Question

A metal has an fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm⁻³. The molar mass of the metal is ______.

(N_A Avogadro's constant = 6.02 × 10²³ mol⁻¹)

Options

• 30 g mol⁻¹

• 27 g mol⁻¹

• 20 g mol⁻¹

• 40 g mol⁻¹

Answer 1

A metal has an fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm⁻³. The molar mass of the metal is 27 g mol⁻¹.

Explanation:

N_A Avogadro's constant = 6.02 × 10²³ mol⁻¹

Density is given by d = `("Z" xx "M")/("N"_"A""a"^3)`;

Where Z = number of formula units present in the unit cell, which is 4 for fcc.

a = edge length of the unit cell.

M = Molecular mass = 2.72

= `(4 xx "M")/(6.02 xx 10^23 xx (404 xx 10^-10)^3)` ...(∵ 1 pm = 10⁻¹⁰ cm)

M = `(2.72 xx 6.02 xx (404)^3)/(4 xx 10^7)`

= 26.99

= 27 g mol⁻¹