Question

A unit cell of sodium chloride has four formula units. The edge length of the unit cell is $0.564nm$. What is the density of sodium chloride?

Answer 1

Analyzing the given data:

For Sodium chloride unit cell

$Z=4$

$a=0.564nm=5.64A^o$

$\text{Molecular mass of}NaCl=23+35.5=58.5$

Formula for calculating density of Sodium chloride unit cell

$\rho =\frac{Z\times M_A}{N_A\times a^3}$

$\rho =\text{Density}$

$Z=\text{Effective number of atom}$

$N_A=\text{Avogadro number}=6.022\times {10}^{23}$

$a=\text{Edge length}$

$\rho =\frac{4\times 58.5}{6.022\times {10}^{23}\times (5.64\times {10}^{-8}cm{)}^3}$

$\rho =\frac{4\times 58.5}{6.023\times {10}^{23}\times 179.40\times {10}^{-24}}g/c{m}^3$

$\rho =2.16$ $g/c{m}^3$