Which of the following complexes formed by `Cu^(2+)` ions is most stable ?

Options

A. `Cu^(2+) + 4NH_(3) hArr [Cu(NH_(3))_(4)]^(2+) , log K = 11.6`
B. `Cu^(2+) + 4 CN^(-) hArr [Cu(CN)_(4)]^(2-) , log K = 27.3`
C. `Cu^(2+) + 2 en hArr [Cu(en)_(2) ]^(2+) , log K = 15.4 `
D. `Cu^(2+) + 4H_(2)O hArr [Cu(H_(2)O)_(4)]^(2+) , log K = 8.9`

Explanation

To determine which complex formed by \( \text{Cu}^{2+} \) ions is the most stable, we need to analyze the stability constants of the complexes provided in the options. The stability of a coordination complex is often quantified by its stability constant, denoted as \( K \). A higher value of \( K \) indicates a more stable complex.

### Step-by-Step Solution:

1. **Understand Stability Constants**: The stability constant \( K \) is a measure of the stability of a complex in solution. The larger the value of \( K \), the more stable the complex is. This can also be expressed in logarithmic form as \( \log K \).

2. **Evaluate Given Options**: We need to look at the complexes formed by \( \text{Cu}^{2+} \) ions and their corresponding stability constants or \( \log K \) values.

3. **Identify the Highest \( \log K \)**: Among the options provided, we need to identify which complex has the highest \( \log K \) value. The complex with the highest \( \log K \) will be the most stable.

4. **Conclusion**: After evaluating the options, we find that the complex with \( \text{Cu}^{2+} + 4 \text{CN}^- \) forms the tetra cyano copper(II) complex, which has the highest \( \log K \) value of 27.3. Therefore, this complex is the most stable.

5. **Final Answer**: The most stable complex formed by \( \text{Cu}^{2+} \) ions is the tetra cyano copper(II) complex.