Question

Aluminium has fcc structure. The edge length of the unit cell is $404$ pm. If the density of the metal is $2.7$ g cm${}^{-3}$, the molar mass (in gmol${}^{-1}$) of Al atom is :

• A. $28.20$
• B. $30.40$
• C. $26.80$
• D. $25.20$

Answer 1

The correct option is C $26.80$

The expression for density is as follows:

$d=\frac{ZM}{N_A{a}^3}$

where $Z=4$ for fcc

$d=\frac{4\times M}{{6.023\times 10}^{23}\times {(404\times {10}^{-10})}^3}=2.7$ g cm${}^{-3}$

$⟹M=26.80$ g mol${}^{-1}$

Hence , the molecular mass is $26.80$ gmol${}^{-1}$.