Connect 1 Semester Access Card for General Chemistry: The Essential Concepts
Connect 1 Semester Access Card for General Chemistry: The Essential Concepts
7th Edition
ISBN: 9781259692543
Author: Raymond Chang Dr.; Kenneth Goldsby Professor
Publisher: McGraw-Hill Education
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Chapter 12, Problem 12.48QP
Interpretation Introduction

Interpretation:

The edge length of unit cell of Europium crystal lattice has to be calculated.

Concept Introduction:

In packing of atoms in a crystal structure, 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 forms two types of lattices – body – centered lattice and face – centered lattice.

In body-centered cubic unit cell, each of the six corners is occupied by every single atom. Center of the cube is occupied by one atom.  Each atom in the corner is shared by eight unit cells and a single atom in the center of the cube remains unshared.  Thus the number of atoms per unit cell in BCC unit cell is,

                      8×18atomsincorners+1atomatthecenter=1+1=2atoms

                    The edge length of one unit cell is given bya=4R3where  a=edge length of unit cellR=radiusofatom.

Expert Solution & Answer
Check Mark

Answer to Problem 12.48QP

The edge length of unit cell of Europium is calculated as 458 pm.

Explanation of Solution

Record the given data.

densityofEu=5.26g/cm3

Density of Europium is given which is related to mass and volume by the following equation density=massvolume.

Calculate the mass of unit cell of Europium.

Average mass of one Eu atom=atomicmassofEuAvogadronumber=152.0g6.022×1023=25.24×10-23gEachunit cell contains2Eu atoms. therefore,MassofaunitcellofEuropium=2×25.24×10-23g  =50.48×10-23g

Each unit cell contains 2 Europium atoms.  Therefore two times the average mass of one Europium atom gives mass of a unit cell of Europium.

Calculate the volume of unit cell of Ti.

knowndata:mass=50.48×10-23gdensity=5.26g/cm3density=massvolumevolume=massdensity=50.48×10-23g5.26g/cm3=9.6×10-23cm3=96×10-24cm3

Density of Eu is given and mass of the titanium is calculated in the previous step.  Substituting these two values in the equation density=massvolume and rearranging it, volume of the unit cell is obtained.

Determine the edge length of unit cell of Eu.

a3=96×10-24cm3a=396×10-24=4.58×10-8cm=458pm

Volume of the bcc unit cell of Europium is calculated in the previous step. Cube root of the volume of a bcc unit cell, gives the edge length of bcc unit cell of Europium.

Conclusion

The edge length of the unit cell of Europium was calculated.

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Chapter 12 Solutions

Connect 1 Semester Access Card for General Chemistry: The Essential Concepts

Ch. 12.7 - Prob. 1RCCh. 12 - Prob. 12.1QPCh. 12 - Prob. 12.2QPCh. 12 - Prob. 12.3QPCh. 12 - Prob. 12.4QPCh. 12 - Prob. 12.5QPCh. 12 - Prob. 12.6QPCh. 12 - Prob. 12.7QPCh. 12 - Prob. 12.8QPCh. 12 - Prob. 12.9QPCh. 12 - Prob. 12.10QPCh. 12 - Prob. 12.11QPCh. 12 - Prob. 12.12QPCh. 12 - Prob. 12.13QPCh. 12 - 12.14 Diethyl ether has a boiling point of 34.5°C,...Ch. 12 - Prob. 12.15QPCh. 12 - Prob. 12.16QPCh. 12 - Prob. 12.17QPCh. 12 - 12.18 What kind of attractive forces must be...Ch. 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 - 12.36 A solid is hard, brittle, and electrically...Ch. 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 - 12.63 What is the relationship between...Ch. 12 - Prob. 12.64QPCh. 12 - 12.65 Why is solid carbon dioxide called dry ice? Ch. 12 - Prob. 12.66QPCh. 12 - 12.67 Referring to Figure 12.28, estimate the...Ch. 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 - 12.75 These compounds are liquid at −10°C; their...Ch. 12 - 12.76 Freeze-dried coffee is prepared by freezing...Ch. 12 - Prob. 12.77QPCh. 12 - 12.78 Steam at 100°C causes more serious burns...Ch. 12 - 12.79 Vapor pressure measurements at several...Ch. 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. 12.89QPCh. 12 - 12.90 Name the kinds of attractive forces that...Ch. 12 - Prob. 12.91QPCh. 12 - Prob. 12.92QPCh. 12 - Prob. 12.93QPCh. 12 - Prob. 12.94QPCh. 12 - Prob. 12.95QPCh. 12 - Prob. 12.96QPCh. 12 - Prob. 12.97QPCh. 12 - Prob. 12.98QPCh. 12 - 12.99 The liquid-vapor boundary line in the phase...Ch. 12 - Prob. 12.100QPCh. 12 - Prob. 12.101QPCh. 12 - Prob. 12.102QPCh. 12 - Prob. 12.103QPCh. 12 - Prob. 12.104QPCh. 12 - Prob. 12.105QPCh. 12 - Prob. 12.106QPCh. 12 - 12.107 The following graph shows approximate plots...Ch. 12 - Prob. 12.108QPCh. 12 - Prob. 12.109QPCh. 12 - Prob. 12.110QPCh. 12 - Prob. 12.111QPCh. 12 - Prob. 12.112QPCh. 12 - Prob. 12.113QPCh. 12 - Prob. 12.114QPCh. 12 - 12.115 Use the concept of intermolecular forces to...Ch. 12 - Prob. 12.116QPCh. 12 - 12.117 What is the origin of dark spots on the...Ch. 12 - Prob. 12.118QPCh. 12 - 12.119 The electrical conductance of copper metal...Ch. 12 - Prob. 12.120SPCh. 12 - Prob. 12.121SPCh. 12 - Prob. 12.122SPCh. 12 - Prob. 12.123SPCh. 12 - Prob. 12.124SPCh. 12 - 12.125 The boiling point of methanol is 65.0°C and...Ch. 12 - Prob. 12.126SPCh. 12 - Prob. 12.127SPCh. 12 - Prob. 12.128SPCh. 12 - Prob. 12.129SP
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