Question

A metal has afcc lattice. The edge length of the unit cell is $404\text{pm}$. The density of the metal is $2.72{\text{g cm}}^{-3}$.
The molar mass of the metal is ($N_A$ Avogadro's constant = $6.02\times {10}^{23}{\text{mol}}^{-1}$)

• A. $27{\text{g mol}}^{-1}$
• B. $40{\text{g mol}}^{-1}$
• C. $20{\text{g mol}}^{-1}$
• D. $30{\text{g mol}}^{-1}$

Answer 1

The correct option is A $27{\text{g mol}}^{-1}$

$d=\frac{M}{N_A{a}^3}(Z=4forfcc)M=\frac{d\times N_A\times a^3}{Z}=\frac{2.72\times 6.023\times {10}^{23}\times (404\times {10}^{-10}{)}^3}{4}=27gmo{l}^{-1}$