Question

The density of crystalline sodium chloride is 2.165 g cm⁻³. What is the edge length of the cubic unit cell? What would be the dimension of a cube containing one mole of NaCl?

Answer 1

A unit cell of sodium chloride contains four Na⁺Cl⁻ units, i.e., Z = 4.

Formula mass of NaCl = 23 + 35.5 = 58.5

∵ `rho = (Z xx M)/(a^3 xx N_A)`

∴ `rho = ((Z xx M)/(rho xx N_A))^(1/3)`

= `((4 xx 58.5)/(2.165 xx 6.022 xx 10^23))^(1/3)`

= `((234)/(130.37 xx 10^23))^(1/3)`

= `(1.79 xx 10^23)^(1/3)`

= 5.64 × 10⁻⁸ cm

∴ The edge length of the unit cell = 5.64 × 10⁻⁸ cm

Volume of 1 mole of NaCl = `M/rho`

= `58.5/2.165`

= 27.02 cm³

If one mole of NaCl are assumed to the packed in a cube of volume 27.02 cm³, the edge length of this cube will be given by

x³ = 27.02 cm³

∴ x = `(27.02)^(1/3)`

∴ x = 3.0 cm