A solid compound is formed by atoms of A (cations), B (cations) and O (anions). Atoms of O form hcp lattice.…
A solid compound is formed by atoms of A (cations), B (cations) and O (anions). Atoms of O form hcp lattice. Atoms of A occupy 25\% of tetrahedral holes and atoms of B occupy $50 \%$ octahedral holes. What is the molecular formula of solid?
$\mathrm{AB}_2 \mathrm{O}_4$
$\mathrm{ABO}_3$
$\mathrm{ABO}_2$
$\mathrm{A}_2 \mathrm{BO}_4$
Solution
$\mathrm{A}=25 \%$ Tetrahedral holes
No. of Tetrahedral voids in a Lattice $=12$
$25 \%$ Tetrahedral holes $=\frac{25}{100} \times 12=3$
$\mathrm{B}=50 \%$ Octahedral holes
No. of Octahedral voids in a Lattice $=6$
$50 \%$ Octahedral voids $=\frac{50}{100} \times 6=3$
O is hcp Lattice. The no. of voids in hcp is 6 .
The molecular formula is $\mathrm{A}_3 \mathrm{~B}_3 \mathrm{O}_6$
$\mathrm{ABO}_2$