   # The CsCl structure is a simple cubic array of chloride ions with a cesium ion at the center of each cubic array (see Exercise 69). Given that the density of cesium chloride is 3.97 g/cm 3 , and assuming that the chloride and cesium ions touch along the body diagonal of the cubic unit cell, calculate the distance between the centers of adjacent Cs + and Cl − ions in the solid. Compare this value with the expected distance based on the sizes of the ions. The ionic radius of Cs + is 169 pm, and the ionic radius of Cl − is 181 pm. ### Chemistry: An Atoms First Approach

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

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 9, Problem 79E
Textbook Problem
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## The CsCl structure is a simple cubic array of chloride ions with a cesium ion at the center of each cubic array (see Exercise 69). Given that the density of cesium chloride is 3.97 g/cm3, and assuming that the chloride and cesium ions touch along the body diagonal of the cubic unit cell, calculate the distance between the centers of adjacent Cs+ and Cl− ions in the solid. Compare this value with the expected distance based on the sizes of the ions. The ionic radius of Cs+ is 169 pm, and the ionic radius of Cl− is 181 pm.

Interpretation Introduction

Interpretation:

The distance between Cesium ions and Chlorine ions in Cesium chloride unit cell has to be calculated using edge length value and compared with the theoretically calculated value.

Concept introduction:

Cesium chloride is made of simple cubic unit cells in its lattice structure. The Cesium and Chlorine ions touch each other along the body diagonal of unit cell.

In simple cubic unit cell, each atom in the corner is shared by eight unit cells. Thus, number of atoms per simple cubic unit cell is,

8×18atomsincorners=1atom

Each Cesium ion is surrounded by eight Chlorine ions and each Chlorine ion is surrounded by eight Cesium ions. Each unit cell contains one Cesium chloride molecule that is one Cs+ ion and one Cl- ion. The edge length of simple cubic unit cell is represented by the formula   “ l=2r ”. The length of body diagonal is 3l .

### Explanation of Solution

Calculate the mass of unit cell.

Average mass of one CsClmolecule=molecularmassofCsClAvogadronumber=168.36g6.022×1023=27.95×10-23gEachunit cell contains1CsClmolecule. therefore,Massofaunitcell=27.95×10-23g

Each unit cell contains one Cesium chloride molecule. Therefore the average mass of one Cesium chloride gives mass of a unit cell.

Calculate the volume of unit cell of Cesium chloride.

knowndata:mass=27.95×10-23gdensity=3.97g/cm3density=massvolumevolume,l3=massdensity=27

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