Question

Find the molar mass of an element that crystallises forming unit cell structure having edge length 4 × 10^-8 cm and containing 4 particles. (ρ = 19.7 g cm^-3).

Options

• 140.2 g mol^-1

• 220.0 g mol^-1

• 189.8 g mol^-1

• 160.5 g mol^-1

Answer 1

189.8 g mol^-1 

Explanation:

For fcc unit cell, the number of atoms per unit cell, Z = 4

Density, d = `"ZM"/("N"_"A""a"^3)`

M = molar mass, N_A = 6.022 × 10²³ mol^-1 = Avogadro's number

Given: a = 4 × 10^-8 cm

Density, d = 19.7 g cm^-3

`19.7 = (4 xx "M")/(6.022 xx 10^23 xx (4 xx 10^-8)^3)`

`19.7 = (1 xx "M")/(6.022 xx 10^23 xx 64 xx 10^-24)`

`=> "M" = (19.7 xx 6.022 xx 10^-1 xx 64)/4`

= 189.8 g mol^-1