Indian Forest Service (Mains), Chemistry optional · 2025 · Paper I
Q1(b). Formula from occupied crystal voids
Question
In a cubic close-packed mixed oxide, oxide ions form the lattice, one-eighth of tetrahedral voids are occupied by divalent A ions and one-half of octahedral voids by trivalent B ions. Find the formula.
Answer in brief
The oxide has formula AB₂O₄.
Key points
- If there are N close-packed oxide ions, the lattice contains 2N tetrahedral holes and N octahedral holes.
- A occupies (1/8)(2N) = N/4 sites; B occupies (1/2)N = N/2 sites.
- The ratio A : B : O = N/4 : N/2 : N = 1 : 2 : 4, giving AB₂O₄.
- Charge neutrality checks the result: 1(+2) + 2(+3) + 4(−2) = 0.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
Coverstetrahedral voidsoctahedral voidscubic close packingspinel AB₂O₄formula from voids
All parts of Question 1
- 1(a) Equivalent bonds in nitrate8 marks
- 1(b) Formula from occupied crystal voids8 marks
- 1(c) Formation free energy of uranium hydride8 marks
- 1(d) Pressure dependence of solid Gibbs energy8 marks
- 1(e) Fast and slow electrode systems8 marks