Question

determine the number of formula units of

a) CaF2 in a unit cell of fluorite

b) TiO2 in a unit cell of rutile

c) unit cell of a diamond

**** please explain how to go about this ***

Answer 1

(a). CaF2 in a unit cell of fluorite.

Edge length of CaF2 unit cell = 546.26 pm

= 5.4626 x 10^-8 cm

Volume of unit cell = (5.4626 x 10^-8 cm)³ = 1.63 x 10^-22 cm³

Density of CaF2 unit cell = 3.180 g/cm³

Mass of unit cell = 3.180 g/cm³ * 1.63 x 10^-22 cm³

= 5.1835 x 10^-22 g

Molar mass of CaF2 = 78.074 g/mol

Mass of one formula unit of CaF2 = 78.074 / (6.022 x 10²³)

= 1.2965 x 10^-22 g

Number of formula units = (5.1835 x 10^-22) / (1.2965 x 10^-22)

= 4

(b). TiO2 in a unit cell of rutile

Edge length of TiO2 unit cell = 458.4 pm

= 4.584 x 10^-8 cm

Volume of unit cell = (4.584 x 10^-8 cm)³ = 9.61 x 10^-23 cm³

Density of TiO2 unit cell = 4.23 g/cm³

Mass of unit cell = 4.23 g/cm³ * 9.61 x 10^-23 cm³

= 4.065 x 10^-22 g

Molar mass of TiO2 = 79.866 g/mol

Mass of one formula unit of TiO2 = 79.866 / (6.022 x 10²³)

= 1.326 x 10^-22 g

Number of formula units = (4.065 x 10^-22) / (1.326 x 10^-22)

= 3

(c). unit cell of a diamond

Edge length of diamond unit cell = 356.69 pm

= 3.567 x 10^-8 cm

Volume of unit cell = (3.567 x 10^-8 cm)³ = 4.53 x 10^-23 cm³

Density of diamond unit cell = 3.51 g/cm³

Mass of unit cell = 3.51 g/cm³ * 3.567 x 10^-23 cm³

= 9.84 x 10^-23 g

Molar mass of diamond = 12.01 g/mol

Mass of one formula unit of diamond = 12.01 / (6.022 x 10²³)

= 1.99 x 10^-23 g

Number of formula units = (9.84 x 10^-23) / (1.99 x 10^-23)

= 5