Question

The radius of ${\text{N}}{{\text{a}}^ + }$ ions is ${\text{95 pm}}$ and that of ${\text{C}}{{\text{l}}^ - }$ is ${\text{181 pm}}$. Predict whether the coordination number of ${\text{N}}{{\text{a}}^ + }$ ion is 6 or 4.

Answer 1

Hint: 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:
Determine the limiting radius ratio as follows:
The ratio of the ionic radii of the positive ion to the negative ion is known as the limiting radius ratio. Thus,
${\text{Limiting radius ratio}} = \dfrac{{{\text{Ionic radius of N}}{{\text{a}}^ + }}}{{{\text{Ionic radius of C}}{{\text{l}}^ - }}}$
Substitute ${\text{95 pm}}$ for the ionic radius of ${\text{N}}{{\text{a}}^ + }$, ${\text{181 pm}}$ for the ionic radius of ${\text{C}}{{\text{l}}^ - }$. Thus,
${\text{Limiting radius ratio}} = \dfrac{{{\text{95 pm}}}}{{{\text{181 pm}}}}$
${\text{Limiting radius ratio}} = 0.524$
Thus, the limiting radius ratio is $0.524$.
Determine the coordination number of ${\text{N}}{{\text{a}}^ + }$ ion 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 – 0.732	8
0.732 – 0.414	6
0.414 – 0.225	4
0.225 – 0.155	3
0.155 - 0	2

The limiting radius ratio is ${\text{0}}{\text{.524}}$.
Thus, from the above table. the coordination number of ${\text{N}}{{\text{a}}^ + }$ ion is 6.

Additional Information: The significance of the limiting radius ratio is as follows:
The limiting radius ratio helps in predicting the structures of the ionic solids.
The structure of an ionic compound mainly depends on the size of its constituent ions and the stoichiometry.
In the crystal lattice, the cations are surrounded by the largest number of possible anions.
As the limiting radius ratio increases, the coordination number increases.
If the size of cations is very small and that of anions is larger, the limiting radius ratio is very small then the packing of anions is very close. But as the anions have the same charge they repel and the structure becomes unstable.


Note:
As the radius ratio increases the size of the cation also increases. As a result the coordination number of the cation increases.