A compound is formed by atoms of A, B and C. Atoms of C form hcp lattice. Atoms of A occupy 50\% of…
A compound is formed by atoms of A, B and C. Atoms of C form hcp lattice. Atoms of A occupy 50\% of octahedral voids and atoms of B occupy $\frac{2}{3}$ rd of tetrahedral voids. What is the molecular formula of the solid?
$\mathrm{A}_3 \mathrm{~B}_8 \mathrm{C}_6$
$\mathrm{A}_2 \mathrm{~B}_8 \mathrm{C}_6$
$\mathrm{AB}_4 \mathrm{C}_3$
$\mathrm{A}_5 \mathrm{~B}_8 \mathrm{C}_6$
Solution
hcp contribution i.e $(C)=4$
Total octahedral void $=4$
A contribute $=4 \times 50 \%=2$
Total tetrahedral void $=8 \quad \therefore B^{\prime}$ 'contribute $=8 \times \frac{2}{3}=\frac{16}{3}$
$\begin{aligned}
\therefore \quad & A_2 B_{16 / 3} C_4 \\
& A_6 B_{16} C_{12}
\end{aligned}$
By simplify we get
$\mathrm{A}_3 \mathrm{~B}_8 \mathrm{C}_6$