Arrange the following electrolytes in the increasing order of coagulation power for the coagulation of `As_(2)S_(3)` sol :
`K_(2)SO_(4) " " CaCl_(2)" " Na_(3)PO_(4) " " AlCl_(3)`

Options

A. `Ilt II lt IIIlt IV`
B. `I=III lt II lt IV`
C. `II lt IV lt I lt II`
D. ` II lt III lt IV lt I`

Answer

To arrange the given electrolytes in the increasing order of coagulation power for the coagulation of `As_(2)S_(3)` sol, we will follow these steps:

### Step 1: Identify the charge of the colloidal sol
The colloidal sol in question is arsenic sulfide (`As_(2)S_(3)`), which is negatively charged. This means we need to consider positively charged ions from the electrolytes for coagulation.

### Step 2: List the electrolytes and their dissociation
The given electrolytes are:
1. `K_(2)SO_(4)` → dissociates into `2 K^+` and `SO₄^(2-)`
2. `CaCl_(2)` → dissociates into `Ca^(2+)` and `2 Cl^-`
3. `Na_(3)PO_(4)` → dissociates into `3 Na^+` and `PO₄^(3-)`
4. `AlCl_(3)` → dissociates into `Al^(3+)` and `3 Cl^-`

### Step 3: Determine the valency of the positive ions
Now, we will identify the valency of the positive ions from each electrolyte:
- `K^+` has a valency of 1.
- `Ca^(2+)` has a valency of 2.
- `Na^+` has a valency of 1.
- `Al^(3+)` has a valency of 3.

### Step 4: Apply Hardy-Souls rule
According to Hardy-Souls rule, the coagulating power of an electrolyte increases with the valency of the oppositely charged ion. Therefore, we can rank the electrolytes based on the valency of their positive ions:
- `K_(2)SO_(4)` (valency 1)
- `Na_(3)PO_(4)` (valency 1)
- `CaCl_(2)` (valency 2)
- `AlCl_(3)` (valency 3)

### Step 5: Arrange in increasing order of coagulation power
Based on the valency of the positive ions, we can arrange the electrolytes in increasing order of coagulation power:
1. `K_(2)SO_(4)` (valency 1)
2. `Na_(3)PO_(4)` (valency 1)
3. `CaCl_(2)` (valency 2)
4. `AlCl_(3)` (valency 3)

Thus, the increasing order of coagulation power for the coagulation of `As_(2)S_(3)` sol is:
`K_(2)SO_(4) < Na_(3)PO_(4) < CaCl_(2) < AlCl_(3)`