/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 67 Iron is present in the earth's c... [FREE SOLUTION] | 91影视

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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
In hematite (Fe鈧侽鈧), the oxidation state of iron is +3. In magnetite (Fe鈧僌鈧), the ratio of Fe鲁鈦 to Fe虏鈦 ions is 2 : 1, with two Fe鲁鈦 ions and one Fe虏鈦 ion present. The formula FeO路Fe鈧侽鈧 makes sense for magnetite, as it represents the combination of one Fe虏鈦 ion from FeO and two Fe鲁鈦 ions from Fe鈧侽鈧 to form magnetite's formula, Fe鈧僌鈧.

Step by step solution

01

1. Determine oxidation state of Iron in hematite (Fe鈧侽鈧)

For hematite (Fe鈧侽鈧), we let x be the oxidation state of iron (Fe). Since oxygen has an oxidation state of -2, we can write these down in an equation: $$2x + 3(-2) = 0$$ Solve this equation to find the value of x, which is the oxidation state of iron in hematite.
02

2. Determine oxidation state of Iron in magnetite (Fe鈧僌鈧)

For magnetite (Fe鈧僌鈧), the oxidation state of iron is a mixture of Fe鲁鈦 and Fe虏鈦 ions, which means it has more than one value. Let's call the amount of Fe鲁鈦 ions a and the amount of Fe虏鈦 ions b. Since there are 3 iron atoms in total, we have a + b = 3. Next, since oxygen has an oxidation state of -2, we can write these down in another equation involving the oxidation states: $$3a + 2b + 4(-2) = 0$$ We now have two equations with two unknowns, a and b: $$a + b = 3$$ $$3a + 2b = 8$$
03

3. Solve the system of equations to find the ratio of Fe鲁鈦 to Fe虏鈦 ions in magnetite

To solve these equations, we can first multiply the first equation by -2 and then add the two equations: $$-2(a + b) = -6$$ $$-2a - 2b = -6$$ $$3a + 2b - 2a - 2b = 8 - 6$$ $$a = 2$$ Now we can plug the value of a back into the first equation to find the value of b: $$2 + b = 3$$ $$b = 1$$ Since a = 2 and b = 1, we now know there are two Fe鲁鈦 ions and one Fe虏鈦 ion in magnetite. So, the ratio of Fe鲁鈦 to Fe虏鈦 ions in magnetite is 2 : 1.
04

4. Analyzing the formula FeO路Fe鈧侽鈧 for Magnetite

We know magnetite can be written as Fe鈧僌鈧, now let's analyze whether the formula FeO路Fe鈧侽鈧 makes sense or not. If we split the two compounds within the formula, we have: - FeO, which contains 1 Fe虏鈦 ion and 1 O虏鈦 ion - Fe鈧侽鈧, which contains 2 Fe鲁鈦 ions and 3 O虏鈦 ions As seen, the FeO part of the formula corresponds to the Fe虏鈦 ions, while the Fe鈧侽鈧 part corresponds to the Fe鲁鈦 ions. Adding up the ions in these two compounds, we have: Fe鈧侽鈧: 2 Fe鲁鈦 ions + 3 O虏鈦 ions FeO: 1 Fe虏鈦 ion + 1 O虏鈦 ion Combining both gives us the formula Fe鈧僌鈧, which is the formula for magnetite. Therefore, the given formula FeO路Fe鈧侽鈧 does make sense for magnetite.

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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, primarily consisting of compounds formed by iron and oxygen. These minerals are significant due to their role in various industrial and geological processes. Among the most well-known iron oxide minerals are hematite and magnetite. These minerals differ in their iron oxidation states, influencing their chemical properties and uses. Understanding these states is key to exploring their functions and how they are processed for industrial applications.
  • Hematite (\( ext{Fe}_2 ext{O}_3\)): Known for its reddish-brown streak and metallic luster.
  • Magnetite (\( ext{Fe}_3 ext{O}_4\)): Notable for its magnetic properties and presence of both \( ext{Fe}^{3+}\) and \( ext{Fe}^{2+}\) ions.
hematite
Hematite is an iron oxide mineral with the chemical formula \( ext{Fe}_2 ext{O}_3\). This mineral is recognizable by its metallic luster and reddish hues, often used as a pigment in paints and as the main ore of iron extraction. In hematite, iron predominantly exists in the \( ext{Fe}^{3+}\) oxidation state.

To find the oxidation state of iron in hematite, we can consider the formula \( ext{Fe}_2 ext{O}_3\):
  • Iron (Fe) has an unknown oxidation state, denoted as \(x\).
  • Oxygen (O) typically has an oxidation state of \(-2\).
Using these, the equation becomes: \(2x + 3(-2) = 0\).

Solving this equation, you find that \(x\) equals +3, confirming the presence of \( ext{Fe}^{3+}\) ions in hematite.
magnetite
Magnetite, with the formula \( ext{Fe}_3 ext{O}_4\), is an impressive mineral due to its magnetic properties, a trait that differentiates it from other iron oxides. It is a significant iron ore source and a major component in the steel-making process.

A unique feature of magnetite is its mixed iron oxidation states, containing both \( ext{Fe}^{3+}\) and \( ext{Fe}^{2+}\). This mix contributes to its magnetic behavior, making magnetite essential in various technological applications, including magnetic storage media and catalysis.

Understanding how these oxidation states balance explains why magnetite maintains charge neutrality and illustrates how different mineral compositions can influence physical properties.
Fe鲁鈦 and Fe虏鈦 ions
In iron oxide minerals, particularly in magnetite, the presence of both \( ext{Fe}^{3+}\) and \( ext{Fe}^{2+}\) ions is crucial. These ions have differing oxidation states, \(+3\) and \(+2\), respectively, and they influence the overall charge balance and properties of the mineral.

In magnetite \( ext{Fe}_3 ext{O}_4\), a combination of these ions is within the mineral's structure, creating a balance:
  • The formula explains the coexistence of two \( ext{Fe}^{3+}\) ions and one \( ext{Fe}^{2+}\) ion.
  • This 2:1 ratio maintains an average oxidation state of \(+2.67\) per iron atom, which sustains the mineral's magnetic properties.
When calculating and analyzing these ions, it becomes clear how their proportions affect the mineral's functionality, demonstrating an interplay between chemistry and material properties.
magnetite formula analysis
The formula for magnetite, \( ext{Fe}_3 ext{O}_4\), provides an interesting insight into its composition. Sometimes represented as \( ext{FeO} \, \cdot \, ext{Fe}_2 ext{O}_3\), this formula breakdown aids in understanding how magnetite's structure is arranged.

Breaking it into separate parts:
  • \( ext{FeO}\): Contains one \( ext{Fe}^{2+}\) ion corresponding to its part in the structure.
  • \( ext{Fe}_2 ext{O}_3\): Comprising two \( ext{Fe}^{3+}\) ions, aligned with its function in the mineral.
Combining these ions (1 \( ext{Fe}^{2+}\) and 2 \( ext{Fe}^{3+}\)) results in the proper structure of \( ext{Fe}_3 ext{O}_4\).

Understanding this formula confirms the charge balance, explaining how different parts of the formula contribute to overall stability. It validates the structural integrity of magnetite, ensuring that it accurately reflects both its physical and chemical properties.

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Most popular questions from this chapter

Write electron configurations for each of the following. a. \(\mathrm{Cr}, \mathrm{Cr}^{2+}, \mathrm{Cr}^{3+}\) b. \(\mathrm{Cu}, \mathrm{Cu}^{+}, \mathrm{Cu}^{2+}\) c. \(\mathrm{V}, \mathrm{V}^{2+}, \mathrm{V}^{3+}\)

Consider the pseudo-octahedral complex ion of \(\mathrm{Cr}^{3+}\), where \(\mathrm{A}\) and \(\mathrm{B}\) represent ligands. Ligand A produces a stronger crystal field than ligand B. Draw an appropriate crystal field diagram for this complex ion (assume the A ligands are on the \(z\) -axis).

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