Question

What is the volume of 1 mole of a crystalline solid having unit cell edge length 16 × 10^-8 cm, if its unit cell contains 24 molecules?

Options

• 159.3 cm³ mol^-1

• 404.0 cm³ mol^-1

• 102.7 cm³ mol^-1

• 142.1 cm³ mol^-1

Answer 1

102.7 cm³ mol^-1 

Explanation:

a = 16 × 10^-8 cm

Volume of one unit cell = a³

= (16 × 10^-8)³

= 4096 × 10^-24 cm³

Volume of 24 molecules = 4096 × 10^-24 cm³

∴ Volume of 1 molecule = `(4096 xx 10^-24)/24 = 170.67 xx 10^-24 "cm"^3`

∴ Volume of 1 mole of a crystalline solid = 170.67 × 10^-24 × 6.022 × 10²³ 

= 1027.77 × 10^-1 

= 102.7 cm³ mol^-1