General Chemistry
General Chemistry
7th Edition
ISBN: 9780073402758
Author: Chang, Raymond/ Goldsby
Publisher: McGraw-Hill College
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Chapter 12, Problem 12.49QP
Interpretation Introduction

Interpretation:

The number of Silicon atoms in unit cell of Silicon cubic lattice has to be determined.

Concept introduction:

In crystalline solids, the components are packed in regular pattern and neatly stacked. The components are imagined as spheres and closely packed. This phenomenon is called “close packing” in crystals. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing.

Expert Solution & Answer
Check Mark

Answer to Problem 12.49QP

The number of Silicon atoms in unit cell of Iron cubic lattice is 8.

Explanation of Solution

Record the given data:

    edgelengthofunitcell=543pmdensity of Silicon=2.33g/cm3

The unit cell is assumed that of a cubic shape and the edge length of the unit cell is given. Density of Silicon is given.

Calculate the volume of one unit cell of cubic lattice of Silicon.

   givendata:edgelength,a=543pm=543×10-12mvolume,a3=(543×10-12m)3=1.60×10-28m3=1.60×10-22cm3

Edge length of the cubic unit cell is given. The cubic value of edge length gives the volume of the unit cell.

Calculate the mass of one unit cell of cubic lattice of Silicon.

knowndata: density = 2.33 g/cm3volume=1.60×10-22cm3density=massvolumemass=volume×density=1.60×10-22cm3×2.33g/cm3massofaunitcell=3.73×10-22g

Density of the unit cell is given. The mass of unit cell is calculated using the equation density=massvolume. the values are substituted in the equation and rearranged to obtain mass of the unit cell of Silicon lattice.

Calculate the average mass of one Silicon atom in unit cell.

  Average mass of one Silicon atom=atomicmassofSiliconAvogadronumber=28.086.022×1023=4.66×10-23g

The average mass of one Silicon atom in its crystal lattice is related to number of atoms per unit cell as follows –

Average mass of one Silicon atom=massofunitcellno.ofSiliconatomsperunitcellno.ofSiliconatomsperunitcell=massofunitcellAverage mass of one Silicon atom

Using this equation, the number of Silicon atoms present per unit cell has been calculated.

The average mass of one Silicon atom in its crystal lattice is calculated using the atomic mass value of Silicon.

Calculate the number of Silicon atoms present in a unit cell.

Average mass of one Silicon atom=massofunitcellno.ofSiliconatomsperunitcellno.ofSiliconatomsperunitcell=massofunitcellAverage mass of one Silicon atom=3.73×10-22g4.66×10-23g=0.80×101=8

Conclusion

The number of Silicon atoms in unit cell of Silicon cubic lattice was calculated.

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Chapter 12 Solutions

General Chemistry

Ch. 12.7 - Prob. 1RCCh. 12 - Prob. 12.1QPCh. 12 - Prob. 12.2QPCh. 12 - Prob. 12.3QPCh. 12 - Prob. 12.4QPCh. 12 - Prob. 12.5QPCh. 12 - Prob. 12.6QPCh. 12 - Prob. 12.7QPCh. 12 - Prob. 12.8QPCh. 12 - Prob. 12.9QPCh. 12 - Prob. 12.10QPCh. 12 - Prob. 12.11QPCh. 12 - Prob. 12.12QPCh. 12 - Prob. 12.13QPCh. 12 - 12.14 Diethyl ether has a boiling point of 34.5°C,...Ch. 12 - Prob. 12.15QPCh. 12 - Prob. 12.16QPCh. 12 - Prob. 12.17QPCh. 12 - 12.18 What kind of attractive forces must be...Ch. 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 - 12.36 A solid is hard, brittle, and electrically...Ch. 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 - 12.63 What is the relationship between...Ch. 12 - Prob. 12.64QPCh. 12 - 12.65 Why is solid carbon dioxide called dry ice? Ch. 12 - Prob. 12.66QPCh. 12 - 12.67 Referring to Figure 12.28, estimate the...Ch. 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 - 12.75 These compounds are liquid at −10°C; their...Ch. 12 - 12.76 Freeze-dried coffee is prepared by freezing...Ch. 12 - Prob. 12.77QPCh. 12 - 12.78 Steam at 100°C causes more serious burns...Ch. 12 - 12.79 Vapor pressure measurements at several...Ch. 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. 12.89QPCh. 12 - 12.90 Name the kinds of attractive forces that...Ch. 12 - Prob. 12.91QPCh. 12 - Prob. 12.92QPCh. 12 - Prob. 12.93QPCh. 12 - Prob. 12.94QPCh. 12 - Prob. 12.95QPCh. 12 - Prob. 12.96QPCh. 12 - Prob. 12.97QPCh. 12 - Prob. 12.98QPCh. 12 - 12.99 The liquid-vapor boundary line in the phase...Ch. 12 - Prob. 12.100QPCh. 12 - Prob. 12.101QPCh. 12 - Prob. 12.102QPCh. 12 - Prob. 12.103QPCh. 12 - Prob. 12.104QPCh. 12 - Prob. 12.105QPCh. 12 - Prob. 12.106QPCh. 12 - 12.107 The following graph shows approximate plots...Ch. 12 - Prob. 12.108QPCh. 12 - Prob. 12.109QPCh. 12 - Prob. 12.110QPCh. 12 - Prob. 12.111QPCh. 12 - Prob. 12.112QPCh. 12 - Prob. 12.113QPCh. 12 - Prob. 12.114QPCh. 12 - 12.115 Use the concept of intermolecular forces to...Ch. 12 - Prob. 12.116QPCh. 12 - 12.117 What is the origin of dark spots on the...Ch. 12 - Prob. 12.118QPCh. 12 - 12.119 The electrical conductance of copper metal...Ch. 12 - Prob. 12.120SPCh. 12 - Prob. 12.121SPCh. 12 - Prob. 12.122SPCh. 12 - Prob. 12.123SPCh. 12 - Prob. 12.124SPCh. 12 - 12.125 The boiling point of methanol is 65.0°C and...Ch. 12 - Prob. 12.126SPCh. 12 - Prob. 12.127SPCh. 12 - Prob. 12.128SPCh. 12 - Prob. 12.129SP
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