Aluminum crystallizes with a face-centered-cubic unit cell. The radius of an Al atom is 143 pm. Calculate the density of solid crystalline Al in g/cm3.
Convert pm to cm:
143 pm x (1 cm/1010 pm) = 1.43 x 10¯8 cm
Determine the edge length of the unit cell:
Use the Pythagorean Theorem
r = d ÷ 2(√2)
1.43 x 10¯8 cm = d ÷ 2(√2)
d = 4.044 x 10¯8 cm
Determine the volume of the unit cell:
(4.044 x 10¯8 cm)3 = 6.616 x 10¯23 cm3
Determine mass of 4 atoms of Al in a unit cell
26.98 g/mol divided by 6.022 x 1023 atoms/mol = 4.479 x 10¯23 g/atom
4.479 x 10¯23 g/atom times 4 atoms = 1.791 x 10¯22 g
Determine density:
1.791 x 10¯22 g divided by 6.616 x 10¯23 cm3 = 2.708 g/cm3
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