Question

An element with density 6 g cm⁻³ forms a fcc lattice with edge length of 4 × 10⁻⁸ cm. The molar mass of the element is ______.

(N_A = 6 × 10²³ mol⁻¹)

Options

• 57.6 g mol⁻¹

• 28.8 g mol⁻¹

• 82.6 g mol⁻¹

• 62 g mol⁻¹

Answer 1

An element with density 6 g cm⁻³ forms a fcc lattice with edge length of 4 × 10⁻⁸ cm. The molar mass of the element is 57.6 g mol⁻¹.

Explanation:

We know that Number of atoms per unit cell of FCC = 4Z = 4

Given: d = 6g/cm³,

a = edge length = 4 × 10⁻⁸ cm

N_A = 6 × 10²³ 

`d = ("ZM")/(a^3N_A)`

M = molar mass of element.

∴ 6g/cm³ = `(4 xx "M")/((4 xx 10^-8)^3 xx 6 xx 10^23 "mol"^-1)`

⇒ 6 × 64 × 10⁻²⁴ × 6 × 10²³ 

= 4 M

⇒ M = `(6 xx 6 xx 64 xx 10^-1)/4` g/mol

∴ M = 57.6 g/mol