Question

Pick out the correct statement(s) for ${\text{CsCl}}$ crystal:
Coordination number for ${\text{C}}{{\text{s}}^ + }$ and ${\text{C}}{{\text{l}}^ - }$ is 8.
$\dfrac{{{{\text{r}}_{{\text{C}}{{\text{s}}^ + }}}}}{{{{\text{r}}_{{\text{C}}{{\text{l}}^ - }}}}} = 0.732$
The structure changes to ${\text{NaCl}}$ structure at $760{\text{ K}}$.
${\text{C}}{{\text{l}}^ - }$ ions are present at cubic sites.

Answer 1

The number of atoms or ions that can surround the central atom in a crystal lattice is known as the coordination number of the atom or ion. The coordination number of the cation in the crystal structure depends on the limiting radius ratio.

Complete step-by-step answer:
The structure of ${\text{CsCl}}$ crystal is a body-centered cubic (bcc) type of structure. Thus, the ${\text{C}}{{\text{s}}^ + }$ or ${\text{C}}{{\text{l}}^ - }$ ion sits at the centre of the cube and the ${\text{C}}{{\text{s}}^ + }$ or ${\text{C}}{{\text{l}}^ - }$ ions sit at the eight corners of the cube.
Thus, the coordination number for ${\text{C}}{{\text{s}}^ + }$ and ${\text{C}}{{\text{l}}^ - }$ is 8.
We will determine the limiting radius as follows:
The coordination numbers with respect to the values of limiting radius ratio are as shown in the table.

LIMITING RADIUS RATIO	COORDINATION NUMBER
1	12
1-0.0732	8
0.732-0.414	6
0.414-0.225	4
0.225-0.155	3
0.155-0	2

As the coordination number is 8, the limiting radius lies between 1 – 0.732. Thus, the limiting radius ratio is ${\text{0}}{\text{.732}}$. The structure of ${\text{CsCl}}$ can be converted to ${\text{NaCl}}$ structure by heating it at $760{\text{ K}}$.
In the structure of ${\text{CsCl}}$, any of the ions ${\text{C}}{{\text{s}}^ + }$ or ${\text{C}}{{\text{l}}^ - }$ are present at the cubic sites.

Thus, all the statements for ${\text{CsCl}}$ structure are correct.

Note: The significance of the limiting radius ratio is as follows:
1-The limiting radius ratio helps in predicting the structures of the ionic solids.
2-The structure of an ionic compound mainly depends on the size of its constituent ions and the stoichiometry.
3-In the crystal lattice, the cations are surrounded by the largest number of possible anions.