The coagulation value in millimoles per litre of the electrolyes used for the coagulation of `As_(2)S_(3)` are given below:
I. `(NaCl)=52` , II. `(BaCl_(2))=0.69`
III. `(MgSO_(4))=0.22`
The correct order of their coagulating power is

Options

A. `I gt II gt III`
B. `II gt I gt III`
C. `III gt II gt I`
D. `III gt I gt II`

Explanation

To determine the correct order of coagulating power of the electrolytes used for the coagulation of As₂S₃ (arsenic sulfide), we need to analyze the given coagulation values for each electrolyte. The coagulating power is inversely proportional to the coagulation value; that is, a lower coagulation value indicates a higher coagulating power.

### Step-by-Step Solution:

1. **Identify the Coagulation Values**:
- NaCl: 52 millimoles per liter
- BaCl₂: 0.69 millimoles per liter
- MgSO₄: 0.22 millimoles per liter

2. **Understand the Relationship**:
- Coagulating power is inversely proportional to coagulation value. This means:
\[ \text{Coagulating Power} \propto \frac{1}{\text{Coagulation Value}} \]

3. **Calculate the Coagulating Power**:
- For NaCl: Coagulating Power = 1/52
- For BaCl₂: Coagulating Power = 1/0.69
- For MgSO₄: Coagulating Power = 1/0.22

4. **Compare the Coagulating Powers**:
- Since we are looking for the highest coagulating power, we need to find which of the three values is the smallest:
- MgSO₄ has the smallest coagulation value (0.22), hence it has the highest coagulating power.
- BaCl₂ has a coagulation value of 0.69, which is higher than MgSO₄ but lower than NaCl.
- NaCl has the highest coagulation value (52), hence it has the lowest coagulating power.

5. **Order the Coagulating Powers**:
- Highest Coagulating Power: MgSO₄ (0.22)
- Second Highest: BaCl₂ (0.69)
- Lowest Coagulating Power: NaCl (52)

6. **Final Order**:
- The correct order of coagulating power from highest to lowest is:
\[ \text{MgSO₄} > \text{BaCl₂} > \text{NaCl} \]

### Conclusion:
The correct order of coagulating power is:
- **MgSO₄ > BaCl₂ > NaCl**