Q.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?

The anions $Y$ build the ccp lattice. In a close-packed arrangement of $N$ atoms there are exactly $N$ octahedral voids. Since $X$ occupies all octahedral voids, number of $X$ = number of $Y$.

Step 1 – Count the ccp atoms.

Let there be $N$ atoms of $Y$ forming the cubic close-packed (ccp) lattice.

Step 2 – Count the voids of each type.

In any close packing of $N$ spheres:

Step 3 – Fill the octahedral voids.

$X$ occupies all octahedral voids, so

Step 4 – Ratio and formula.

Use the void-counting rule for close packing: N packing atoms give N octahedral and 2N tetrahedral voids. Match the fraction of voids filled to the number of packing atoms and reduce the ratio.

• Confusing the number of octahedral voids ($N$) with tetrahedral voids ($2N$).
• Forgetting that "all" octahedral voids means the full $N$, not a fraction.
• Writing $X_2Y$ or $XY_2$ by mis-assigning which element is in the voids.