   # The compounds Na 2 O, CdS, and ZrI 4 . all can be described as cubic closest packed anions with the cations in tetrahedral holes. What fraction of the tetrahedral holes is occupied for each case? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 9, Problem 72E
Textbook Problem
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## The compounds Na2O, CdS, and ZrI4. all can be described as cubic closest packed anions with the cations in tetrahedral holes. What fraction of the tetrahedral holes is occupied for each case?

Interpretation Introduction

Interpretation:

The fraction of occupied ions in tetrahedral holes of given cases should be calculated.

Concept Introduction:

• The atoms or ions are arranged in a cleared manner it is called closest packing. The closest packing are commonly Cubic close packing and hexagonal close packing.
• The ions are arranged in closest packing is to maximizes the electrostatic forces.
•  The empty space of closest packing is called holes.
• In cubic close packing the octahedral holes are equal to number of anion present in the unit cell and tetrahedral holes are equal to number of twice the number of anion present in the unit cell.
• Fraction of ions is ratio of cation and anion in the formula thus,

Ratioofcation and anoin=NumberofcationNumberofanion......(1)

### Explanation of Solution

Explanation

Record the given data:

In the cubic closest packing anions and cations are arranged in tetrahedral holes.

The given ionic arrangement in closest packed crystal is recorded as shown above.

To determine the fraction of occupied ions in tetrahedral holes of given compounds.

• One array of anion have two tetrahedral holes.

For Na2O ,

Fractionof Na2O=21=2f1f=1

The fraction of Na2O is 1 so the One Na+ ion is filled by the all tetrahedral holes.

For CdS ,

Fractionof CdS=11=2f1&#

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