Which of the following electrolytes will have maximum coagulating value for `Ag//Ag^(+)` sol?

Options

A. `Na_(2)S`
B. `Na_(3)PO_(4)`
C. `Na_(2)SO_(4)`
D. NaCl

Explanation

To determine which electrolyte will have the maximum coagulating value for the `Ag//Ag^(+)` sol, we need to understand the concept of coagulation and the role of electrolytes.

### Step-by-Step Solution:

1. **Understanding Coagulation**: Coagulation is the process by which colloidal particles aggregate to form a precipitate. In the case of a positively charged sol like `Ag//Ag^(+)`, we need to add an electrolyte that can neutralize the positive charge.

2. **Identifying the Electrolytes**: The given electrolytes are:
- Na2S (Sodium sulfide)
- Na3PO4 (Sodium phosphate)
- Na2SO4 (Sodium sulfate)
- NaCl (Sodium chloride)

3. **Analyzing the Electrolytes**:
- **Na2S**: This dissociates into 2 Na⁺ ions and 1 S²⁻ ion. The S²⁻ ion can neutralize two positive charges.
- **Na3PO4**: This dissociates into 3 Na⁺ ions and 1 PO4³⁻ ion. The PO4³⁻ ion can neutralize three positive charges.
- **Na2SO4**: This dissociates into 2 Na⁺ ions and 1 SO4²⁻ ion. The SO4²⁻ ion can neutralize two positive charges.
- **NaCl**: This dissociates into Na⁺ and Cl⁻ ions. The Cl⁻ ion can neutralize one positive charge.

4. **Comparing Coagulating Values**: The coagulating value is inversely proportional to the number of charges that the ions can neutralize. The more charges an ion can neutralize, the lower the coagulating value. Therefore, we need to find the electrolyte that can neutralize the most positive charges:
- Na2S: Neutralizes 2 positive charges.
- Na3PO4: Neutralizes 3 positive charges.
- Na2SO4: Neutralizes 2 positive charges.
- NaCl: Neutralizes 1 positive charge.

5. **Conclusion**: Since Na3PO4 can neutralize the maximum number of positive charges (3), it has the maximum coagulating value for the `Ag//Ag^(+)` sol.

### Final Answer:
**Na3PO4 (Sodium phosphate) will have the maximum coagulating value for `Ag//Ag^(+)` sol.**