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Chapter 10: Problem 76

The structure of manganese fluoride can be described as a simple cubic array of manganese ions with fluoride ions at the center of each edge of the cubic unit cell. What is the charge of the manganese ions in this compound?

Short Answer

Expert verified
The given structure has 1 Mn ion and 3 F ions within the unit cell. Fluoride ions carry a -1 charge each. Using charge balance, let x represent the charge of the Mn ion: \( 1 * x + 3 * (-1) = 0 \). Solving for x, the charge of the manganese ions is +3. Thus, the compound is MnF鈧� with manganese ions having a +3 charge.

Step by step solution

01

Understand the arrangement of ions in the unit cell

In the given structure, Mn ions are arranged in a simple cubic array, and F ions are at the center of each edge of the cubic unit cell. In a simple cubic unit cell, there is one ion at each corner, which makes a total of 8 ions. There are 12 edges in a simple cubic unit cell, and since F ions are at the center of each edge, there are 12 F ions.
02

Count Mn and F ions in the unit cell

In the simple cubic arrangement of Mn ions, we have 1 Mn ion per corner. Since there are 8 corners, there are 8 * 1 = 8 Mn ions in the unit cell. Each Mn ion, however, is shared by 8 adjacent cubes, so it contributes 1/8 of an Mn ion per unit cell: \( Mn_{contributed} = 8 * \frac{1}{8} = 1 \) For the F ions, there is 1 F ion at the center of each of the 12 edges. Each F ion is shared by 4 adjacent cubes, so they contribute 1/4 of an F ion per unit cell: \( F_{contributed} = 12 * \frac{1}{4} = 3 \) So, in the unit cell, we have a total of 1 Mn ion and 3 F ions.
03

Use charge balance to determine the charge of Mn ions

In order to determine the charge of Mn ions, we need to consider charge balance in the compound. The overall charge of the compound should be zero. Fluoride ions carry a charge of -1 each. Let x be the charge of the Mn ion. Then, considering the charge balance: \( (1 Mn) * x + (3 F) * (-1) = 0 \) Solving for x, we get: \( x = +3 \) Therefore, the charge of the manganese ions in this compound is +3. The compound formula would be MnF鈧�.

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Key Concepts

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

Simple Cubic Unit Cell
In crystallography, the simple cubic unit cell is one of the most fundamental and common structures. It features atoms positioned at each of the eight corners of a cube. What makes it 'simple' is the uniformity and straightforwardness of this arrangement. Each atom in a simple cubic lattice is shared with 8 adjacent unit cells. Thus, each unit cell effectively contains only one complete atom when considering the distribution across the lattice.

In the case of manganese fluoride, the Mn ions are placed at these corners. Meanwhile, the F ions in this structure occupy positions at the center of the cube's edges. This unique configuration helps determine various properties of the material, such as density and ionic interactions.
Charge Balance
Charge balance is a key concept in chemistry, especially when dealing with ionic compounds. Every ionic compound is electrically neutral, which means the total positive charge must equal the total negative charge.

To find the charge of the Mn ions in manganese fluoride, we use this principle. Assuming that the F ions each have a -1 charge, we can set up an equation: 1 times the charge of Mn plus 3 times the charge of F must equal zero. By solving this equation, we can determine that the manganese ion has a charge of +3. This ensures that the total positive and negative charges cancel each other out, maintaining neutrality.
Ionic Structure
The ionic structure of manganese fluoride is a classic example of how ions arrange themselves in a solid. In ionic structures, oppositely charged ions attract one another and organize into a regular pattern or lattice. This arrangement maximizes attraction and minimizes repulsion, contributing to the stability of the compound.

Manganese ions (Mn) and fluoride ions (F) in this compound fit into a three-dimensional array. The Mn ions provide the framework around which the F ions cluster. Such structures define the compound's characteristics, affecting how it conducts electricity, interacts with other substances, or responds to changes in environment.
Fluoride Ions
Fluoride ions are negatively charged ions derived from fluorine atoms. They play a crucial role in the structure and stability of many compounds.

In manganese fluoride, each F ion carries a -1 charge. These ions are located at the center of the edges of the cubic unit cell. This unique positioning helps stabilize the entire system by creating a balance with the positively charged Mn ions.

The fluoride ions' interactions with manganese ions are pivotal, ensuring the compound's overall electrical neutrality and influencing its chemical properties and reactivity.

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Most popular questions from this chapter

You have three covalent compounds with three very different boiling points. All of the compounds have similar molar mass and relative shape. Explain how these three compounds could have very different boiling points.

Explain the following: You add \(100 \mathrm{~mL}\) water to a \(500-\mathrm{mL}\) round-bottom flask and heat the water until it is boiling. You remove the heat and stopper the flask, and the boiling stops. You then run cool water over the neck of the flask, and the boiling begins again. It seems as though you are boiling water by cooling it.

The temperature inside a pressure cooker is \(115^{\circ} \mathrm{C}\). Calculate the vapor pressure of water inside the pressure cooker. What would be the temperature inside the pressure cooker if the vapor pressure of water was \(3.50 \mathrm{~atm}\) ?

Rationalize the difference in boiling points for each of the following pairs of substances: a. \(n\) -pentane \(\quad \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) \(36.2^{\circ} \mathrm{C}\) neopentane CC(C)(C)C \(9.5^{\circ} \mathrm{C}\) b. HF \(20^{\circ} \mathrm{C}\) \(\mathrm{HCl} \quad-85^{\circ} \mathrm{C}\) c. HCl \(-85^{\circ} \mathrm{C}\) \(\mathrm{LiCl} \quad 1360^{\circ} \mathrm{C}\) d. \(n\) -pentane \(\quad \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) \(36.2^{\circ} \mathrm{C}\) \(\begin{array}{lll}n \text { -hexane } & \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3} & 69^{\circ} \mathrm{C}\end{array}\)

Why do liquids have a vapor pressure? Do all liquids have vapor pressures? Explain. Do solids exhibit vapor pressure? Explain. How does vapor pressure change with changing temperature? Explain.
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