Chapter 12.6, Problem 3.4ACP

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Determine the percentage of space occupied by tin atoms in both the tetragonal and cubic crystal lattices. The atomic radius of tin is 141 pm.

Interpretation Introduction

Interpretation:

The percentage of the space occupied by the tin atoms in tetragonal and cubic crystal lattice has to be calculated.

Concept introduction:

The volume of the atom is given below,

V=(a)3

The density of the unit cell is calculated as follows,

Massvolume = density

Mass = number of moles × molar massNumber of moles = Number of atoms per unit cellAvogadro number

The Volume of the one atom is given below

V = 43Πr3

Explanation

Number of atoms per unit is given below,

It has 8 atoms in the corner, 6 atom in the face, 4 atoms in the body.

NumberÂ ofÂ atomsÂ perÂ unitâ€‰=(8â€‰cornerâ€‰atomsâ€‰Ã—â€‰1/8â€‰+â€‰6â€‰faceâ€‰atomâ€‰Ã—â€‰1/2â€‰+4â€‰bodyâ€‰atomsâ€‰Ã—â€‰1)NumberÂ ofÂ atomsÂ perÂ unitâ€‰=â€‰8densityÂ =â€‰5.769â€‰g/cm3molarâ€‰massâ€‰ofâ€‰tinâ€‰=â€‰118.710Â g/mol

Z = number of atoms per unit.

Massâ€‰ofâ€‰theâ€‰unitâ€‰cellâ€‰=â€‰8Â Ã—Â 118.7106.023Ã—1023Massâ€‰ofâ€‰theâ€‰unitâ€‰cellâ€‰=â€‰1.5767â€‰Ã—10-21â€‰g

Volumeâ€‰=â€‰MassDensityVolumeâ€‰=â€‰1.5767â€‰Ã—10-21â€‰g5.769â€‰g/cm3Volumeâ€‰=â€‰2.733â€‰Ã—10-22â€‰cm3Volumeâ€‰=â€‰2.733â€‰Ã—108â€‰pm3

Volume of the one atom is given below

Â VÂ =Â 43Î r3

Therefore, Volume of the eight atoms is given below,

Â VÂ =Â 8Ã—43Î r3where,â€‰r=141pmVÂ =Â 8Ã—43Î (141Â pm)3VÂ =Â 9.397Ã—107Â pm3

The percentage of space occupied is

TheÂ percentageÂ ofÂ spaceÂ occupiedÂ isâ€‰=â€‰Â 9.397Ã—107Â pm32.733â€‰Ã—108â€‰pm3Ã—100=â€‰0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started