Question

A solid compound is formed by atoms of A (cations), B (cations), and O (anions). Atoms of O form an hcp lattice. Atoms of A occupy 25% of tetrahedral holes and atoms of B occupy 50% of octahedral holes. What is the molecular formula of the solid? 

• A. \( AB_2O_4 \)
• B. \( ABO_3 \)
• C. \( ABO_2 \)
• D. \( A_2BO_4 \)

Hint:

In an hcp lattice, - Tetrahedral voids are twice the number of anions. - Octahedral voids are equal to the number of anions. - To determine the formula, use the occupancy percentage of voids by cations.

Answer 1

The Correct Option is C

In an hcp lattice, the number of atoms forming the lattice (oxygen in this case) is 6.

1. Oxygen (O): Forms the hcp lattice, so there are 6 O atoms.
2. A (cation): Occupies 25% of tetrahedral holes. An hcp lattice has 12 tetrahedral holes, so the number of A atoms is 12 * 0.25 = 3.
3. B (cation): Occupies 50% of octahedral holes. An hcp lattice has 6 octahedral holes, so the number of B atoms is 6 * 0.50 = 3.

Therefore, the ratio of atoms A : B : O is 3 : 3 : 6, which simplifies to 1 : 1 : 2.

The molecular formula of the solid is \(ABO_2\).