Question

If an hypothetical metal crystallises in a face centered cubic unit cell having density $\left(d\right)=100{\text{g/cm}}^3$ and edge length of the unit cell is $100\text{pm}$, then, what is the molar mass of the metal:
[1 Mark]

• A. $15.05\text{g/mol}$
• B. $10.02\text{g/mol}$
• C. $16.90\text{g/mol}$
• D. $9.06\text{g/mol}$

Answer 1

The correct option is A $15.05\text{g/mol}$

Given,
$\text{Density (d)}=100{\text{g/cm}}^3$
We know,
$\text{Density}=\frac{Z\times M}{N_A\times V}=\frac{Z\times M}{N_A\times a^3}$
Where, $a=\text{edge length of unit cell}=100\text{pm}$
$M=\text{Molar mass}$
$M=\frac{N_A\times a^3\times d}{Z}=\frac{6.02\times {10}^{23}\times (100\times {10}^{-10}{)}^3\times 100}{4}=15.05\text{g/mol}$