Question

For the spinel structure ${\mathrm{MgAl}}_2{\mathrm{O}}_4$, the correct statement is/are -

This question has multiple correct options

• A. $50\%$ of the octahedral voids are occupied by ions
• B. ${\mathrm{Al}}^{3+}$ ions are equally distributed in tetrahedral voids and octahedral voids.
• C. Oxide ions occupy CCP lattice
• D. $12.5\%$ of the tetrahedral voids are occupied by ions.

Answer 1

Answer: (A), (C), (D)

$12.5\%$ of the tetrahedral voids are occupied by ions.

Explanation for correct Answers:

Option (A) $50\%$ of the octahedral voids are occupied by ions

• Cubic close packing is a type of packing of atoms in which the atoms are so closely packed. ‘
• The unit cell in cubic close packing (CCP) is face-centered cubic (FCC).
• FCC unit cell contributes four atoms, one-eighth of the atom from the atoms placed in the corner, one atom which is placed in the center of the cube and is not shared by a nearby lattice, and half of an atom from the six atoms present in the faces.
• The general formula of spinel structure is ${\mathrm{AB}}_2{\mathrm{O}}_4$ where the $\mathrm{A}$ atoms occupy one-eighth of the tetrahedral voids and $\mathrm{B}$ atoms occupy half of the octahedral voids
• In ${\mathrm{MgAl}}_2{\mathrm{O}}_4$, the ${\mathrm{Al}}^{3+}$ atoms occupy half of the octahedral voids.
• The percentage occupied by ${\mathrm{Al}}^{3+}$is $\frac{1}{2}\times 100=50\%$.
• Hence, the correct option.

Option (C) Oxide ions occupy CCP lattice

• The Oxide ions are arranged in CCP and have an FCC unit cell.
• Hence, the correct option

Option (D) $12.5\%$ of the tetrahedral voids are occupied by ions.

• In ${\mathrm{MgAl}}_2{\mathrm{O}}_4$, the ${\mathrm{Mg}}^{2+}$ occupy one-eighth of the tetrahedral voids.
• Therefore, the percentage occupied by ${\mathrm{Mg}}^{2+}$is$\frac{1}{8}\times 100=12.5\%$
• Hence, the correct option.

Explanation for Incorrect Answers:

Option (B) ${\mathrm{Al}}^{3+}$ ions are equally distributed in tetrahedral voids and octahedral voids.

• In ${\mathrm{MgAl}}_2{\mathrm{O}}_4$, the ${\mathrm{Al}}^{3+}$ atoms occupy half of the octahedral voids and the ${\mathrm{Mg}}^{2+}$ occupy one-eighth of the tetrahedral voids.
• Hence, incorrect option.

Therefore, the options (A),(C), and (D) are correct.