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Chapter 23: Problem 20

The most important oxides of iron are magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) and hematite, \(\mathrm{Fe}_{2} \mathrm{O}_{3} .\) (a) What are the oxidation states of iron in these compounds? (b) One of these iron oxides is ferrimagnetic, and the other is antiferromagnetic. Which iron oxide is more likely to be ferrimagnetic? Explain.

Short Answer

Expert verified
The oxidation states of iron in magnetite (Fe3O4) are +2 and +3, while in hematite (Fe2O3), it is +3. Magnetite is likely to be ferrimagnetic due to the mixture of its oxidation states resulting in a partially aligned magnetic moment, whereas hematite is likely to be antiferromagnetic due to its single iron atom oxidation state, suggesting an antiparallel alignment and no net external magnetic field.

Step by step solution

01

Identify the oxidation states of oxygen

In both compounds, the oxidation state of oxygen is -2. We will use this information to find the oxidation states of iron in both compounds.
02

Determine the oxidation states of iron in both compounds

Fe3O4 (magnetite) and Fe2O3 (hematite) are the given compounds. For magnetite: \(3x + 4(-2) = 0\) \(3x = 8\) \(x = \frac{8}{3}\) However, this fractional oxidation state suggests that there must be a mixture of two oxidation states in Fe3O4. By observing the ratio of Fe to O atoms, we can infer that two Fe atoms have an oxidation state of +3, while one Fe atom has an oxidation state of +2. For hematite: \(2x + 3(-2) = 0\) \(2x = 6\) \(x = 3\) Therefore, the oxidation states of iron in magnetite are +2 and +3, and in hematite, it is +3.
03

Understand ferrimagnetic and antiferromagnetic materials

Ferrimagnetic materials have magnetic moments that are aligned in parallel, leading to a net magnetic moment and magnetization, even in the absence of an external field. Antiferromagnetic materials have magnetic moments that are aligned in an antiparallel configuration with no net external magnetic field.
04

Determine which iron oxide is likely to be ferrimagnetic

In magnetite (Fe3O4), we have two Fe atoms with an oxidation state of +3 and one Fe atom with an oxidation state of +2. The mixed oxidation states result in a partially aligned magnetic moment, which could result in a net magnetic moment. Thus, it is likely that magnetite (Fe3O4) is ferrimagnetic. On the other hand, hematite (Fe2O3) has only one kind of iron atom with oxidation state +3, suggesting that it most probably has antiparallel alignment leading to no net external magnetic field. Hence, hematite (Fe2O3) can be considered as antiferromagnetic. In conclusion, magnetite (Fe3O4) is likely to be ferrimagnetic while hematite (Fe2O3) is likely to be antiferromagnetic.

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Key Concepts

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

Oxidation States
Understanding the oxidation states in iron oxides is crucial to grasp various chemical properties including their magnetic behaviors. Oxidation states denote the degree of oxidation of an atom within a compound, which is crucial for determining the compound's electronic structure. In the case of magnetite (\textbf{Fe}\(_3\)O\(_4\)), there is a mixed oxidation state of +2 and +3 due to the presence of two types of iron ions. In contrast, hematite (Fe\(_2\)O\(_3\)) possesses iron ions all in the +3 oxidation state.

This information sets the stage to comprehend their distinct magnetic properties and makes it easier to predict how these compounds will interact with magnetic fields. By looking at the electronegativity and the exchange interaction between adjacent iron ions, we can build a vivid picture of the internal magnetic moments within these iron oxides.
Ferrimagnetic Materials
Ferrimagnetic materials, which are often found in iron oxides, exhibit a magnetic ordering where magnetic moments of atoms align in a staggered pattern. However, unlike antiferromagnetic materials, the opposing moments are unequal, leading to a net magnetic moment. The inherent properties of ferrimagnetic materials make them valuable in various applications ranging from magnetic recording to transformers.

This characteristic magnetic behavior emerges from the interactions among cations in different oxidation states. With magnetite functioning as a classic example, its unique molecular structure paves the way for ferrimagnetism, showcasing the value of understanding oxidation states in predicting material properties.
Antiferromagnetic Materials
Antiferromagnetic materials exhibit an intriguing magnetic order where adjacent ions’ magnetic moments cancel each other out due to their antiparallel alignment. Such materials are often complex and offer a curious case for study in materials science and condensed matter physics. Hematite, with iron in a uniform +3 oxidation state, presents as antiferromagnetic at temperatures below its Néel temperature.

With no net external magnetic field produced, they display unique characteristics like the magneto-caloric effect, which is of significant interest for refrigeration technology. Thus, understanding antiferromagnetism in compounds like hematite provides a window into cutting-edge technological applications.
Magnetite
Magnetite (Fe\(_3\)O\(_4\)), a naturally occurring iron oxide, exhibits a unique combination of oxidation states that bestow it with ferrimagnetic properties. Its composition includes both Fe\(^{2+}\) and Fe\(^{3+}\) ions, which leads to a complex internal magnetic landscape where the moments are not entirely canceled out. This staggering of spin moments is why magnetite shows a collective magnetization.

Magnetite's ability to be magnetized even in the absence of an external magnetic field makes it a significant ferrimagnetic material used in various industrial and technological applications, from magnetic storage devices to biomedical imaging.
Hematite
Hematite (Fe\(_2\)O\(_3\)), another principal form of iron oxide, is identified by its reddish-brown streak and is primarily used as an ore of iron. The uniform oxidation state of +3 for iron in hematite leads to a material that is antiferromagnetic in nature. This implies that the internal magnetic moments of the iron ions neutralize each other.

However, when powdered, hematite can exhibit weak ferromagnetic properties—a phenomenon known as parasitism. Such intricate magnetic behavior underlies the vast realm of applications for hematite, from pigmentation in art to environmental remediation. Exploring the chemistry and physics of such materials not only increases our understanding of fundamental science but also has direct implications for innovative technology.

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Most popular questions from this chapter

(a) In early studies it was observed that when the complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{Br}\) was placed in water, the electrical conductivity of a 0.05\(M\) solution changed from an initial value of 191 \(\mathrm{ohm}^{-1}\) to a final value of 374 \(\mathrm{ohm}^{-1}\) over a period of an hour or so. Suggest an explanation for the observed results.(See Exercise 23.69 for relevant comparison data.) (b) Write a balanced chemical equation to describe the reaction. (c) \(A 500\)-mL solution is made up by dissolving 3.87g of the complex. As soon as the solution is formed, and before any change in conductivity has occurred, a 25.00-mL portion of the solution is titrated with 0.0100 \(\mathrm{M} \mathrm{AgNO}_{3}\) solution. What volume of AgNO \(_{3}\) solution do you expect to be required to precipitate the free \(\operatorname{Br}^{-}(a q) ?(\mathbf{d})\) Based on the response you gave to part (b), what volume of \(\mathrm{AgNO}_{3}\) solution would be required to titrate a fresh 25.00 -mL sample of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{Br}\) after all conductivity changes have occurred?

The \(E^{\circ}\) values for two low-spin iron complexes in acidic solution are as follows: \(\left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}(a q)+\mathrm{e}^{-} \Longrightarrow\) \(\quad\quad\quad\quad\quad\quad\quad\) \(\left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{2+}(a q) \quad E^{\circ}=1.12 \mathrm{V}\) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(a q)+\mathrm{e}^{-} \rightleftharpoons\) \(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}(a q) \quad E^{\circ}=0.36 \mathrm{V}\) (a) Is it thermodynamically favorable to reduce both Fe(III) complexes to their Fe(II) analogs? Explain. (b) Which complex, \(\left[\mathrm{Fe}(o-\mathrm{phen})_{3}\right]^{3+}\) or \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-},\) is more difficult to reduce? (c) Suggest an explanation for your answer to (b).

The ion \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) has one unpaired electron, whereas \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\) has five unpaired electrons. From these results, what can you conclude about whether each complex is high spin or low spin? What can you say about the placement of \(\mathrm{NCS}^{-}\) in the spectrochemical series?

A palladium complex formed from a solution containing bromide ion and pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}\) (a good electron-pair donor), is found on elemental analysis to contain 37.6\(\%\) bromine, 28.3\(\%\) carbon, 6.60\(\%\) nitrogen, and 2.37\(\%\) hydrogen by mass. The compound is slightly soluble in several organic solvents; its solutions in water or alcohol do not conduct electricity. It is found experimentally to have a zero dipole moment. Write the chemical formula, and indicate its probable structure.

Write the formula for each of the following compounds, being sure to use brackets to indicate the coordination sphere: (a) hexamminechromium(III) nitrate (b) tetraamminecarbonatocobalt(III) sulfate (c) dichlorobis(ethylenediamine)platinum(IV) bromide (d) potassium diaquatetrabromovanadate(III) (e) bis(ethylenediamine) zinc(II) tetraiodomercurate(II)
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