Chapter 12.6, Problem 3.2ACP

### 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

# Using the dimensions of the unit cell (Figure 2) and the molar mass of tin, calculate the density of white tin (in g/cm3).Figure 2 A tetragonal unit cell of white tin (β-tin). The tetragonal unit cod has 90° angles at each corner. Two of the three sides are equal in length (583 pm) while the third side is shorter (318 pm) (Note that the lines connecting atoms are not bonds They are meant only to show the spatial relationship of the atoms.)

Interpretation Introduction

Interpretation:

The density of the white tin has to be identified.

Concept introduction:

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

Explanation

Cube with a two side of white tin is 583Â pm, and one side with 318Â pm. The conversion of pm to cm is 5.83Â Ã—Â 10-8â€‰cm and 3.18Â Ã—Â 10-8â€‰cm

Â Â Vâ€‰=â€‰(a)3CubeÂ withÂ aÂ twoÂ sideÂ ofÂ whiteÂ tinÂ isâ€‰â€‰583Â pm,Â andÂ oneÂ sideÂ â€‰318â€‰pmV=â€‰(5.83Ã—10âˆ’8cm)2(3.18â€‰Ã—â€‰10-8â€‰cm)V=â€‰1.081â€‰Ã—â€‰10-22â€‰cm

Â Â MolarÂ massÂ ofÂ tinÂ isÂ 118.7Â gVolumeÂ ofÂ theÂ unitÂ cellÂ Â =â€‹â€‰1.081â€‰Ã—â€‰10-22â€‰cm3

Â Â MassÂ =Â numberÂ ofÂ molesÂ Ã—Â molarÂ massNumberÂ ofÂ molesÂ =Â NumberÂ ofÂ atomsÂ perÂ unitÂ cellAvogadroÂ numberÂ NumberÂ ofÂ molesÂ =Â 46

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