, as it correctly represents the ratio of Fe虏鈦�, Fe鲁鈦�, and O虏鈦� ions in the compound.

Step by step solution

01

Determine the oxidation state of iron in hematite (Fe鈧侽鈧�)

In this mineral, we have 2 Fe atoms and 3 O atoms. Since the oxidation state of oxygen is -2, the total charge of the 3 oxygens is -6. Therefore, the total charge of the 2 Fe atoms must be +6 to make the compound electrically neutral. Let x be the oxidation state of iron in hematite, then we have: 2x + (-6) = 0 Solve for x: 2x = 6 x = 3 Therefore, the oxidation state of iron in hematite is +3.
02

Determine the oxidation state of iron in magnetite (Fe鈧僌鈧�)

In magnetite, there is a mixture of Fe虏鈦� and Fe鲁鈦� ions, and we are given Fe鈧僌鈧� as the mineral composition. Since the oxidation state of oxygen is -2, the total charge of the 4 oxygens is -8. Let x and y be the oxidation states of iron in magnetite, then we have: 3x + 4y = 0 Since we know the oxidation states of Fe虏鈦� and Fe鲁鈦� are +2 and +3, respectively, we substitute these values into the equation: 3(+2) + (+3) = 0 Solve for x, y and z: x = 1 (number of Fe虏鈦� ions) y = 2 (number of Fe鲁鈦� ions) Therefore, the ratio of Fe鲁鈦� to Fe虏鈦� ions in magnetite is 2:1.
03

Verify if the formula of magnetite can be written as FeO 路 Fe鈧侽鈧�

To verify if this formula makes sense, let's split the given formula into FeO and Fe鈧侽鈧� components as follows: FeO: 1 Fe虏鈦� ion (+2 charge) 1 O虏鈦� ion (-2 charge) Total charge = 0 Fe鈧侽鈧�: 2 Fe鲁鈦� ions (+6 charge) 3 O虏鈦� ions (-6 charge) Total charge = 0 Now, let's combine them: Fe虏鈦� + O虏鈦� + 2Fe鲁鈦� + 3O虏鈦� As we can see, we have recreated the magnetite formula Fe鈧僌鈧�, with 1 Fe虏鈦�, 2 Fe鲁鈦�, and 4 O虏鈦� ions. This demonstrates that the formula FeO 路 Fe鈧侽鈧� does make sense in representing magnetite. In conclusion, the oxidation state of iron in hematite is +3, while the ratio of Fe鲁鈦� to Fe虏鈦� ions in magnetite is 2:1. Additionally, magnetite can be represented by the formula FeO 路 Fe鈧侽鈧�, as this expresses the correct ratio of Fe虏鈦�, Fe鲁鈦�, and O虏鈦� ions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Iron Oxide Minerals
Iron oxide minerals are abundant in the Earth's crust and are among the most important sources of iron in nature. These minerals often exhibit vibrant colors ranging from yellow to deep red and black. They also play a significant role in geology, soil science, and metallurgy. The oxidation state of the iron within these minerals is a key factor that determines their properties and, consequently, their various applications. For instance, iron oxides are commonly used as pigments in paints and coatings due to their coloration attributes, while in industry, they are vital for producing iron and steel. Understanding the oxidation states within minerals like hematite and magnetite isn't just academic; it has real-world implications in various fields.
Chemical Composition of Hematite
Hematite, with the chemical formula \( \mathrm{Fe}_2\mathrm{O}_3 \), is an iron oxide mineral known for its shiny, metallic lustre and reddish-brown streak. The chemical composition of hematite reveals that it contains two iron atoms and three oxygen atoms. Calculating the oxidation state, we find that each iron atom has an oxidation state of +3. This +3 oxidation state is a result of the oxygen atoms, each with an oxidation state of -2, attempting to balance the overall charge of the compound. In addition to being a valuable iron ore, hematite has significant applications in jewelry and has historically been used as a pigment.
Chemical Composition of Magnetite
Magnetite, denoted as \( \mathrm{Fe}_3\mathrm{O}_4 \) or \( \mathrm{FeO}\cdot\mathrm{Fe}_2\mathrm{O}_3 \), contains a mixed oxidation state for iron, which sets it apart from hematite. Magnetite's composition includes both \( \mathrm{Fe}^{2+} \) and \( \mathrm{Fe}^{3+} \) ions, leading to the 2:1 ratio in favor of the +3 state. Because of this unique attribute, magnetite not only serves as a significant iron ore but also exhibits magnetic properties, making it valuable in various technological applications. When evaluating the compound, the combined analysis of \( \mathrm{FeO}\) and \(\mathrm{Fe}_2\mathrm{O}_3\) helps to rationalize the composition and indicates how the elemental iron is distributed among its two oxidation states. Such knowledge is essential when studying magnetic properties and the process of metal extraction from ores.

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Most popular questions from this chapter

Henry Taube, 1983 Nobel Prize winner in chemistry, has studied the mechanisms of the oxidation-reduction reactions of transition metal complexes. In one experiment he and his students studied the following reaction: \(\begin{aligned} \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}(a q)+& \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}^{2+}(a q) \\\ \longrightarrow & \mathrm{Cr}(\mathrm{III}) \text { complexes }+\mathrm{Co}(\mathrm{II}) \text { complexes } \end{aligned}\) Chromium(III) and cobalt(III) complexes are substitutionally inert (no exchange of ligands) under conditions of the experiment. Chromium(II) and cobalt(II) complexes can exchange ligands very rapidly. One of the products of the reaction is \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{Cl}^{2+} .\) Is this consistent with the reaction proceeding through formation of \(\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{Cr}-\mathrm{Cl}-\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\) as an intermediate? Explain.

Both \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\) and \(\mathrm{Ni}(\mathrm{SCN})_{4}^{2-}\) have four ligands. The first is paramagnetic, and the second is diamagnetic. Are the complex ions tetrahedral or square planar? Explain.

Qualitatively draw the crystal field splitting of the \(d\) orbitals in a trigonal planar complex ion. (Let the \(z\) axis be perpendicular to the plane of the complex.)

Give formulas for the following complex ions. a. tetrachloroferrate(III) ion b. pentaammineaquaruthenium(III) ion c. tetracarbonyldihydroxochromium(III) ion d. amminetrichloroplatinate(II) ion

One of the classic methods for the determination of the manganese content in steel involves converting all the manganese to the deeply colored permanganate ion and then measuring the absorption of light. The steel is first dissolved in nitric acid, producing the manganese(II) ion and nitrogen dioxide gas. This solution is then reacted with an acidic solution containing periodate ion; the products are the permanganate and iodate ions. Write balanced chemical equations for both of these steps.
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