Question

A crystal is formed by X (cations) and Y (anions). Atoms of Y form ccp and atoms of X occupy half of octahedral voids and half of tetrahedral voids. What is the molecular formula of the crystal?

• A. \(X_2Y_3\)
• B. \(XY_3\)
• C. \(X_3Y\)
• D. \(X_3Y_2\)

Hint:

- In a ccp structure, the number of octahedral voids equals the number of atoms in the unit cell.
- The number of tetrahedral voids is twice the number of atoms in the unit cell.
- When cations occupy voids, their ratio can be determined accordingly.

Answer 1

The Correct Option is D

To determine the molecular formula of the crystal composed of cations X and anions Y:

1. Crystal structure: Anions Y form a cubic close-packed (ccp) structure.
2. Void occupation:
   • Cations X occupy half of the octahedral voids.
   • Cations X occupy half of the tetrahedral voids.

In a ccp structure:

1. Number of anions per unit cell = \(4\)
2. Number of octahedral voids per unit cell = \(4\)
3. Number of tetrahedral voids per unit cell = \(8\)

Now, X occupies half of these voids:

• Octahedral voids occupied = \( \frac{4}{2} = 2 \)
• Tetrahedral voids occupied = \( \frac{8}{2} = 4 \)

Total cations X = \(2 + 4 = 6\)

Anions Y = \(4\)

Ratio:

\[ X : Y = 6 : 4 = 3 : 2 \]

Final Molecular Formula: \(X_3Y_2\)