The coagulating power of electrolytes having inos `Na^(o+),Al^(3+)` and `Ba^(2+)` for arsenic sulphide sol increases in the order
(a)`Na^(o+)ltBa^(2+)ltAl^(3+)`
(b)`Ba^(2+)ltNa^(o+)ltAl^(3+)`
(c)`Al^(3+)ltNa^(o+)ltBa^(2+)`
(d)`Al^(3+)ltBa^(2+)ltNa^(o+)`

Options

A. `Na^(o+)ltBa^(2+)ltAl^(3+)`
B. `Ba^(2+)ltNa^(o+)ltAl^(3+)`
C. `Al^(3+)ltNa^(o+)ltBa^(2+)`
D. `Al^(3+)ltBa^(2+)ltNa^(o+)`

Explanation

To determine the coagulating power of electrolytes with ions \( \text{Na}^+, \text{Al}^{3+}, \text{Ba}^{2+} \) for arsenic sulfide sol, we will apply the Hardy-Schulze rule. This rule states that the coagulating power of an electrolyte is directly related to the charge of the ions present.

### Step-by-Step Solution:

1. **Identify the Nature of the Colloid:**
- Arsenic sulfide (\( \text{As}_2\text{S}_3 \)) forms a negatively charged sol. This means it will attract positively charged ions (cations) from the electrolytes.

2. **List the Cations and Their Charges:**
- Sodium ion (\( \text{Na}^+ \)) has a charge of +1.
- Barium ion (\( \text{Ba}^{2+} \)) has a charge of +2.
- Aluminum ion (\( \text{Al}^{3+} \)) has a charge of +3.

3. **Apply the Hardy-Schulze Rule:**
- According to the Hardy-Schulze rule, the coagulating power increases with the increase in the charge of the cation. Therefore, we can rank the cations based on their charges:
- \( \text{Al}^{3+} \) (highest charge, highest coagulating power)
- \( \text{Ba}^{2+} \) (medium charge)
- \( \text{Na}^+ \) (lowest charge)

4. **Establish the Order of Coagulating Power:**
- From the charges, we can conclude that the coagulating power increases in the order:
- \( \text{Na}^+ < \text{Ba}^{2+} < \text{Al}^{3+} \)

5. **Select the Correct Option:**
- The order \( \text{Na}^+ < \text{Ba}^{2+} < \text{Al}^{3+} \) corresponds to option (a) \( \text{Na}^+ < \text{Ba}^{2+} < \text{Al}^{3+} \).

### Final Answer:
The coagulating power of electrolytes for arsenic sulfide sol increases in the order:
**(a) \( \text{Na}^+ < \text{Ba}^{2+} < \text{Al}^{3+} \)**