Question

A well known mineral fluorite is chemically calcium fluoride. It is known that in one unit cell of this mineral there are 4 Ca²⁺ ions and 8 F⁻ ions and that Ca²⁺ ions are arranged in a fcc lattice. The F⁻ ions fill all the tetrahedral holes in fcc lattice of Ca²⁺ ions. The edge of the unit cell is 5.46 × 10⁻⁸ cm in length. The density of the solid is 3.18 g cm⁻³. Use this information to calculate Avogadro’s number. (Molar mass of CaF₂ = 78.08 g mol⁻¹)

Answer 1

Given:

Edge of unit cell=5.46*10(power-8)

Density of Solid , d=3.18 g cm cube

Molar Mass of CaF2,M=78.08 gmol-1

Since Lattice is fcc type,Z=4

Density of unit cell,d=zM/a3,NA

NA=zM/a3d

     =4*78.08gmol-1/(5.46*10-8cm)3*3.18gmcm-3

     =6.03*10 23