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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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