Question

A compound is formed by cation C and anion A. The anions form hexagonal close packed (HCP) lattice and the actions occupy ${\text{75% }}$ of octahedral voids. The formula of the compound is:
(A) ${C_2}{A_3}$
(B) ${C_3}{A_2}$
(C) ${C_3}{A_4}$
(D) ${C_4}{A_3}$

Answer 1

Hint: In hexagonal close packing, layers of spheres are packed so that the spheres which are in alternating layers overlie one another. And the three-dimensional structure of a crystal lattice, the gaps in between the spheres are the voids. As we know that tetrahedral voids are triangular in shape when two such voids combine, from two different layers then they form an octahedral void.

Complete step by step answer:
As we know that,
In hexagonal close packed (HCP) lattice the number of atoms ${\text{ = }}\,{\text{6}}$
And the number of atoms is always equal to no. of octahedral voids and the tetrahedral voids are double of octahedral voids.
So here we are talking about octahedral voids therefore.
No. of octahedral voids ${\text{ = }}\,{\text{6}}$
And it is given in question that captions occupy ${\text{75% }}$ of octahedral voids.
$\therefore 6 \times \dfrac{{75}}{{100}} = \dfrac{9}{2}$ by solving this we get therefore, $\dfrac{9}{2}$ octahedral voids are occupied
We can’t write its formula because it is in fractions so firstly convert into whole no. by writing the ratio of cations and anions.
Cations: anions
$\dfrac{9}{2}:6$
$9:12$
$3:4$
${C_3}{A_4}$

ALTERNATIVE METHOD:
As we know that,
No of atoms and number of octahedral voids both are equal to ${\text{6}}$
And anions are fully occupied whereas cations occupied ${\text{75% }}$ that is $\dfrac{3}{4}$
${C_{\dfrac{3}{4}}}A.$
Therefore, by simplifying the ratio we get ${C_3}{A_4}$.

Hence, option C is correct.

Note: In CCP ${\text{4}}$ octahedral voids are present because as we learnt above that octahedral voids are equal to the number of atoms.
-Moreover, there is a difference between hexagonal close packing and cubic close packing is that, a unit all of hexagonal close packing has 6 spheres and a unit cell of, cubic close packing has 4spheres.