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

Step 1: Understanding the Crystal Structure 
- The Y atoms form a cubic close-packed (ccp) structure, meaning they occupy the lattice points. 
- The X atoms occupy half of the octahedral voids and half of the tetrahedral voids. 

Step 2: Calculation of Ratio 
- In a ccp structure, the number of octahedral voids = number of Y atoms. 
- The number of tetrahedral voids = twice the number of Y atoms. 
- Since X occupies half of both voids, we get: 
- X atoms from octahedral voids = \( \frac{1}{2} \times Y \) 
- X atoms from tetrahedral voids = \( \frac{1}{2} \times 2Y = Y \) 
- Total X atoms = \( Y + \frac{1}{2} Y = \frac{3}{2} Y \) 

Step 3: Simplifying the Formula 
- The ratio of X:Y = \(3:2\), leading to the formula \(X_3Y_2\).

 Step 4: Verifying the Answer 
- The molecular formula is \(X_3Y_2\), which matches Option (4).