Question

A compound forms a hexagonal close packed structure. What is the number of octahedral voids in $0.5$ moles of it?

Answer 1

To answer this question, you must recall the structure of a hexagonal close packed structure. In a hexagonal close packing, each unit cell contains 6 atoms. The number of octahedral voids in this arrangement is equal to the number of atoms in the unit cell.

Complete step by step solution:
We are given a compound in hexagonal close packing arrangement. To find the number of octahedral voids in $0.5$ moles of the compound, we first need to find the number of molecules present in the given amount of the compound. For this, we must recall Avogadro's number. The Avogadro’s constant or Avogadro’s number gives the number of molecules/ atoms/ ions present in one mole of a substance. The value of Avogadro’s constant is $6.023 \times {10^{23}}$ and it is represented as ${N_A}$ .
Thus, 1 mole of any substance contains $6.023 \times {10^{23}}$ particles.
Number of atoms $= 0.5 \times 6.023 \times {10^{23}} = 3.011 \times {10^{23}}$
So the octahedral voids are also $= 3.011 \times {10^{23}}$ .

Note:
A hexagonal crystal lattice has the atoms in each layer packed in a plane triangular lattice with each atom having a coordination number of 6. Let the first layer of this plane triangle structure be A. In the next layer, say B having the same two dimensional structure, the atoms sit in the holes present between the atoms of the first layer. The third layer, say C also sits in the holes of B but, its arrangement is the same as A. Hence, as the layers pile up in the same order, the structure can be written as ABABABABAB…….. This packing is the hexagonal close packing arrangement.