A compound is formed by two elements X and Y. The element Y forms cubic close packed arrangement and those of element X occupy one third of the tetrahedral voids. What is the formula of the compound?

Solution

Chemistry ma’am · 3 steps

Take N atoms of Y: that makes 2N tetrahedral voids, and X fills one third of them.

1. Count the voids. In any close packing of N atoms there are 2N tetrahedral voids and N octahedral voids. Here Y forms the ccp lattice, so take N atoms of Y and 2N tetrahedral voids.
2. Count X. X sits in one third of the tetrahedral voids, so the number of X atoms is 1/3 × 2N = 2N/3.

   X : Y = 2N/3 : N = 2 : 3

3. So. The formula is X₂Y₃, option (d).

The idea to keep. Always count voids from the atoms that form the packing: N packed atoms give 2N tetrahedral and N octahedral voids. Multiply by the fraction filled, then take the ratio.

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