The minimum concentration of an electrolyte required to cause coagulation of a sol is called its flocculation value.It is expressed in millimoles per litre.If the flocculation value of `MgSO_4` for standard `As_2S_3` sol is 3.33. How many milligrams of `MgSO_4` is to be added to 20ml standard `As_2S_3` sol so that flocculation just state ?

Explanation

To solve the problem, we need to determine how many milligrams of \( MgSO_4 \) are required to cause coagulation of a \( As_2S_3 \) sol, given that the flocculation value of \( MgSO_4 \) is 3.33 millimoles per liter.

### Step-by-Step Solution:

1. **Understand the Flocculation Value**:
The flocculation value of \( MgSO_4 \) is given as 3.33 millimoles per liter. This means that to cause coagulation in 1 liter of \( As_2S_3 \) sol, we need 3.33 millimoles of \( MgSO_4 \).

2. **Calculate the Required Millimoles for 20 ml**:
Since we only need to treat 20 ml of the solution, we need to find out how many millimoles of \( MgSO_4 \) are required for this volume.
\[ \text{Millimoles required} = \left( \frac{3.33 \, \text{mmol}}{1000 \, \text{ml}} \right) \times 20 \, \text{ml} = 0.0666 \, \text{mmol} \]

3. **Convert Millimoles to Moles**:
To convert millimoles to moles, we divide by 1000:
\[ \text{Moles of } MgSO_4 = \frac{0.0666 \, \text{mmol}}{1000} = 0.0000666 \, \text{mol} \]

4. **Calculate the Molar Mass of \( MgSO_4 \)**:
The molar mass of \( MgSO_4 \) is calculated as follows:
- Molar mass of \( Mg \) = 24.31 g/mol
- Molar mass of \( S \) = 32.07 g/mol
- Molar mass of \( O \) = 16.00 g/mol (4 oxygen atoms)
\[ \text{Molar mass of } MgSO_4 = 24.31 + 32.07 + (4 \times 16.00) = 120.37 \, \text{g/mol} \]

5. **Calculate the Mass of \( MgSO_4 \) Required**:
Now, we can calculate the mass of \( MgSO_4 \) required using the formula:
\[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \]
\[ \text{Mass of } MgSO_4 = 0.0000666 \, \text{mol} \times 120.37 \, \text{g/mol} = 0.00801 \, \text{g} = 8.01 \, \text{mg} \]

6. **Final Result**:
Therefore, the amount of \( MgSO_4 \) that needs to be added to 20 ml of \( As_2S_3 \) sol to achieve coagulation is approximately **8.01 mg**.

### Conclusion:
To cause coagulation of 20 ml of \( As_2S_3 \) sol, you need to add approximately **8 mg** of \( MgSO_4 \).