Problem 89 - A Complete Resource Book in Chemistry for JEE Main

Question

The stability constants of the complexes formed by a metal ions \(\left(\mathrm{M}^{+}\right)\)with \(\mathrm{NH}_{3}, \mathrm{CN}^{-}, \mathrm{H}_{2} \mathrm{O}\) and 'en' are of the order of \(10^{11}, 10^{27}, 10^{15}\) and \(10^{8}\) respectively. Then (en = ethylene diamine) (a) en is the strongest ligand (b) these values cannot predict the strength of the ligand (c) \(\mathrm{CN}^{-}\)is the strongest ligand (d) all ligands are equally strong

Step-by-Step Solution

Answer

(c) \( \mathrm{CN}^{-} \) is the strongest ligand.

Step 1: Understanding stability constants

Stability constants, represented as \( K_f \), measure the strength of the interaction between a metal ion and a ligand. A higher stability constant indicates a stronger ligand that forms a more stable complex with the metal ion.

Step 2: Identifying the given stability constants

The stability constants for the complexes are: \( [M(NH_3)] = 10^{11} \), \( [M(CN)^{-}] = 10^{27} \), \( [M(H_2O)] = 10^{15} \), and \( [M(en)] = 10^{8} \).

Step 3: Comparing stability constants

Compare the given stability constants directly by considering their exponents. The largest \( K_f \) represents the strongest ligand as it forms the most stable complex. Here, \( 10^{27} > 10^{15} > 10^{11} > 10^{8} \), indicating that \( ext{CN}^- \) provides the strongest interaction with the metal ion.

Step 4: Making a conclusion

Since \( ext{CN}^- \) has the highest stability constant of \( 10^{27} \), it is the strongest ligand among those listed.

Key Concepts

Stability Constants

Stability constants, denoted as \( K_f \), are pivotal in understanding how strongly a ligand binds to a metal ion, forming what is known as a metal-ligand complex. The higher the value of \( K_f \), the more stable the complex. This means the ligand forms a stronger bond with the metal ion, making the complex less likely to fall apart.
For instance, in the given problem, the stability constants are used to compare how well different ligands, such as \( \mathrm{NH}_3 \), \( \mathrm{CN}^- \), \( \mathrm{H}_2\mathrm{O} \), and 'en' (ethylene diamine), bind to a metal ion \( \mathrm{M}^+ \). With these values being in the order of \( 10^{11} \), \( 10^{27} \), \( 10^{15} \), and \( 10^{8} \) respectively, it is clear that \( \mathrm{CN}^- \) forms the most stable complex, indicative of the strongest interaction with the metal ion.

Ligand Strength

The concept of ligand strength is closely tied to the stability constants. A ligand's strength is determined by its ability to form a stable complex with a metal ion. A stronger ligand will form a complex with a higher stability constant because it binds more tightly to the metal ion.
In the exercise, we see that \( \mathrm{CN}^- \) is the strongest of the discussed ligands, given its high stability constant of \( 10^{27} \). Conversely, 'en', represented by the value \( 10^{8} \), is comparatively weaker. This demonstrates that ligand strength is quantified by how effectively a ligand can stabilize a metal-ligand complex.

Metal-ligand Complexes

A metal-ligand complex is a coordination compound featuring a central metal ion bonded to surrounding ligands. Ligands are molecules or ions capable of donating an electron pair to the metal, forming a coordinate covalent bond. These complexes are fundamental in many chemical processes, ranging from biological systems to industrial catalysis.
The stability of these complexes is influenced by the electronic effects of ligands, their sterics, and their ability to donate electron pairs. For example, in the given problem, the metal-ligand complexes involve different ligands and their respective stability constants show how some ligands like \( \mathrm{CN}^- \) can form much stronger and more stable complexes compared to others, thus reflecting a deeper understanding of their chemical behavior.

Coordination Chemistry

Coordination chemistry is the study of the structures and properties of coordination compounds, which include metal-ligand complexes. It provides a framework for understanding how metals interact with ligands in various chemical environments.
This branch of chemistry covers principles such as electron configuration, oxidation states, and coordination numbers. Coordination numbers tell us how many ligands are attached to the central metal. For example, complexes with a high stability constant, like the \( \mathrm{CN}^- \) metal complex in the exercise, illustrate how coordination chemistry principles explain the assembly and stability of metal-ligand arrangements.