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Pyrolusite is a mineral containing manganese ions and oxide ions. Its structure can best be described as a body-centered cubic array of manganese ions with two oxide ions inside the unit cell and two oxide ions each on two faces of the cubic unit cell. What is the charge on the manganese ions in pyrolusite?

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Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

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Section
BuyFindarrow_forward

Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 9, Problem 125CWP
Textbook Problem
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Pyrolusite is a mineral containing manganese ions and oxide ions. Its structure can best be described as a body-centered cubic array of manganese ions with two oxide ions inside the unit cell and two oxide ions each on two faces of the cubic unit cell. What is the charge on the manganese ions in pyrolusite?

Interpretation Introduction

Interpretation:

The charge on the Manganese ion in Pyrolusite mineral in which Manganese ions are arranged in BCC lattice has to be calculated.

Concept Introduction:

In packing of atoms/ions in a crystal structure, they are imagined as spheres. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing.

Cubic close packing has two types – Face-centered cubic close packing (FCC) and Body – centered cubic close packing (BCC). In body-centered cubic unit cell, each of the eight corners is occupied by every single atom. Center of the cube is occupied by one atom.

Each atom in the corner is shared by eight unit cells and a single atom in the center of the cube remains unshared. Thus the number of atoms per unit cell in BCC unit cell is,

                  8×18atomsincorners+1atomatthecenter=1+1=2atoms

Explanation of Solution

Explanation

Deduce the empirical formula of Pyrolusite.

Givendata:2 oxide ions occupy inside the BCC unit cell and 2 oxide ions each occupy two faces of the cubic unit cell.

          8corners×18Mnionsatcorners+1Mnionatthecenterofthecube=2Mnions.2faces×12Oionsatfaces+2Oionsatthecenterofthecube=3Oions.

Thus the empirical formula is Mn2O3.

Pyrolusite mineral has Manganese and Oxygen ions. They are packed in body – centered cubic lattice. BCC lattice has BCC unit cells. Each BCC unit cell contains eight Manganese ions at each corner of the cubic unit cell and one Manganese ion at the center of the cube. The Manganese ion at each corner of the cubic unit cell is shared by eight adjacent unit cells. Thus, each BCC unit cell of Pyrolusite lattice has 2 Manganese ions. The oxide ions are occupied as follows – two oxide ions occupy center of the unit cell and two oxide ions occupy two faces

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Chemistry: An Atoms First Approach
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