Problem 84 - A Complete Resource Book in Chemistry for JEE Main

Question

Predict which is the strongest ligand from the stability constant (hypothetical values) given below? (a) \(\mathrm{Cu}^{2+}+4 \mathrm{H}_{2} \mathrm{O} \rightleftharpoons\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{2^{+}}, \mathrm{K}=9.5 \times 10^{8}\) (b) \(\mathrm{Cu}^{2}+2 \mathrm{en} \rightleftharpoons\left[\mathrm{Cu}(\mathrm{en})_{2}\right]^{+}, \quad \mathrm{K}=3.0 \times 10^{15}\) (c) \(\mathrm{Cu}^{2+}+4 \mathrm{CN} \rightleftharpoons\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{2}, \quad \mathrm{~K}=2.0 \times 10^{27}\) (d) \(\mathrm{Cu}^{2^{+}}+4 \mathrm{NH}_{3} \rightleftharpoons\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2^{+}}, \mathrm{K}=4.5 \times 10^{11}\)

Step-by-Step Solution

Answer

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

Step 1: Understand Stability Constants

Stability constants (K) indicate the strength of a complex formed between a metal ion and ligands. A larger K value suggests a stronger ligand because it indicates a more stable complex formation.

Step 2: Compare Stability Constants

List the stability constants for each ligand: (a) Water: \(9.5 \times 10^{8}\), (b) En: \(3.0 \times 10^{15}\), (c) CN: \(2.0 \times 10^{27}\), (d) NH3: \(4.5 \times 10^{11}\). The largest constant indicates the strongest ligand.

Step 3: Identify the Strongest Ligand

Compare the values and note that the stability constant for \(\mathrm{CN}^{-}\) is \(2.0 \times 10^{27}\), which is the largest among all the given values.

Step 4: Conclusion

Based on the comparison, \(\mathrm{CN}^{-}\) is the strongest ligand due to having the highest stability constant.

Key Concepts

Stability Constant

The stability constant, often referred to as the formation constant, is a key concept in understanding metal-ligand interactions. It is a quantitative measure of how strongly a ligand binds to a metal ion in solution. Mathematically, it is represented by the equilibrium constant, denoted as \( K \), of the complex-forming reaction. A higher \( K \) value signifies a more stable complex, meaning the metal-ligand bond is stronger.

Here’s what you need to consider about stability constants:

• Higher values of \( K \) indicate stronger ligands as they form more stable complexes.
• The logarithmic measure of \( K \) can be used for more manageable calculations, often denoted as \( \log K \).
• Stability constants are vital for predicting the chemical behavior of metal ions in various environments.

In practice, stability constants help chemists understand which ligands are more effective at sequestering metal ions, thereby influencing reactions and the formulation of substances.

Complex Formation

Complex formation is a process whereby metal ions combine with ligands to form a complex. These complexes are formed through coordinate covalent bonds, where both electrons in the bond originate from the ligand. This union results in a new chemical species that often has properties distinct from its components.

In the context of the exercise, each complex formed was:

• \( \mathrm{Cu}^{2+} \) with water forming \([\mathrm{Cu}(\mathrm{H}_{2}\mathrm{O})]^{2+}\).
• \( \mathrm{Cu}^{2+} \) with ethylenediamine \((\mathrm{en})\) forming \([\mathrm{Cu}(\mathrm{en})_{2}]^{+}\).
• \( \mathrm{Cu}^{2+} \) with cyanide \((\mathrm{CN})\) forming \([\mathrm{Cu}(\mathrm{CN})_{4}]^{2-}\).
• \( \mathrm{Cu}^{2+} \) with ammonia forming \([\mathrm{Cu}(\mathrm{NH}_{3})_{4}]^{2+}\).

Complex formation is critical in various fields, including biochemistry and industrial processes, as it affects the solubility, reactivity, and the overall chemical stability of substances.

Metal-Ligand Interaction

Metal-ligand interactions are foundational in the formation of complexes. The strength and characteristics of these interactions are influenced by various factors such as the nature of the metal ion, the type of ligand, and the environment in which they react.

Key points about metal-ligand interactions include:

• Metal ions have vacant orbitals that can accept electron pairs donated by ligands, which usually possess lone pairs.
• The geometry of the complex, determined by the number of ligands attached, can influence the metal ion's properties and reactivity.
• Ligands can be classified based on their binding properties, such as monodentate (one donor atom) and polydentate (multiple donor atoms).
• Different ligands influence the color, magnetism, and bioavailability of the metal complexes.

Understanding these interactions aids in tailoring complexes for specific roles, from catalysts in industrial reactions to agents for metal detoxification in medicine.