Formula of a Compound and Number of Voids Filled

When particles are close-packed resulting in either ccp or hcp structure, two types of voids are generated. While the number of octahedral voids present in a lattice is equal to the number of close packed particles, the number of tetrahedral voids generated is twice this number. In ionic solids, the bigger ions (usually anions) form the close packed structure and the smaller ions (usually cations) occupy the voids. If the latter ion is small enough then tetrahedral voids are occupied, if bigger, then octahedral voids. All octahedral or tetrahedral voids are not occupied. In a given compound, the fraction of octahedral or tetrahedral voids that are occupied, depends upon the chemical formula of the compound.

In a binary solid (A⁺B^-), B^- ion constitutes CCP lattice and A⁺ ions occupies 25% of tetrahedral holes. What is the formula of the solid?

AB₂

The correct answer is option 3. AB₂

In a binary solid (A⁺B^-),

B^- ion constitutes CCP lattice

FCC unit cell is present in CCP lattice

Total number of B^- ions = \(\frac{1}{8} \times 8 + \frac{1}{2} \times 6 = 1 + 3 = 4\)

A⁺ ions occupies 25% of tetrahedral holes

Total number of T-voids = 8

Total number of A⁺ ions = \(\frac{25}{100}\) x 8 = 2

A : B = 2 : 4

or

A : B = 1 : 2

Hence, the chemical formula of the compound is AB₂.