Question

A diatomic molecule X₂ has a body-centered cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6.47 g cm⁻³. The number of molecules present in 200 g of X₂ is ______.

Options

• 4 N_A

• 2 N_A

• 40 N_A

• 8 N_A

Answer 1

A diatomic molecule X₂ has a body-centered cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6.47 g cm⁻³. The number of molecules present in 200 g of X₂ is `bbunderline(4 N_A)`.

Explanation:

Given: For BCC (Z) = 2

a = 300 pm

= `300 xx 1/10^10` 

= 3 x 10⁻⁸ cm

d = 6.47 g cm⁻³

Mass of sample = 200 g

N_A = 6.022 × 10²³

In bcc number of atoms per unit cell is 2.

Formula: Density `rho = (Z * M)/(N_A * a^3)`

`M = (d xx N_A xx a^3)/Z`

`M = (6.47 xx 6.022 xx 10^23 xx (3 xx 10^-8)^3)/2`

`M = (38.96 xx 10^23 xx 27 xx 10^-24)/2`

`M = (1051.9 xx 10^-1)/2`

`M = (1051.9 xx 0.1)/2`

`M = (105.19)/2`

`M = 52.59` g/mol

∴ Number of moles = `("Mass")/("molar mass")`

= `200/52.59`

= 3.84 moles ≈ 4 moles

∴ Number of molecules = 4 N_A.