Question

A metal crystallizes in fcc structure with a unit cell side of $500\text{pm}$. If the density of the crystal is $1.33\text{g/cc}$, the molar mass(in g/mol) of the metal is: (Give your answer to the nearest integer value)

Answer 1

Given, unit cell is fcc
For fcc unit cell $Z_{eff}=4$
$Edgelength,a=500\text{pm}=5.00\times {10}^{-8}\text{cm}$
Density of metla, d = $1.33\text{g/cc}$
$N_A=6.02\times {10}^{23}{\text{mol}}^{-1}$
Molar mass of the metal, M = ?
We know,
$d=\frac{z\times M}{a^3\times N_A}$
$\Rightarrow M=\frac{d\times N_A\times a^3}{z}$
$\Rightarrow M=\frac{1.33\times (5.00\times {10}^{-8}{)}^3\times 6.02\times {10}^{23}}{4}$
$\Rightarrow M=\frac{1000\times {10}^{-1}}{4}$
Hence, M = $25$