Question

The stability constant of the complexes formed by a metal ion (${{M}^{3+}}$) with $N{{H}_{3}}$, $C{{N}^{-}}$, ${{H}_{2}}O$ and $en$ are of the order ${{10}^{11}}$, ${{10}^{27}}$, ${{10}^{15}}$ and ${{10}^{8}}$ respectively. Then:

(A)- $en$ is the strongest ligand
(B)- $C{{N}^{-}}$ is the strongest ligand
(C)- these values cannot predict the strength of the ligand
(D)- all ligands are equally strong

Answer 1

Hint: The stability constant of a complex defines the extent or degree of association of a metal ion with ligands in the state of equilibrium. The stability of a complex depends on the strength of the bond between metal and ligand. The stability constant for the formation of a complex of the type $M{{L}_{n}}$ is given as
     \[M+nL\rightleftarrows M{{L}_{n}}\]
Stability constant, \[{{\beta }_{n}}=\dfrac{\left[ M{{L}_{n}} \right]}{\left[ M \right]{{\left[ L \right]}^{4}}}\].

Complete step by step answer:
Let us try to find the strength of the ligands based on the stability constants of the complexes of ${{M}^{3+}}$ with $N{{H}_{3}}$, $C{{N}^{-}}$, ${{H}_{2}}O$ and $en$.
The stability constant of a complex is the measure of the stability of the complex in the solution.
Stability of the complex is directly proportional to the strength of the metal-ligand bond.
It means that greater the magnitude of the stability constant, greater is the strength of the metal-ligand bond.

Thus, the ligand is not easily replaced by some other ligand. Hence, the ligand is a strong ligand.
Therefore, we can also say that the stability constant of a complex defines the resistance of a ligand to be displaced by other ligands.
The magnitude of the stability constants of the complexes of ${{M}^{3+}}$ with $N{{H}_{3}}$, $C{{N}^{-}}$, ${{H}_{2}}O$ and $en$ are tabulated below:

Complex of ${{M}^{3+}}$ with the ligands	Stability constant
$N{{H}_{3}}$	${{10}^{11}}$
$C{{N}^{-}}$	${{10}^{27}}$
${{H}_{2}}O$	${{10}^{15}}$
$en$	${{10}^{8}}$

From the above discussion, it is clear that the value of the stability constant for the complex of ${{M}^{3+}}$ with $C{{N}^{-}}$ is of the highest order. Therefore, $C{{N}^{-}}$ is the strongest ligand.
So, the correct answer is “Option C”.

Note: We can predict the strength of the ligand from the stability constant, it is directly proportional to the stability constant. Keep in mind while answering the question that greater is the value of the stability constant, stronger is the metal ligand bond, lesser dissociation into the solution, and hence, more stable is the complex.