A diatomic molecule X₂ has a body-centred cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6.17 g cm –3 . The number of molecules present in 200 g of X₂ is :
(Avogadro constant (N A ) = 6 × 10²³ mol –1 )

Solution

Chemistry ma’am · 4 steps

Use the density formula to find the molar mass of X2, then 200 g tells you how many moles you have.

1. Set up density. Density links the unit cell to the molar mass: d = (Z M)/(a³ N_A). In a bcc cell Z = 2: 8 corners give 8 × 1/8 = 1, and the body centre gives 1. Each lattice point here is one X₂ molecule, so M is the molar mass of X₂.
2. Cell volume. a = 300 pm = 3 × 10⁻⁸ cm, so a³ = 27 × 10⁻²⁴ cm³.

   M = (d a³ N_A)/Z = (6.17 × 27 × 10⁻²⁴ × 6 × 10²³)/2 = 6.17 × 8.1 ≈ 50 g mol⁻¹

3. Count moles. 200 g of X₂ is 200/50 = 4 mol of molecules.
4. So. The number of X₂ molecules is 4 N_A, which is option (c).

The idea to keep. In d = ZM/(a³ N_A), Z counts whatever sits at the lattice points. Get Z right for the cell type, and convert pm to cm before you cube it.

Answer from the NTA final answer key. Solution by PrepWiser.