Which mixture of the solutions will lead to the formation of negatively charged colloidal `[Agl]^(-)` sol. ?

Options

A. 50 mL of 0.1 M `AgNO_3` + 50 mL of 0.1 M Kl
B. 50 mL of 0.1 M `AgNO_3` + 50 mL of 0.2 M Kl
C. 50 mL of 0.2 M `AgNO_3` + 50 mL of 0.1 M Kl
D. 50 mL of 0.2 M `AgNO_3` + 50 mL of 0.2 M Kl

Answer

To determine which mixture of solutions will lead to the formation of a negatively charged colloidal AgI^- sol, we need to consider the reaction between silver nitrate (AgNO3) and potassium iodide (KI). The formation of a negatively charged colloidal solution requires an excess of iodide ions (I^-).

### Step-by-Step Solution:

1. **Understand the Reaction**:
The reaction between silver nitrate and potassium iodide can be represented as:
\[ \text{AgNO}_3 + \text{KI} \rightarrow \text{AgI} + \text{KNO}_3 \]
This reaction produces silver iodide (AgI) as a precipitate.

2. **Identify the Requirement for Negatively Charged Colloidal Solution**:
To form a negatively charged colloidal AgI^- sol, we need an excess of iodide ions (I^-). The presence of extra I^- ions will help surround the AgI particles, giving them a negative charge.

3. **Evaluate the Options**:
- **Option 1**: 50 ml of 0.1 M AgNO3 and 50 ml of 0.1 M KI
- Here, the concentrations of AgNO3 and KI are equal. Thus, there will not be an excess of I^- ions. This option cannot lead to the formation of a negatively charged sol.

- **Option 2**: 50 ml of 0.1 M AgNO3 and 50 ml of 0.2 M KI
- In this case, the concentration of KI is higher than that of AgNO3. This means there will be an excess of I^- ions, which can lead to the formation of a negatively charged colloidal AgI^- sol. This option is a potential candidate.

- **Option 3**: 50 ml of 0.2 M AgNO3 and 50 ml of 0.1 M KI
- Here, the concentration of AgNO3 is higher than that of KI, which means there will not be enough I^- ions to surround the AgI. This option cannot lead to the formation of a negatively charged sol.

- **Option 4**: 50 ml of 0.2 M AgNO3 and 50 ml of 0.2 M KI
- Similar to Option 1, the concentrations are equal, so there will not be an excess of I^- ions. This option cannot lead to the formation of a negatively charged sol.

4. **Conclusion**:
Based on the analysis, the only option that provides an excess of I^- ions, which is necessary for the formation of a negatively charged colloidal AgI^- sol, is **Option 2**.

### Final Answer:
The correct mixture of solutions that will lead to the formation of a negatively charged colloidal AgI^- sol is **Option 2: 50 ml of 0.1 M AgNO3 and 50 ml of 0.2 M KI**.