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

Question

The stability constants of the complexes formed by a metal ions \(\left(\mathrm{M}^{2^{+}}\right)\)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: Identifying Stability Constants

The stability constant of a complex is a measure of its stability; larger values indicate a more stable complex. In this problem, the stability constants are given for complexes of a metal ion with different ligands: \(\mathrm{NH}_3\) is \(10^{11}\), \(\mathrm{CN}^-\) is \(10^{27}\), \(\mathrm{H}_2\mathrm{O}\) is \(10^{15}\), and 'en' is \(10^8\).

Step 2: Comparing Stability Constants

To determine which ligand forms the most stable complex, compare their stability constants. The larger the constant, the stronger the ligand is considered. Among the given constants, \(10^{27}\) for \(\mathrm{CN}^-\) is the largest.

Step 3: Understanding Ligand Strength

Based on the stability constants, the ligand \(\mathrm{CN}^-\) has the highest constant at \(10^{27}\), indicating it forms the strongest and most stable complex with the metal ion \(\mathrm{M}^{2+}\). Thus, \(\mathrm{CN}^-\) is the strongest ligand among the options given.

Key Concepts

Understanding Ligand Strength

Ligands are molecules or ions that bind to a central metal ion to form a complex. The strength of a ligand is evaluated based on its ability to form stable complexes with metal ions. The stability of a complex is measured by its stability constant. A higher stability constant means the complex is more stable, and hence, the ligand is stronger.

Some key points:

• Ligand strength is directly related to the magnitude of the stability constant.
• Various factors such as ligand charge, size, and electron-donating ability influence the strength.

In our example, \(\mathrm{CN}^{-}\) has the highest stability constant of \(10^{27}\), making it the strongest ligand. This means it forms the most stable complex with \(\mathrm{M}^{2+}\) among the ligands given.

Nature of Complex Formation

Complexes are formed when ligands donate electrons to metal ions to create a coordinated structure. This process is a fundamental aspect of coordination chemistry.

During complex formation:

• Metal ions act as Lewis acids as they accept electron pairs.
• Ligands, being electron donors, act as Lewis bases.
• This interaction leads to the formation of a complex, characterized by its geometry and stability.

In the example provided, the strength of the formed complex depends significantly on the nature of the ligand, which is elucidated through its stability constant. \(\mathrm{CN}^{-}\) forms the most stable complex with the metal ion in question, indicating a strong bond formation.

Role of Metal Ions in Complexes

Metal ions play a pivotal role in the chemistry of complexes. Often, these metal ions are transition metals that have vacant d-orbitals, allowing them to accept electron pairs from ligands.

Key aspects of metal ions in complexes include:

• The oxidation state of the metal influences the number of ligands it can coordinate with.
• The electronic configuration of the metal ion affects the complex's overall geometry and magnetic properties.

In coordination chemistry, \(\mathrm{M}^{2+}\), a generic representation in exercises like these, serves as the central ion to which ligands like \(\mathrm{CN}^{-}, \, \mathrm{NH}_3\), and others bind, affecting the stability and structure of the resulting complex.

Basics of Coordination Chemistry

Coordination chemistry is the study of complexes formed between ligands and metal ions. It encompasses the synthesis, properties, and behaviors of these complexes.

Some fundamental concepts include:

• Coordination number: the number of ligand atoms directly bonded to the central metal ion.
• Ligand field strength: proxies like stability constants help predict how ligands separate d-orbitals in metals.
• Isomerism: complexes can show various isomers due to different spatial arrangements of ligands.

Understanding coordination chemistry allows us to predict and rationalize the behavior of metal complexes, such as explaining why \(\mathrm{CN}^{-}\) is a particularly strong ligand in forming stable complexes with metals like \(\mathrm{M}^{2+}\). This field forms the backbone of numerous applications in industrial and biological chemistry.