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.

A compound is formed by two elements X and Y. Atoms of the element Y (as anions) make ccp and those of the element X (as cations) occupy all the octahedral voids. What is the formula of the compound?

XY

The correct answer is option 2. XY

Atoms of the element Y (as anions) form CCP

FCC is the unit cell in CCP Lattice

No. of atoms of Y (as anions) \(= \frac{1}{8} \times 8 + \frac{1}{2} \times 6 = 1 + 3 = 4\)

Element X (as cations) occupy all the octahedral voids.

Total no. of Octahedral voids = 4 = No. of atoms of Element X (as cations)

\(X : Y = 4 : 4\)

or \(X : Y = 1 : 1\)

Hence, the chemical formula of the compound is XY.