Question

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

Short answer

The strongest ligand is cyanide (CN).

Step-by-step solution

Analyze the Stability Constants

Examine the given stability constants for each reaction:- (a) with water: \( K = 9.5 \times 10^8 \)- (b) with ethylenediamine (en): \( K = 3.0 \times 10^{15} \)- (c) with cyanide (CN): \( K = 2.0 \times 10^{27} \)- (d) with ammonia (NH3): \( K = 4.5 \times 10^{11} \) The stability constant \( K \) indicates the tendency of a complex to form; a larger \( K \) means a more stable complex.

Compare the Stability Constants

Arrange the stability constants in descending order to find the strongest ligand:- \( K = 2.0 \times 10^{27} \) for \([\mathrm{Cu}( ext{CN})_4]^{2-}\)- \( K = 3.0 \times 10^{15} \) for \([\mathrm{Cu}( ext{en})_2]^{2+}\)- \( K = 4.5 \times 10^{11} \) for \([\mathrm{Cu}( ext{NH}_3)_4]^{2+}\)- \( K = 9.5 \times 10^8 \) for \([\mathrm{Cu}( ext{H}_2 ext{O})_4]^{2+}\)The compound with the highest \( K \) value is considered to form the most stable complex and is thus the strongest ligand.

Identify the Strongest Ligand

From the ordered list, \( \text{CN}^- \) (cyanide) has the highest stability constant, \( K = 2.0 \times 10^{27} \). Therefore, \( \text{CN}^- \) is the strongest ligand among the given options.

Key concepts

Understanding Stability Constants

Stability constants are an essential concept in coordination chemistry. They measure the tendency of a metal ion to form a stable complex with a ligand. The stability constant, represented by the symbol \( K \), is derived from the equilibrium constant of a complex formation reaction. It indicates the strength and stability of the resulting complex.
For example, if the reaction of a metal ion \( ext{Cu}^{2+} \) with a ligand \( ext{CN}^- \) forms a complex \([ ext{Cu}( ext{CN})_4]^{2-}\), then the stability constant for this reaction would be given by the expression:
\[ K = \frac{[ ext{Cu}( ext{CN})_4]^{2-}}{[ ext{Cu}^{2+}][ ext{CN}^-]^4} \]
In general, the higher the value of \( K \), the more stable the complex is, meaning the metal ion has a stronger affinity for the ligand. Thus, large stability constants suggest the formation of strong and stable complexes, a crucial indicator when predicting which ligand forms the most robust complexes.

The Essentials of Coordination Chemistry

Coordination chemistry is a fascinating field that explores how metal ions interact with ligands to form complexes. A coordination complex consists of a central metal atom or ion that is bonded to surrounding molecules or ions, known as ligands. These ligands donate electrons to the metal ion to form "coordinate bonds", strengthening the structure.
In the example of copper(II) ions bonding with various ligands, each ligand influences the electron distribution and geometry of the resulting complex.

• Water (H₂O), ammonia (NH₃), and ethylenediamine (en) are common ligands that form coordinate bonds with metal ions.
• Each ligand has a different number of donor atoms that play a role in coordination. For instance, en is a bidentate ligand, meaning it has two atoms that can donate electrons, providing additional stability compared to monodentate ligands like CN^-.

Understanding the basic principles of how ligands coordinate and bond with metal ions helps in predicting the overall stability of these complexes and their potential applications.

The Process of Complex Formation

Complex formation is a dynamic process that occurs when ligands and metal ions interact to form coordination complexes. During this process, electron pairs from the ligands are donated to empty orbitals on the metal ion, forming coordinate covalent bonds.

• The nature of the complex depends on factors like the type of ligand, metal ion, and the environmental conditions (e.g., pH, temperature).
• Bidentate and polydentate ligands often create more stable complexes due to the chelate effect, where the ligand binds more tightly by forming multiple bonds.

The strength and number of these coordinate covalent bonds influence the overall stability of the complex. For instance, in the reaction with cyanide, the extremely high stability constant \( K = 2.0 \times 10^{27} \) indicates that the formed complex is highly stable, largely due to cyanide's strong donating capacity and the establishment of a stable electronic structure within the complex.

Comparing Ligand Strength

Ligand comparison is essential to interpret and predict the behavior of different complexing agents in coordination chemistry. Ligands vary in their ability to form stable complexes with metal ions, primarily influenced by their electronic, steric, and chemical properties.

• Cyanide ion \( ext{CN}^- \) is considered a strong ligand due to its high donor ability and tendency to form highly stable complexes, as reflected in its high stability constant.
• Ethylenediamine, being a bidentate ligand, often forms relatively stable complexes, surpassing monodentate ligands like ammonia in stability due to its dual donation sites.
• Ammonia and water are generally weaker ligands because of their moderate electron-donating properties. This is reflected in their lower stability constants when forming complexes with \( ext{Cu}^{2+} \).

When comparing ligand strength using stability constants, one can predict how effectively different ligands will stabilize a metal ion in a complex. This information is crucial when selecting ligands for various chemical processes and applications.