Question

In a solid, oxide ions $({O^{2 - }})\;$are arranged in ccp, cation $({A^{3 + }})\;$occupies one-sixth of tetrahedral void and cations $({B^{3 + }})\;$ occupy one-third of the octahedral voids. What is the formula of the compound?
A.$AB{O_3}$
B.$A{B_2}{O_3}$
C.${A_2}B{O_3}$
D.$AB{O_2}$

Answer 1

To answer this question you should recall the concept of close packing in a solid crystal. Voids refer to the gaps between the constituent particles. These voids in solid crystals mean the vacant space between the constituent particles. The number of ions in packing is equal to the number of octahedral voids. The number of tetrahedral voids are twice the number of octahedral voids.

Complete step by step answer:
Crystalline solids show regular and repeating pattern arrangement of constituent particles. In the question we know that
Number of ${O^{2 - }}$ions in packing = 4, Number of octahedral voids = 4, Number of tetrahedral voids = 8. Now using the information, we can calculate the number of anions and cations.
Number of ${A^{3 + }}$ $= \dfrac{1}{6} \times 8 = \dfrac{4}{3}$and Number of ${B^{3 + }} = \dfrac{1}{3} \times 4 = \dfrac{4}{3}$.
$\therefore$The ratio of the components in the crystal can be written as:
${A^{3 + }}:{B^{3 + }}:{O^{2 - }} = \dfrac{4}{3}:\dfrac{4}{3}:4 = 1:1:3$.
Hence, the formula of the compound =$AB{O_3}$.

Therefore, the correct answer to this question is option A.

Additional information: Tetrahedral voids: In case of a cubic close-packed structure, the second layer of spheres is present over the triangular voids of the first layer. This results in each sphere touching the three spheres of the first layer. When we join the centre of these four spheres, we get a tetrahedron and the space left over by joining the centre of these spheres forms a tetrahedral void.
Octahedral voids: Adjacent to tetrahedral voids you can find octahedral voids. When the triangular voids of the first layer coincide with the triangular voids of the layer above or below it, we get a void that is formed by enclosing six spheres. This vacant space which is formed by the combination of the initial formed triangular voids of the first layer and that of the second layer is known as Octahedral Voids.

Note:
A crystal is a solid where a periodic arrangement of atoms is formed. Not all crystals are solids. One example of this phenomenon is that when liquid water starts to freeze, the transition in the process begins with tiny ice crystals rising until they merge, creating a polycrystalline structure.