what is the correct sequence of the decreasing coagultion value of the following electrolyte for the coagultion of ferric hydroxide sol ?
`(I) Na_(3) PO_(4) (II)KCl (III) K_(2)SO_(4) (IV)K_(4)[Fe(CN)_(6)]`

Options

A. `IVgtIgt IIIgt II`
B. `IIgtIIIgt Igt IV`
C. ` I gt II gt III gt IV `
D. ` IV gt III gt II gt I`

Answer

To determine the correct sequence of the decreasing coagulation value of the given electrolytes for the coagulation of ferric hydroxide sol, we need to analyze the charge of the ions involved and apply the Hardy-Schulze rule.

### Step-by-Step Solution:

1. **Identify the Charge of Ferric Hydroxide Sol**:
- Ferric hydroxide (Fe(OH)₃) is a positively charged sol. Therefore, it will be coagulated by negatively charged ions.

2. **Analyze the Given Electrolytes**:
- (I) Sodium phosphate (Na₃PO₄): Contains Na⁺ and PO₄³⁻. The PO₄³⁻ ion has a charge of -3.
- (II) Potassium chloride (KCl): Contains K⁺ and Cl⁻. The Cl⁻ ion has a charge of -1.
- (III) Potassium sulfate (K₂SO₄): Contains K⁺ and SO₄²⁻. The SO₄²⁻ ion has a charge of -2.
- (IV) Potassium hexacyanoferrate (K₄[Fe(CN)₆]): Contains K⁺ and [Fe(CN)₆]⁴⁻. The [Fe(CN)₆]⁴⁻ ion has a charge of -4.

3. **Determine the Coagulating Power**:
- According to the Hardy-Schulze rule, the coagulating power of an electrolyte is directly proportional to the charge of the oppositely charged ion. The higher the charge, the greater the coagulating effect.
- Comparing the charges:
- K₄[Fe(CN)₆] has a charge of -4 (highest)
- Na₃PO₄ has a charge of -3
- K₂SO₄ has a charge of -2
- KCl has a charge of -1 (lowest)

4. **Sequence the Electrolytes Based on Coagulating Power**:
- The correct sequence of decreasing coagulation value for the electrolytes is:
1. K₄[Fe(CN)₆] (charge -4)
2. Na₃PO₄ (charge -3)
3. K₂SO₄ (charge -2)
4. KCl (charge -1)

5. **Final Answer**:
- The correct order is: K₄[Fe(CN)₆] > Na₃PO₄ > K₂SO₄ > KCl.