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  3. Chemistry
  4. A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm-3. The molar mass of the metal is

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Q. A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is $2.72\, g\, cm^{-3}$. The molar mass of the metal is

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Solution:

$d = \frac{ZM}{N_{A}a^{3}}$ ($Z = 4$ for fcc)
$M = \frac{d\times N_{A}\times a^{3}}{Z} = \frac{2.72\times 6.023\times 10^{23}\times \left(404\times 10^{-10}\right)^{3}}{4}$
$M = 27\, g \,mol^{-1}$