Question

A metal has a fcc lattice. The edge length of the cell is 404 pm. The density of the metal is $2.72gc{m}^{-3}$ . The molar mass of the metal is
($N_A$ Avogadro's constant = $6.02\times {10}^{23}mo{l}^{-1}$)

• A. $27gmo{l}^{-1}$
• B. $20gmo{l}^{-1}$
• C. $40gmo{l}^{-1}$
• D. $30gmo{l}^{-1}$

Answer 1

The correct option is A

$27gmo{l}^{-1}$

For fcc, Z=4

Note: We will convert all units to cm from m, this is an important step as density is given in g/cc. This will take care of the units of molar weight as well - g/mol.
$d=\frac{ZM}{N_A{a}^3}\Rightarrow M=\frac{d\times N_A\times a^3}{Z}=\frac{2.72\times 6.023\times {10}^{23}\times (404\times {10}^{-10}{)}^3}{4}M=26.99\simeq 27gmo{l}^{-1}$