Connect 1 Semester Access Card for General Chemistry: The Essential Concepts
Connect 1 Semester Access Card for General Chemistry: The Essential Concepts
7th Edition
ISBN: 9781259692543
Author: Raymond Chang Dr.; Kenneth Goldsby Professor
Publisher: McGraw-Hill Education
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Chapter 12, Problem 12.126SP
Interpretation Introduction

Interpretation:

From the calculation of radius and density the unknown alkali metal has to be identified.

Concept Introduction:

The radius of a body-centered cubic unit cell:

r=34×aa=edgelength

Volume of the cubic unit cell:

V=a3

The edge length of the cubic unit cell:

a=V3

Expert Solution & Answer
Check Mark

Answer to Problem 12.126SP

The unknown alkali-metal is found to be Sodium.

Explanation of Solution

Given data:

Vapor pressure (P) : 19.2mmHg

Temperature (T):1235K

Volume (V): 0.843L

It is known that

R=Gasconstant=0.0821L.atm

Calculating the number of moles of the unknown alkali metal:

The ideal gas equation is n=PVRT

Converting pressure from mmHg into atm:

19.2mmHg=19.2mmHg×1atm760mmHg1atm=760mmHg=0.02526atm

Substituting all the values in the ideal gas equation:

=(0.02526atm)(0.843L)(0.0821L.atm/K.mol)(1235K)=2.10×10-4mol

So, the number of moles of the unknown alkali metal is 2.10×10-4mol

Calculating the volume/mol:

Given: Edge length is 0.171cm.

The relation between volume and the edge length is V=a3

V=(0.171cm)3=5.00×103cm3

Thus, the volume of the body centered cubic unit cell is 5.00×103cm3 which is the volume of 2.10×10-4mol unknown alkali metal.  So, it is simply the volume/mol.

Converting volume/mol into volume/unit cell:

=5.00×10-3cm32.10×10-4mol×1mol6.022×1023atoms×2atoms1unitcell=7.91×10-23cm3/unitcell

Thus the volume of the unit cell is 7.91×10-23cm3/unitcell.

Calculating the edge length with respect to this volume:

a=V3

a=7.91×10-23cm33=4.2927×108cm

Thus the edge length is a=4.2927×108cm

It is known that all alkali metals have a body-centered cubic structure.

So, calculating the radius of the unknown alkali-metal in the body-centered cubic structure.

The radius of for a body-centered cubic unit cell can be expressed as follows:

r=34×a

=34×4.2927×108cm=1.8576×108cm

Converting radius from centimeters into picometers:

1.8576×108cm=1.8576×108cm×(1×10-2m1cm×1pm1×10-12m)=1.8576×108×1010pm=1.8576×102pm=185.76pm

Thus the radius is 185.76pm186pm

Figure

This calculated radius is the radius of sodium metal.

So, the unknown metal is found to be sodium metal.

Calculating the mass of sodium metal:

Since sodium metal is in body-centered cubic lattice, hence there will be 2 atoms per unit cell.

The molar mass of sodium is 23 amu which is the mass of 1 sodium atom and the mass of 6.023×1023amu is equal to 1g of sodium.

So, the 2 atoms of sodium per unit cell can be calculated as follows:

2atoms×23amu1Naatom×1g6.023×1023amu=7.6374×10-23g

So, the mass of 2atoms per unit cell is 7.6374×10-23g.

The volume of the unit cell has been calculated as 7.91×10-23cm3/unitcell.

With all these calculations, calculating the density of sodium metal:

Density=MassVolume=7.6374×10-23g7.91×10-23cm3/unitcell=0.9655g/cm3/unitcell0.97g/cm3/unitcell

The actual density of sodium is known to be 0.97g which exactly matches with the calculated density of sodium. This proves the identification of the sodium metal.

Conclusion

From the calculation of radius, the unknown alkali metal has been identified and from the calculation of density, the identification has been proved.

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Chapter 12 Solutions

Connect 1 Semester Access Card for General Chemistry: The Essential Concepts

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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