
To find:
a) If lithium, gold, and titanium can form substitutional alloy with
b) The density of

Answer to Problem 18.132QA
Solution:
a) Lithium,
b) Density of
Explanation of Solution
a) Substitutional alloys may form when the difference in atomic radii between the alloying elements is less than 15%.
1) Concept:
Aluminum forms alloys with different elements; hence it acts as a host metal. Other metals, such as lithium, gold, and titanium form alloys with a particular metal, so they are called non-host metals. The atomic radii of all the elements is given, and the ratio between the radii of non-host elements and host elements will determine whether they will form substitutional alloys.
2) Formula:
3) Given:
i) Atomic radii of
ii) Atomic radii of
iii) Atomic radii of
iv) Atomic radii of
4) Calculations:
For
For
For
Since all the ratios of the above alloys is less than
b) Calculate the density of
1) Concept:
To calculate the density of LiAl, we will calculate the mass and volume of the unit cell from the number of atoms present in bcc structure. First we will calculate the edge length from the atomic radii and calculate the volume of the unit cell. We will calculate the mass of the unit cell by using number of atoms present in per unit cell and molar mass.
2) Formulae:
i)
ii)
iii)
3) Given:
i) Atomic radius of
ii) Atomic radius of
iii) Atomic mass of
iv) Atomic mass of
v) Number of atoms in the unit cell
vi) Avogadro’s Number
4) Calculations:
First calculate the edge length of the
The value of body diagonal has been calculated as
Edge length of the alloy:
Volume of unit cell:
Molar mass of the alloy
Mass of the unit cell:
Density of the alloy:
Hence, the density of the
Conclusion:
The substitutional alloy is found from the atomic radii, and the density of LiAl is calculated from the volume of unit cell and mass of unit cell.
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Chapter 18 Solutions
Chemistry: An Atoms-Focused Approach
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