Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 4.8, Problem 57SEP
To determine

What is the theoretical atom % of each element in the compound FeO, what is the corresponding wt% of each element in the compound and write your conclusion.

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Answer to Problem 57SEP

The theoretical atom % of FeandO element in the compound FeO is 50% respectively, and wt% of FeandO element is 77.7%and23.3% respectively.

Explanation of Solution

Express mass of one Fe atom.

 mFe=MFeN                                                                                          (I)

Here, atomic or molar mass of Fe is MFe and number of atom per mole is N.

Express mass of one O atom.

 mO=MON                                                                                         (II)

Here, atomic or molar mass of O is MO.

Express wt% of Fe.

 wt%Fe=mFemFe+mO(100%)                                                              (III)

Express wt% of O.

 wt%O=100%wt%Fe                                                                    (IV)

Conclusion:

Write the reaction for FeO.

 FeOFe+O

Here, iron oxide is FeO, iron is Fe and oxygen is O.

The atom percentage of FeandO in FeO is 50% each, since there is one O atom for each Fe atom.

Hence, the theoretical atom % of FeandO element in the compound FeO is 50% respectively.

Write the atomic mass of iron and oxygen.

 MFe=55.85gMO=16g

Write the number of atom per mole or Avogadro number.

 N=6.02×1023atoms

Substitute 55.85g for MFe and 6.02×1023atoms for N in Equation (I).

 mFe=55.85g6.02×1023atoms=9.27×1023g

Substitute 16g for MO and 6.02×1023atoms for N in Equation (II).

 mO=16g6.02×1023atoms=2.66×1023g

Substitute 9.27×1023g for mFe and 2.66×1023g for mO in Equation (III).

 wt%Fe=9.27×1023g9.27×1023g+2.66×1023g(100%)=77.7%

Substitute 77.7% for wt%Fe in Equation (IV).

 wt%O=100%77.7%=23.3%

Hence, the wt% of FeandO element in the compound FeO is 77.7%and23.3% respectively.

From above calculations of wt%andatom%, it is clear that both are different from each other. The weight percentage is given as weight of solute divided by weight of solvent whereas the percentage of each atom in the given alloy is atom percentage.

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Chapter 4 Solutions

Foundations of Materials Science and Engineering

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