Question

The radius of $A{g^ + }$ is $126pm$ while that of $C{l^ - }$ ion is $216pm$ . The coordination number of $A{g^ + }$ in $AgCl$ is:
(A) $2$
(B) $8$
(C) $6$
(D) $4$

Answer 1

The ratio of the ionic radius of a cation and that of an anion is called the cation-anion radius ratio. This ratio helps in determining the type of lattice and the coordination of the metallic ion in its crystal lattice.

Complete Step By Step Answer:
The ionic salts that are formed as a result of strong electrostatic forces of attraction exist in rigid crystal lattices in which the positive and negative ions occupy specific positions to form specific shapes.
The negatively charged ions are called anions and they have comparatively large ionic radii. The positively charged ions are called cations and they have smaller ionic radii. Due to the larger sizes, the anions tend to occupy specific lattice sites and the cations fit inside the voids formed by the anions.
Thus the relative sizes of both the ions influence the type of lattice and therefore determine the coordination number of the ions involved in the formation of the lattice. The cation-anion radius ratio can be used to identify the range in which the ions lie and then it can be used to determine the coordination number.
The radius ratio for $AgCl$ can be calculated as follows:
$\dfrac{{{r_ + }}}{{{r_ - }}} = \dfrac{{radius(A{g^ + })}}{{radius(C{l^ - })}} = \dfrac{{126}}{{216}} = 0.5834$
$\Rightarrow$ This radius ratio lies in the range $0.414 - 0.732$ which indicates that $AgCl$ has a coordination number of $6$ .
Therefore option (C) is correct.

Note:
The cations are always smaller than their parent atoms and the anions are always larger than their parent atoms due to which the difference in size of a cation and anion exists. The variation in this size difference is mainly responsible for the different radius ratio ranges observed for different coordination numbers.