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Chapter 9: 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 structure of manganese fluoride(MnF3) has one manganese(Mn) ion and three fluoride(F) ions in a cubic unit cell. The fluoride ions have a charge of -1 each. To balance the total charge, the manganese ion has a charge of +3.

Step by step solution

01

Determine the number of ions in the unit cell

Find the number of manganese ions and fluoride ions in a unit cell by multiplying the number of ions at each lattice point by the number of lattice points they occupy.
02

Determine the formula of the compound

Combine the manganese ions and fluoride ions from Step 1 to create the formula of the compound.
03

Determine the charge of the manganese ion

Use the formula of the compound from Step 2 and the known charge of the fluoride ions (-1) to find the charge of the manganese ions.
04

Determine the number of ions in the unit cell

For a simple cubic structure: - Manganese (Mn) ions are located at the corners. There are 8 corners in a cube, and each corner is shared by 8 unit cells. So, each unit cell has \(\frac{1}{8}\) of a manganese ion at each corner, resulting in \(8 \times \frac{1}{8} = 1\) Mn ion per unit cell. - Fluoride (F) ions are located at the center of each edge. There are 12 edges in a cube, and each edge is shared by 4 unit cells. So, each unit cell has \(\frac{1}{4}\) of a fluoride ion at each edge, resulting in \(12 \times \frac{1}{4} = 3\) F ions per unit cell.
05

Determine the formula of the compound

Combine the results of Step 1 to form the formula of the compound. There is 1 Mn ion and 3 F ions in the unit cell, so the formula is MnF3.
06

Determine the charge of the manganese ion

The unit cell contains 3 fluoride ions, with each having a charge of -1. Therefore, the total negative charge is \(3 \times (-1) = -3\). To neutralize this charge, the manganese ion should have a charge of +3, so the manganese ion charge in manganese fluoride is +3.

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Most popular questions from this chapter

A 0.132 -mole sample of an unknown semiconducting material with the formula XY has a mass of \(19.0 \mathrm{g}\). The element X has an electron configuration of \([\mathrm{Kr}] 5 s^{2} 4 d^{10} .\) What is this semiconducting material? A small amount of the Y atoms in the semiconductor is replaced with an equivalent amount of atoms with an electron configuration of \([\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{5} .\) Does this correspond to n-type or p-type doping?

Which of the following compound(s) exhibit only London dispersion intermolecular forces? Which compound(s) exhibit hydrogen-bonding forces? Considering only the compounds without hydrogen-bonding interactions, which compounds have dipole-dipole intermolecular forces? a. \(\mathrm{SF}_{4}\) b. \(\mathrm{CO}_{2}\) c. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) d. \(\mathrm{HF}\) e. \(\mathrm{ICl}_{5}\) f. \(\mathrm{XeF}_{4}\)

In each of the following groups of substances, pick the one that has the given property. Justify each answer. a. highest boiling point: \(\mathrm{CCl}_{4}, \mathrm{CF}_{4}, \mathrm{CBr}_{4}\) b. lowest freezing point: \(\mathrm{LiF}, \mathrm{F}_{2}, \mathrm{HCl}\) c. smallest vapor pressure at \(25^{\circ} \mathrm{C}: \mathrm{CH}_{3} \mathrm{OCH}_{3}, \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\) d. greatest viscosity: \(\mathrm{H}_{2} \mathrm{S}, \mathrm{HF}, \mathrm{H}_{2} \mathrm{O}_{2}\) e. greatest heat of vaporization: \(\mathrm{H}_{2} \mathrm{CO}, \mathrm{CH}_{3} \mathrm{CH}_{3}, \mathrm{CH}_{4}\) f. smallest enthalpy of fusion: \(\mathrm{I}_{2}, \mathrm{CsBr}, \mathrm{CaO}\)

The compounds \(\mathrm{Na}_{2} \mathrm{O},\) CdS, and \(\mathrm{ZrI}_{4}\) all can be described as cubic closest packed anions with the cations in tetrahedral holes. What fraction of the tetrahedral holes is occupied for each case?

The structure of the compound \(\mathrm{K}_{2} \mathrm{O}\) is best described as a cubic closest packed array of oxide ions with the potassium ions in tetrahedral holes. What percent of the tetrahedral holes are occupied in this solid?
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