The molecular formula of a crystalline solid is X\( _3 \)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?
Show Hint
- \( 66.6 \)
- \( 25 \)
- \( 50 \)
- \( 33.3 \)
The Correct Option is C
Solution and Explanation
Analysis of CCP Lattice in Compound X3Y2
The number of atoms in the CCP lattice is n.
- The number of octahedral voids is n.
- The number of tetrahedral voids is 2n.
In the given compound X3Y2, Y forms the CCP lattice. Therefore, the number of Y atoms is:
n = 2.
- The number of octahedral voids is 2.
- The number of tetrahedral voids is 4.
The X atoms occupy 50% of the octahedral voids. Therefore, the number of X atoms in octahedral voids is:
0.5 × 2 = 1.
Let the number of X atoms in tetrahedral voids be a. The total number of X atoms is 3. Hence, we have:
1 + a = 3, which means a = 2.
The percentage of tetrahedral voids occupied by X atoms is:
\(\frac{2}{4} \times 100 = 50\%\).
The percentage of unoccupied tetrahedral voids is:
100 - 50 = 50%.
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