Chemistry: The Science in Context (Fifth Edition)
Chemistry: The Science in Context (Fifth Edition)
5th Edition
ISBN: 9780393614046
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster, Stacey Lowery Bretz, Geoffrey Davies
Publisher: W. W. Norton & Company
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Chapter 12, Problem 12.97AP
Interpretation Introduction

Interpretation: The given two alloys AuZn and AgZn have the same unit cell. The alloy that is denser is to be identified.

Concept introduction: An alloy is a solution that is made up of mixing of atoms of an element with other element which results in change in properties of the host element. Gold and silver both crystallize in a face centered cubic unit cell.

The density of the unit cell is calculated by the formula,

Densityoftheunitcell=MassoftheunitcellVolumeoftheunitcell

To determine: The alloy that is denser.

Expert Solution & Answer
Check Mark

Answer to Problem 12.97AP

Solution

The alloy AuZn is denser than the alloy AgZn .

Explanation of Solution

Explanation

Gold and silver both crystallize in a face centered cubic unit cell.

There are 4 atoms in an fcc unit cell.

The molar mass of AuZn is 262.29g/mol .

The mass of a unit cell is calculated by the formula,

Massoftheunitcell=Massofeachatom×Numberofatomsinunitcell(n)=AtomicmassAvogadro'snumber×numberofatomsinunitcell(n)

Substitute the value of the molar mass of AuZn in the formula of the mass of the unit cell,

MassofAuZnunitcell=262.29gAuZnmolAuZn×1mol6.023×1023atoms×4atoms=1.741×10-21g

The given edge length is (l) 319pm .

The volume of an AuZn unit cell is calculated by the formula,

v=l3

Substitute the value of the edge length in the above formula.

v=l3=(319pm)3×(10-10cm)3pm3=3.246×10-23cm3

Density is calculated by the formula,

Densityoftheunitcell=MassoftheunitcellVolumeoftheunitcelld=mv

Substitute the value of the mass and volume of the unit cell in the above expression.

d=mv=1.741×10-21g3.246×1023cm3=53.63g/cm3

Therefore, the density of AuZn is 53.63g/cm3 .

The mass of a unit cell is calculated by the formula,

Massoftheunitcell=Massofeachatom×Numberofatomsinunitcell(n)=AtomicmassAvogadro'snumber×numberofatomsinunitcell(n)

The mass of AgZn is calculated by the formula,

MassofAgZnunitcell=173.25gAgZnmolAgZn×1mol6.023×1023atoms×4atoms=1.150×10-21g

The given edge length is (l) 316pm .

The volume of an AuZn unit cell is calculated by the formula,

v=l3

Substitute the value of the edge length in the above formula.

v=l3=(316pm)3×(10-10cm)3pm3=3.155×10-23cm3

Density is calculated by the formula,

Densityoftheunitcell=MassoftheunitcellVolumeoftheunitcelld=mv

Substitute the value of the mass and volume of the unit cell in the above expression.

d=mv=1.150×10-21g3.155×1023cm3=36.45g/cm3

Thus, the density of AgZn is 53.63g/cm3 .

Therefore, the alloy AuZn is denser than the alloy AgZn .

Conclusion

The alloy AuZn is denser than the alloy AgZn .

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Chapter 12 Solutions

Chemistry: The Science in Context (Fifth Edition)

Ch. 12 - Prob. 12.3VPCh. 12 - Prob. 12.4VPCh. 12 - Prob. 12.5VPCh. 12 - Prob. 12.6VPCh. 12 - Prob. 12.7VPCh. 12 - Prob. 12.8VPCh. 12 - Prob. 12.9VPCh. 12 - Prob. 12.10VPCh. 12 - Prob. 12.11VPCh. 12 - Prob. 12.12VPCh. 12 - Prob. 12.13VPCh. 12 - Prob. 12.14VPCh. 12 - Prob. 12.15VPCh. 12 - Prob. 12.16VPCh. 12 - Prob. 12.17QPCh. 12 - Prob. 12.18QPCh. 12 - Prob. 12.19QPCh. 12 - Prob. 12.20QPCh. 12 - Prob. 12.21QPCh. 12 - Prob. 12.22QPCh. 12 - Prob. 12.23QPCh. 12 - Prob. 12.24QPCh. 12 - Prob. 12.25QPCh. 12 - Prob. 12.26QPCh. 12 - Prob. 12.27QPCh. 12 - Prob. 12.28QPCh. 12 - Prob. 12.29QPCh. 12 - Prob. 12.30QPCh. 12 - Prob. 12.31QPCh. 12 - Prob. 12.32QPCh. 12 - Prob. 12.33QPCh. 12 - Prob. 12.34QPCh. 12 - Prob. 12.35QPCh. 12 - Prob. 12.36QPCh. 12 - Prob. 12.37QPCh. 12 - Prob. 12.38QPCh. 12 - Prob. 12.39QPCh. 12 - Prob. 12.40QPCh. 12 - Prob. 12.41QPCh. 12 - Prob. 12.42QPCh. 12 - Prob. 12.43QPCh. 12 - Prob. 12.44QPCh. 12 - Prob. 12.45QPCh. 12 - Prob. 12.46QPCh. 12 - Prob. 12.47QPCh. 12 - Prob. 12.48QPCh. 12 - Prob. 12.49QPCh. 12 - Prob. 12.50QPCh. 12 - Prob. 12.51QPCh. 12 - Prob. 12.52QPCh. 12 - Prob. 12.53QPCh. 12 - Prob. 12.54QPCh. 12 - Prob. 12.55QPCh. 12 - Prob. 12.56QPCh. 12 - Prob. 12.57QPCh. 12 - Prob. 12.58QPCh. 12 - Prob. 12.59QPCh. 12 - Prob. 12.60QPCh. 12 - Prob. 12.61QPCh. 12 - Prob. 12.62QPCh. 12 - Prob. 12.63QPCh. 12 - Prob. 12.64QPCh. 12 - Prob. 12.65QPCh. 12 - Prob. 12.66QPCh. 12 - Prob. 12.67QPCh. 12 - Prob. 12.68QPCh. 12 - Prob. 12.69QPCh. 12 - Prob. 12.70QPCh. 12 - Prob. 12.71QPCh. 12 - Prob. 12.72QPCh. 12 - Prob. 12.73QPCh. 12 - Prob. 12.74QPCh. 12 - Prob. 12.75QPCh. 12 - Prob. 12.76QPCh. 12 - Prob. 12.77QPCh. 12 - Prob. 12.78QPCh. 12 - Prob. 12.79QPCh. 12 - Prob. 12.80QPCh. 12 - Prob. 12.81QPCh. 12 - Prob. 12.82QPCh. 12 - Prob. 12.83QPCh. 12 - Prob. 12.84QPCh. 12 - Prob. 12.85QPCh. 12 - Prob. 12.86QPCh. 12 - Prob. 12.87QPCh. 12 - Prob. 12.88QPCh. 12 - Prob. 12.89APCh. 12 - Prob. 12.90APCh. 12 - Prob. 12.91APCh. 12 - Prob. 12.92APCh. 12 - Prob. 12.93APCh. 12 - Prob. 12.94APCh. 12 - Prob. 12.95APCh. 12 - Prob. 12.96APCh. 12 - Prob. 12.97APCh. 12 - Prob. 12.98APCh. 12 - Prob. 12.99APCh. 12 - Prob. 12.100APCh. 12 - Prob. 12.101APCh. 12 - Prob. 12.102APCh. 12 - Prob. 12.103APCh. 12 - Prob. 12.104APCh. 12 - Prob. 12.105APCh. 12 - Prob. 12.106APCh. 12 - Prob. 12.107APCh. 12 - Prob. 12.108APCh. 12 - Prob. 12.109APCh. 12 - Prob. 12.110AP
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