The molecular formula of a crystalline solid is $\mathrm{X}_3 \mathrm{Y}_2$. Atoms of Y form ccp lattice,…

The molecular formula of a crystalline solid is $\mathrm{X}_3 \mathrm{Y}_2$. Atoms of Y form ccp lattice, and atoms of X occupy 50\% octahedral voids and $x \%$ of tetrahedral voids. What is the percentage of unoccupied tetrahedral voids?
  1. 66.6
  2. 25
  3. 50
  4. 33.3

Solution

Molecular formula $=\mathrm{X}_3 \mathrm{Y}_2$ $\begin{aligned} & Y \text { atom }=\mathrm{ccp}=4 \\ & \mathrm{X} \text { atom }=\frac{50 \times 4}{100}+\frac{\mathrm{x} \times 8}{100} \quad\left[\begin{array}{l}\text { Td void }=8 \\ \text { Oh void }=4\end{array}\right] \\ & \frac{X \frac{(50 \times 4)}{100}+\frac{\mathrm{x} \times 8}{100}}{2} Y_2 \\ & \therefore \frac{\frac{50 \times 4}{100}+\frac{\mathrm{x} \times 8}{100}}{2}=3 \\ & \text { or, } 2+\frac{8 \mathrm{x}}{100}=6 \\ & \frac{8 \mathrm{x}}{100}=4 \\ & \therefore x=50 \%\end{aligned}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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