Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is __________ × 10²¹. (Round off to the Nearest Integer). [Given : N A = 6.023 × 10₂₃]

Solution

Chemistry ma’am · 3 steps

Find how many Ga atoms you have, then remember every atom in hcp brings three voids with it.

1. Count the atoms. Moles of Ga = 0.581/70 = 0.0083 mol. Number of atoms = 0.0083 × 6.023 × 10²³ = 4.999 × 10²¹.
2. Voids per atom. In any close packed structure, hcp or ccp, there is 1 octahedral void and 2 tetrahedral voids for every atom. That makes 3 voids per atom.

   N_(voids) = 3 × 4.999 × 10²¹ = 14.997 × 10²¹

3. So. The total number of voids is about 15 × 10²¹, so the answer is 15.

The common slip: 10. Counting only the tetrahedral voids (2N) gives 10, not 15. The octahedral voids (N) must be added too.

The idea to keep. For N atoms in close packing, there are N octahedral and 2N tetrahedral voids, so 3N in total. Find N from moles first, then multiply by 3.

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