   # In solid KCl the smallest distance between the centers of a. potassium ion and a chloride ion is 314 pm. Calculate the length of the edge of the unit cell and the density of KCl, assuming it has the same structure as sodium chloride. ### 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 78E
Textbook Problem
179 views

## In solid KCl the smallest distance between the centers of a. potassium ion and a chloride ion is 314 pm. Calculate the length of the edge of the unit cell and the density of KCl, assuming it has the same structure as sodium chloride.

Interpretation Introduction

Interpretation:

• The edge length of KCl unit cell has to be calculated.
• Density of KCl has to be determined.

Concept introduction:

In crystalline solids, the components are packed in regular pattern and neatly stacked. The components are imagined as spheres and closely packed. This phenomenon is called “close packing” in crystals. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell.

In face-centered cubic unit cell, each of the six corners is occupied by every single atom. Each face of the cube is occupied by one atom.

Each atom in the corner is shared by eight unit cells and each atom in the face is shared by two unit cells. Thus the number of atoms per unit cell in FCC unit cell is,

8×18atomsincorners+6×12atomsinfaces=1+3=4atoms   The edge length of one unit cell is given byl=2R2where  l=edgelength of unit cellR=atomicradius

### Explanation of Solution

Calculate the edge length of KCl unit cell.

givendata:distancebetweenK+andCl-ionsis314pm.edgelength,l=2×314pm=628pm.

KCl has FCC structure. Assume the Potassium and Chloride ions touch along the edge of the cube.

Figure 1

The edge length of the unit cell is twice the value of the smallest distance between K+ and Cl- ions.

Calculate the volume of KCl unit cell.

knowndata:edgelength,l=628pmvolume,l3=(628×10-12m)3=2.48×10-22cm3

Edge length of the unit cell is calculated in the previous step. Volume of the unit cell is obtained by cubing the edge length value.

Calculate the mass of KCl unit cell.

Averagemass of one KCl molecule=molecular weightofKClAvogadronumber

=74.55g6.022×1023

=12

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