Q.A compound forms hexagonal close-packed structure. What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids?

Number of atoms in $0.5$ mol $=0.5\times6.022\times10^{23}=3.011\times10^{23}$.

Per close-packed atom there are 2 tetrahedral and 1 octahedral void, i.e. 3 voids total.

$\text{Total voids}=3\times3.011\times10^{23}=9.033\times10^{23}$ …

Step 1 – Number of close-packed atoms.

Step 2 – Voids per atom in a close-packed structure.

In any close packing (hcp or ccp):

• number of octahedral voids $=$ number of atoms $=1$ per atom,
• number of tetrahedral voids $=2\times$ number of atoms $=2$ per atom.

So total voids per atom $=1+2=3$.

Step 3 – Tetrahedral voids.

Step 4 – Total voids. …

Convert moles to number of atoms via $N_A$. Apply the close-packing rule: 1 octahedral + 2 tetrahedral vo …

• Forgetting the factor of 2 for tetrahedral voids (they are twice the number of atoms).
• Taking total voids as $2\times$ atoms instead of $3\times$ (octahedral + tetrahedral). …