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 12.74QP

(a)

Interpretation Introduction

Interpretation: The given question stated that C60 reacts with alkali metals to form M3C60 (where M is Na or K ). The crystal structure of M3C60 contains cubic closest-packed spheres of C60 with metal ions in holes. When radius of an K+ ion is 138pm then the type of holes K+ ion likely to occupy and the density of a crystal of K6C60 is to be explained.

Concept introduction: The cubic closest-packed has eight atoms at the corners of the cube and six atoms at the centers of each face of the cube. The big atoms create the void space in the ccp arrangement and this space is occupied by the small atoms.

To determine: The type of holes K+ ion is likely to occupy and the fraction of the holes that will be occupied.

(a)

Expert Solution
Check Mark

Answer to Problem 12.74QP

Solution

The atomic radii ratio of both the atom is 0.27_ .

The fraction of the hole will be 27%_ .

Explanation of Solution

Explanation

Given

The radius of potassium ion is 138pm .

The calculated radius of C60 is 498.5pm .

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

The cubic closest-packed has eight atoms at the corners of the cube and six atoms at the center of each face of the cube. The big atoms create the void space in the ccp arrangements and this space is occupied by the small atoms.

The atomic radii ratio is calculated by the formula,

Atomicradiiratio=r+r

Where,

  • r+ is the radius of cation.
  • r is the radius of anion

Substitute the value of radius in above formula.

Atomicradiiratio=r+r=138pm498.5pm=0.27

Therefore, the atomic radii ratio of both the atom is 0.27_ .

In ccp arrangement if radius ratio is between 0.410.73 then the atoms having smaller atomic radius will occupy the octahedral hole. And if radius ratio is between 0.220.41 then the atoms will occupy the tetrahedral hole.

Therefore, potassium ion will occupy tetrahedral holes.

The fraction of the holes that will be occupied by potassium ion is 27%_ .

(b)

Interpretation Introduction

To determine: The density of a crystal of K6C60

(b)

Expert Solution
Check Mark

Answer to Problem 12.74QP

Solution

The density of K6C60 is 0.0120g/cm3_ .

Explanation of Solution

Explanation

Given

The calculated radius for C60 is 11.75pm .

The given compound is K6C60 .

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

The number of atoms per unit cell in bcc lattice is 2 .

The molar mass of given compound is 955.23g/mol .

The density of K6C60 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.

The relationship between atomic radius and edge length of bcc lattice is,

a=r0.4330

Where,

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

Substitute the value of radius in above formula.

a=r0.4330=11.750.4330=27.13pm

Conversion of 1pm into cm is done as,

1pm=1010cm

Therefore, conversion of 27.13pm into cm is,

27.13pm=27.13×1010cm

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

d=Z×Ma3×NA=2×955.23(27.13×1010)3×6.023×1023=0.0120g/cm3

Therefore, the density of K6C60 is 0.0120g/cm3_ .

Conclusion

The density of K6C60 is 0.0120g/cm3_ .

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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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