Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393912340
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 18, Problem 18.47QA
Interpretation Introduction

To find:

The type of unit cell of the copper.

Expert Solution & Answer
Check Mark

Answer to Problem 18.47QA

Solution:

The crystalline form of copper has a face-centered unit cell.

Explanation of Solution

1) Concept:

For each type of unit cell, we can determine the number of atoms in the unit cell and calculate the mass of the unit cell using the molar mass of copper. The radius of the atom can be used to calculate the edge length. The volume of the unit cell can be determined from the edge length. Using the mass of the unit cell and its volume, we can determine the density for each type of unit cell. The calculated density that matches with the given density 8.95gcm3 will determine the type of unit cell.

2) Formula:

i) V=l3

ii) d=mVunit cell

iii) r=0.500 l

iv) r=0.4330 l

v) r=0.3536 l

3) Given:

i) Density d=8.95gcm3

ii) Radius r=127.8 pm

4) Calculations:

a. For a simple cubic unit cell:

Number of atoms per unit cell = 1

Mass of 1 atom of copper is calculated as

m=1 atom Cu × 1 mol Cu6.0221 ×1023atoms Mo × 63.55 g Cu 1 mol Cu =1.055 ×10-22g Cu

Calculating the edge length:

r=0.500 ×l

127.8 pm=0.500 ×l

l=127.8 pm0.500=  255.6 pm

Volume of unit cell:

V=l3=255.6 pm3 × 10-10cm 3 1 pm3=1.669 ×10-23cm3

Calculating the density of unit cell:

d=mVunit cell= 1.055 ×10-22g1.669×10-23cm3=6.321gcm3

b. For a bcc unit cell:

Number of atoms per cell = 2

Mass of 2 atoms of copper is calculated as

m=2 atom Cu × 1 mol Cu6.0221 ×1023atoms Cu × 63.55 g Cu 1 mol Cu =2.110 ×10-22g Cu

Calculating the edge length:

r=0.4330 ×l

127.8 pm=0.4330 ×l

l=127.8 pm0.4330=  295.150 pm

Volume of unit cell:

V=l3=295.150 pm3 × 10-10cm 3 1 pm3=2.571 ×10-23cm3

Calculating the density of unit cell:

d=mVunit cell= 2.110 ×10-22g2.571 ×10-23cm3=8.206 gcm3

c. For an fcc unit cell:

Number of atoms per cell = 4

Mass of 4 atoms of copper is calculated as

m=4 atom Cu × 1 mol Cu6.0221 ×1023atoms Cu × 63.55 g Cu 1 mol Cu =4.221 ×10-22g Cu

Calculating the edge length:

r=0.3536 ×l

127.8 pm=0.3536 ×l

l=127.8 pm0.3536=  361.425 pm

Volume of unit cell:

V=l3=361.425pm3 × 10-10cm 3 1 pm3=4.721×10-23cm3

Calculating the density of unit cell:

d=mVunit cell= 4.221×10-22g4.721×10-23cm3=8.94 gcm3

Thus, the calculated density

8.94 gcm3

in case of fcc unit cell matches with the given density

8.95gcm3

Thus, the face-centered cubic unit cell is consistent with the given data.

Conclusion:

The type of unit cell is determined by calculating the density of copper in each type of unit cell and comparing it with the given density.

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Chapter 18 Solutions

Chemistry: An Atoms-Focused Approach

Ch. 18 - Prob. 18.11VPCh. 18 - Prob. 18.12VPCh. 18 - Prob. 18.13VPCh. 18 - Prob. 18.14VPCh. 18 - Prob. 18.15VPCh. 18 - Prob. 18.16VPCh. 18 - Prob. 18.17VPCh. 18 - Prob. 18.18VPCh. 18 - Prob. 18.19QACh. 18 - Prob. 18.20QACh. 18 - Prob. 18.21QACh. 18 - Prob. 18.22QACh. 18 - Prob. 18.23QACh. 18 - Prob. 18.24QACh. 18 - Prob. 18.25QACh. 18 - Prob. 18.26QACh. 18 - Prob. 18.27QACh. 18 - Prob. 18.28QACh. 18 - Prob. 18.29QACh. 18 - Prob. 18.30QACh. 18 - Prob. 18.31QACh. 18 - Prob. 18.32QACh. 18 - Prob. 18.33QACh. 18 - Prob. 18.34QACh. 18 - Prob. 18.35QACh. 18 - Prob. 18.36QACh. 18 - Prob. 18.37QACh. 18 - Prob. 18.38QACh. 18 - Prob. 18.39QACh. 18 - Prob. 18.40QACh. 18 - Prob. 18.41QACh. 18 - Prob. 18.42QACh. 18 - Prob. 18.43QACh. 18 - Prob. 18.44QACh. 18 - Prob. 18.45QACh. 18 - Prob. 18.46QACh. 18 - Prob. 18.47QACh. 18 - Prob. 18.48QACh. 18 - Prob. 18.49QACh. 18 - Prob. 18.50QACh. 18 - Prob. 18.51QACh. 18 - Prob. 18.52QACh. 18 - Prob. 18.53QACh. 18 - Prob. 18.54QACh. 18 - Prob. 18.55QACh. 18 - Prob. 18.56QACh. 18 - Prob. 18.57QACh. 18 - Prob. 18.58QACh. 18 - Prob. 18.59QACh. 18 - Prob. 18.60QACh. 18 - Prob. 18.61QACh. 18 - Prob. 18.62QACh. 18 - Prob. 18.63QACh. 18 - Prob. 18.64QACh. 18 - Prob. 18.65QACh. 18 - Prob. 18.66QACh. 18 - Prob. 18.67QACh. 18 - Prob. 18.68QACh. 18 - Prob. 18.69QACh. 18 - Prob. 18.70QACh. 18 - Prob. 18.71QACh. 18 - Prob. 18.72QACh. 18 - Prob. 18.73QACh. 18 - Prob. 18.74QACh. 18 - Prob. 18.75QACh. 18 - Prob. 18.76QACh. 18 - Prob. 18.77QACh. 18 - Prob. 18.78QACh. 18 - Prob. 18.79QACh. 18 - Prob. 18.80QACh. 18 - Prob. 18.81QACh. 18 - Prob. 18.82QACh. 18 - Prob. 18.83QACh. 18 - Prob. 18.84QACh. 18 - Prob. 18.85QACh. 18 - Prob. 18.86QACh. 18 - Prob. 18.87QACh. 18 - Prob. 18.88QACh. 18 - Prob. 18.89QACh. 18 - Prob. 18.90QACh. 18 - Prob. 18.91QACh. 18 - Prob. 18.92QACh. 18 - Prob. 18.93QACh. 18 - Prob. 18.94QACh. 18 - Prob. 18.95QACh. 18 - Prob. 18.96QACh. 18 - Prob. 18.97QACh. 18 - Prob. 18.98QACh. 18 - Prob. 18.99QACh. 18 - Prob. 18.100QACh. 18 - Prob. 18.101QACh. 18 - Prob. 18.102QACh. 18 - Prob. 18.103QACh. 18 - Prob. 18.104QACh. 18 - Prob. 18.105QACh. 18 - Prob. 18.106QACh. 18 - Prob. 18.107QACh. 18 - Prob. 18.108QACh. 18 - Prob. 18.109QACh. 18 - Prob. 18.110QACh. 18 - Prob. 18.111QACh. 18 - Prob. 18.112QACh. 18 - Prob. 18.113QACh. 18 - Prob. 18.114QACh. 18 - Prob. 18.115QACh. 18 - Prob. 18.116QACh. 18 - Prob. 18.117QACh. 18 - Prob. 18.118QACh. 18 - Prob. 18.119QACh. 18 - Prob. 18.120QACh. 18 - Prob. 18.121QACh. 18 - Prob. 18.122QACh. 18 - Prob. 18.123QACh. 18 - Prob. 18.124QACh. 18 - Prob. 18.125QACh. 18 - Prob. 18.126QACh. 18 - Prob. 18.127QACh. 18 - Prob. 18.128QACh. 18 - Prob. 18.129QACh. 18 - Prob. 18.130QACh. 18 - Prob. 18.131QACh. 18 - Prob. 18.132QACh. 18 - Prob. 18.133QA
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