`Mg^(2+)` can be detected and esitimated in hard water by titrating with `EDTA` at `pH=10` using `NH_(4)OH+NH_(4)Cl` buffer. End point is given by the apearance of blue colour. The indicator used is

Options

A. Solochrome black
B. Eriochrome black `T`
C. Eosin
D. Bromophenol

Explanation

To solve the question regarding the detection and estimation of `Mg^(2+)` in hard water using `EDTA` titration, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Process**:
- The titration of magnesium ions in hard water is performed using EDTA (Ethylene Diamine Tetraacetic Acid) at a pH of 10. This pH is maintained using an `NH4OH` and `NH4Cl` buffer.

2. **Role of EDTA**:
- EDTA acts as a chelating agent that forms stable complexes with metal ions such as magnesium (`Mg^(2+)`) and calcium (`Ca^(2+)`). At pH 10, the EDTA will effectively bind to these ions.

3. **Indicator Used**:
- The indicator used in this titration is **Eriochrome Black T**. This indicator changes color based on the presence of free metal ions in the solution.

4. **Color Change Mechanism**:
- In the presence of magnesium or calcium ions, the Eriochrome Black T indicator forms a complex that appears pink. When EDTA is added, it binds to the magnesium ions, freeing the indicator. This results in a color change from pink to blue.

5. **Endpoint of the Titration**:
- The endpoint of the titration is indicated by the appearance of a blue color in the solution, which signifies that all the magnesium ions have reacted with EDTA.

6. **Conclusion**:
- Therefore, the indicator used in this titration method is **Eriochrome Black T**.

### Final Answer:
The indicator used is **Eriochrome Black T**.