   # Iridium (Ir) has a face-centered cubic unit cell with an edge length of 383.3 pm. Calculate the density of solid iridium. ### 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 54E
Textbook Problem
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## Iridium (Ir) has a face-centered cubic unit cell with an edge length of 383.3 pm. Calculate the density of solid iridium.

Interpretation Introduction

Interpretation:

The density of solid Iridium having face-centered unit cell has to be determined.

Concept introduction:

Packing of atoms in a crystal structure, follow a regular pattern. The atoms 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 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+6×12atoms infaces=1+3=4atoms The edge length of one unit cell is given bya=2R2where  a=edge length of unit cellR=atomicradius

### Explanation of Solution

Explanation

Calculate volume of the FCC unit cell.

givendata:edgelength,a=383.8pm=383.8×10-12mvolume=a3=(383.8×10-12m)3=5.653×10-29m3=5.653×10-23cm3

Edge length of the FCC unit cell is given. Volume of FCC unit cell corresponds to the cubic value of the edge length. So the given value of edge length is cubed to obtain the volume of a unit cell.

Calculate the mass of unit cell.

Average mass of one Ir atom=atomicmassofIrAvogadronumber=192.22g6.022×1023=31

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