Range the following electrolytes in the increasing order of coagulating power for the coagulation of `As_2S_3` sol
(I) `Na_2SO_4`
(II) `MgCl_2`
(III) `AlCl_3`

Options

A. III gt I gtII
B. IgtIIgtIII
C. IIIgtIIgtI
D. IgtIIIgtII

Answer

To determine the increasing order of coagulating power for the coagulation of `As_2S_3` sol, we need to consider the charge of the cations present in the given electrolytes. The coagulating power of an electrolyte is directly proportional to the charge on the cation.

### Step-by-step Solution:

1. **Identify the Electrolytes and Their Cations**:
- (I) `Na_2SO_4` → Cation: `Na^+` (Charge: +1)
- (II) `MgCl_2` → Cation: `Mg^{2+}` (Charge: +2)
- (III) `AlCl_3` → Cation: `Al^{3+}` (Charge: +3)

2. **Understand the Relationship**:
- The coagulating power is directly proportional to the charge on the cation. This means that the higher the charge, the greater the coagulating power.

3. **Rank the Cations by Charge**:
- `Al^{3+}` has the highest charge (+3), so it has the highest coagulating power.
- `Mg^{2+}` has a charge of +2, so it has a moderate coagulating power.
- `Na^+` has the lowest charge (+1), so it has the lowest coagulating power.

4. **Establish the Order**:
- Based on the charges, we can rank the electrolytes in increasing order of coagulating power:
- `Na_2SO_4` (lowest) < `MgCl_2` (moderate) < `AlCl_3` (highest)

### Final Answer:
The increasing order of coagulating power for the coagulation of `As_2S_3` sol is:
`Na_2SO_4` < `MgCl_2` < `AlCl_3`