In a solid AB, A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is AₓB y . The value of x is ____________. [nearest integer]

Solution

Chemistry ma’am · 4 steps

A face atom is shared by two cells, so removing two face atoms costs the cell only one A.

1. Count A in ccp. A ccp (fcc) unit cell has 8 corner atoms shared by 8 cells and 6 face atoms shared by 2 cells. That gives 8 × 1/8 + 6 × 1/2 = 1 + 3 = 4 A atoms per cell.
2. Count B. A ccp cell has as many octahedral voids as atoms, so 4 octahedral voids. All are filled, so there are 4 B atoms and the solid is A₄B₄, that is AB.
3. Remove two face atoms. Each face-centre A atom contributes only 1/2 to this cell. Removing the two on opposite faces takes away 2 × 1/2 = 1 A atom, so A drops from 4 to 3.

   A = 1 + (4 × 1/2) = 3, B = 4

4. So. The new formula is A₃B₄, so x = 3.

The common slip: 2. Taking each removed face atom as a whole atom leaves 4 - 2 = 2 A atoms, giving A₂B₄ and x = 2. Each face atom counts only 1/2.

The idea to keep. When atoms are removed from a unit cell, subtract only their share: a corner atom counts 1/8, an edge atom 1/4, a face atom 1/2, and a body-centre atom 1.

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