Question

The density of crystalline sodium chloride is 5.85 g ${cm}^{-3}$. What is the edge length of the unit cell?

• A. $4.04\times {10}^{-9}$ cm
• B. $1.32\times {10}^{-14}$ cm
• C. $7.8\times {10}^{-23}$ cm
• D. $9.6\times {10}^{-24}$ cm

Answer 1

The correct option is A $4.04\times {10}^{-9}$ cm

Density $\left(d\right)=5.85g{cm}^{-3}$

Molar Mass of Sodium Chloride $\left(m\right)=58.5g/mol$

$N_A=6.022\times {10}^{23}$

Unit Cell Type is $FCC,$ $Z=4$

We know,
$d=\frac{(Z\times M)}{(N_A\times a^3)}$

$=>a^3=\frac{(Z\times m)}{(N_A\times d)}$

$=>a^3=\frac{(4\times 58.5)}{(6.022\times {10}^{23}\times 5.85)}$

$=>a^3=0.066\times {10}^{-24}$

$=>a=0.404\times {10}^{-8}$

So, edge length of the unit cell of NaCl is $0.404\times {10}^{-8}cm.$