Question

The edge of length of the unit cell of sodium chloride is $0.400\text{nm}$. What is the density $\left({\text{in gcm}}^{-3}\right)$ of sodium chloride here?

• A. $4.5$
• B. $8.0$
• C. $6.09$
• D. $3.2$

Answer 1

The correct option is C $6.09$

As we know, the expression for density is as follows:
$\text{Density}=d=\frac{ZM}{V{N}_A}=\frac{ZM}{a^3{N}_A}$ ,
where $Z=\text{Effective number of atoms in one unit cell}$ $M=\text{Molar mass of the compound}=58.5\text{g/mol}$
$V=\text{volume of unit cell}$
$a=\text{Edge length}=0.4\text{nm}$
We know,
For $NaCl,Z=4$
$\text{Density}\left(d\right)=\frac{4\times 58.5}{(0.4\times {10}^{-7}{)}^3(6\times {10}^{23})}=6.09{\text{gcm}}^{-3}$