Question

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?

• A. \( 66.6 \)
• B. \( 25 \)
• C. \( 50 \)
• D. \( 33.3 \)

Hint:

In a ccp lattice, the number of octahedral voids is equal to the number of atoms, and the number of tetrahedral voids is twice the number of atoms.

Answer 1

The Correct Option is C

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%.