Problem 20 - Chemistry: The Central Science in SI Units, Global Edition

Question

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.

Step-by-Step Solution

Answer

In magnetite (Fe3O4), iron has two different oxidation states: Fe(II) with an oxidation state of +2 and Fe(III) with an oxidation state of +3. In hematite (Fe2O3), iron has an oxidation state of +3. Since magnetite has different oxidation states, it is more likely to be ferrimagnetic, while hematite, with only one oxidation state, is more likely to be antiferromagnetic.

Step 1: Determine the oxidation state of iron

The oxidation state of an element in a compound refers to the hypothetical charge that the atom would have if all its bonds were broken, with the bonded electron pairs distributed according to certain rules. In this case, we are looking to determine the oxidation state for iron in both magnetite (Fe3O4) and hematite (Fe2O3). To find the oxidation states of iron in both compounds, we can set up an equation where the total charges of iron atoms in each compound equals the total negative charges of the oxygen atoms. Since the charge on an oxygen atom is -2, the total negative charge for the oxygen atoms in magnetite will be 4*(-2)=-8, and for hematite, it will be 3*(-2)=-6. For example: In magnetite, x*Fe3 = -8 In hematite, y*Fe2 = -6 We need to solve for x and y to find the oxidation states of iron in these compounds.

Step 2: Calculate the oxidation state of iron in magnetite and hematite

In magnetite: Let's assume the oxidation state of iron as x. 3x = -8 x = -8/3 Since iron can't have a fractional oxidation state, this implies that there are two different oxidation states for iron in magnetite. We can rewrite the equation as: 2(Fe(II)) + Fe(III) = -8 Fe(II) represents iron with an oxidation state of +2, and Fe(III) represents iron with an oxidation state of +3. 3(+2) + (+3) = -8 6 + 3 = 9 In hematite: Let's assume the oxidation state of iron as y. 2y = -6 y = -6/2 y = +3 So, the oxidation state of iron in hematite is +3.

Step 3: Identifying ferrimagnetic and antiferromagnetic substances

Ferrimagnetic substances are materials that display magnetic properties based on the different orientations and magnitudes of the atomic magnetic moments within the material. These substances have their unpaired electron spins aligned in opposite directions on different sublattices, resulting in a net spontaneous magnetization. Antiferromagnetic substances are materials in which the magnetic moments of adjacent atoms or ions cancel each other out, resulting in a net magnetic moment of zero. In antiferromagnetic substances, the unpaired electron spins on neighboring atoms align in opposite directions.

Step 4: Determine which iron oxide is likely to be ferrimagnetic

We know that magnetite (Fe3O4) has iron with two different oxidation states, Fe(II) and Fe(III). This difference in oxidation states leads to different magnitudes of magnetic moments within the material. Since ferrimagnetic substances are characterized by a difference in the orientation and magnitude of magnetic moments, it is reasonable to conclude that the iron oxide with different oxidation states, magnetite, is more likely to be ferrimagnetic. On the other hand, hematite (Fe2O3) has iron with only one oxidation state, Fe(III). The equal magnitudes of magnetic moments in hematite make it more likely to be antiferromagnetic, as the moments can cancel each other out and result in a net magnetization of zero. In conclusion, magnetite (Fe3O4) is more likely to be ferrimagnetic, while hematite (Fe2O3) is more likely to be antiferromagnetic.

Key Concepts

Oxidation States

The oxidation state of an element in a compound describes the hypothetical charge the atom would possess if all bonds were completely ionic. Understanding oxidation states is key to analyzing chemical compounds. Let's consider the iron oxides: magnetite (Fe\(_3\)O\(_4\)) and hematite (Fe\(_2\)O\(_3\)).

In magnetite, which consists of Fe and O, each oxygen atom has a -2 charge. Since there are four oxygen atoms, the total negative charge is -8. To balance this, the total charge from iron must be +8. The equation can be represented as:
- 3x = +8
Where x is the charge from one Fe atom. Here, iron appears in two oxidation states, +2 and +3, amounting to different combinations to equal +8. This creates a mixed oxidation scenario: two Fe in +2 and one Fe in +3.

In hematite, the calculation simplifies: oxygen's total charge is -6 from three O atoms (3 * -2). Therefore, to counterbalance, the total positive charge should be +6, coming from two iron atoms. Thus, each Fe atom has an oxidation state of +3 (Fe(III)).

Recognizing these oxidation states helps in understanding the chemical behavior and properties of different iron oxides.

Ferrimagnetism

Ferrimagnetism is a fascinating property seen in certain materials that possess magnetic properties due to unique arrangements of their atomic magnetic dipoles. Unlike paramagnetic materials, where all spins align together, ferrimagnetism involves magnetic moments that are aligned differently on various sub-lattices.

In the context of iron oxides, magnetite (Fe\(_3\)O\(_4\)) demonstrates ferrimagnetism. This is because it contains iron in two oxidation states, Fe(II) and Fe(III), resulting in unequal magnetic moments among the atoms. These are organized such that moments align in opposite directions but do not entirely cancel each other out, leading to a non-zero net magnetic moment.

Ferrimagnetic materials often exhibit spontaneous magnetization due to this imperfect cancellation. This makes them very valuable in various applications like in magnetic recording media, transformers, and electrical components. The structure and uneven distribution of magnetic moments characterize ferrimagnetism, distinguishing it from other magnetic properties.

Antiferromagnetism

Antiferromagnetism is another type of magnetic ordering that occurs in some substances, such as hematite (Fe\(_2\)O\(_3\)). Here, the magnetic moments of adjacent atoms align in opposite directions. This regular pattern leads to complete cancelation of the magnetic forces, resulting in no net magnetic moment.

Hematite is an excellent example. With iron in the +3 oxidation state across the material, the magnetic moments are equivalent and directly opposed. This balanced alignment disappears above a certain temperature known as the Neel temperature, where the material becomes paramagnetic.

Antiferromagnetic materials, while not displaying a magnetic moment under typical conditions, can be used in specialized applications, such as spintronics and magnetic storage devices that exploit this unique lack of magnetization.