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 12.73QP

(a)

Interpretation Introduction

Interpretation: In Buckminsterfullerene, C60 molecules are given to form a cubic closest-packed array of spheres with a unit cell edge length of 1410pm . The density of crystalline C60 and the radius of the C60 molecule is to be calculated.

Concept introduction: The density of crystalline C60 is calculated by formula,

d=Z×Ma3×NA

The relationship between atomic radius and edge length of cubic is,

a=2r

To determine: The density of C60 molecule.

(a)

Expert Solution
Check Mark

Answer to Problem 12.73QP

Solution

The density of C60 crystalline is 1.707g/cm3_ .

Explanation of Solution

Explanation

Given

The edge length of unit cell is 1410pm .

The smallest unit of a crystal is known as a unit cell which repeats itself in different directions to generate the complete crystal lattice.

The cubic closest-packed has eight atoms at the corners of the cube.

Therefore, only 18 of each corner atom are inside each unit cell.

The total corner atoms inside unit cell is,

18×8=1atompercubiccell

The cubic closest-packed contains one center atom and has six atoms at the centers of each face of the cube. Two unit cells are shared by the one face atom.

The total face atoms inside unit cell is,

12×6=3

Therefore, number of atoms per unit cell in ccp lattice is 4 .

The molar mass of C60 molecule is 720.66g/mol .

The density of crystalline C60 is calculated by formula,

d=Z×Ma3×NA

Where,

  • d is the density of unit cell.
  • Z is the number of atoms per unit cell.
  • a is the edge length.
  • NA is the Avogadro constant.
  • M is the molar mass.

Conversion of 1pm into cm is done as,

1pm=1010cm

Therefore, conversion of 1410pm into cm is,

1410pm=1410×1010cm

Substitute the values of Z , a , M , and NA in the above formula.

d=Z×Ma3×NA=4×720.66(1410×1010)3×6.023×1023=1.707g/cm3_

Therefore, the density of C60 crystalline is 1.707g/cm3_ .

(b)

Interpretation Introduction

To determine: The radius of the C60 molecule.

(b)

Expert Solution
Check Mark

Answer to Problem 12.73QP

Solution

The radius of the C60 molecule is 11.75pm_

Explanation of Solution

Explanation

Given

The edge length of C60 molecules is 1410pm .

Therefore, edge length of one molecule is

1molecule=141060=23.5pm

The relationship between atomic radius and edge length of cubic is,

a=2r

Where,

  • a is the edge length
  • r is the radius.

Substitute the value a in above formula.

a=2rr=a2=23.52=11.75pm_ 

Thus, the radius of the C60 molecule is 11.75pm_ .

Conclusion

  1. a. The density of C60 crystalline is 1.707g/cm3_ .
  2. b. The radius of the C60 molecule is 11.75pm_

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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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