Which complex in the following has the highest stability constant at 298 K ?

Options

A. `[CdCl_4]^(2-)`
B. `[CdBr_4]^(2-)`
C. `[CdI_4]^(2-)`
D. `[Cd(CN)_4]^(2-)`

Answer

To determine which complex has the highest stability constant at 298 K, we need to analyze the factors that affect the stability of metal complexes. The stability constant (K) is influenced by three main factors:

1. **Nature of the Central Atom**: The oxidation state of the central atom plays a significant role. A higher oxidation state generally leads to a more positive charge density, which increases the stability of the complex.

2. **Nature of the Ligand**: Ligands can be classified as strong field or weak field ligands. Strong field ligands lead to greater crystal field stabilization energy (CFSE), which enhances the stability of the complex. In contrast, weak field ligands provide less stabilization.

3. **Chelation**: Chelating ligands can form rings with the central atom, which significantly increases stability due to the chelate effect. However, in this case, we are considering monodentate ligands, so we will not focus on chelation.

### Step-by-Step Solution:

1. **Identify the Central Atom and Its Oxidation State**:
- For each complex, identify the central atom and determine its oxidation state. In this case, all complexes involve cadmium (Cd) in the +2 oxidation state.

2. **Evaluate the Ligands**:
- Assess the nature of the ligands attached to the central atom in each complex. The ligands can be halides (Cl⁻, Br⁻, I⁻) or cyanide (CN⁻).
- Halides are weak field ligands, while cyanide (CN⁻) is a strong field ligand.

3. **Compare Stability Based on Ligand Strength**:
- Since all complexes have cadmium in the same oxidation state (+2), the stability will depend primarily on the ligands.
- The complex with cyanide (CN⁻) will have a higher stability constant due to the strong field nature of the ligand, leading to greater CFSE.

4. **Conclusion**:
- Among the given options, the complex with cyanide (CN⁻) will exhibit the highest stability constant due to the strong field effect of the ligand. Therefore, the correct answer is the complex with CN⁻ as the ligand.

### Final Answer:
The complex with the highest stability constant at 298 K is the one containing cyanide (CN⁻) as the ligand.