Flocculation value for `As_2S_3` sol by HCl is 30 mmole `L^( –1)` . Calculate mass of `H_2SO_4` required in gram for 250 mL sol.

Answer

To solve the problem, we need to calculate the mass of \( H_2SO_4 \) required for 250 mL of an arsenic sulfide sol given that the flocculation value for \( As_2S_3 \) sol by HCl is 30 mmole L\(^{-1}\).

### Step-by-Step Solution:

1. **Understand the Flocculation Value**:
The flocculation value of 30 mmole L\(^{-1}\) means that for 1 liter of the sol, 30 mmoles of HCl are required to flocculate the sol.

**Hint**: Remember that the flocculation value indicates how much of a substance is needed to cause a reaction or change in a solution.

2. **Determine the Requirement for \( H_2SO_4 \)**:
Since \( H_2SO_4 \) is a dibasic acid, it can provide 2 moles of \( H^+ \) ions per mole of acid. Therefore, to achieve the same flocculation effect, we need half the amount of \( H_2SO_4 \) compared to \( HCl \).

\[ \text{Required } H_2SO_4 = \frac{30 \text{ mmoles}}{2} = 15 \text{ mmoles L}^{-1} \]

**Hint**: For dibasic acids, remember to divide the required amount by 2 since they release two \( H^+ \) ions.

3. **Calculate the Amount for 250 mL**:
Convert 250 mL to liters:
\[ 250 \text{ mL} = 0.25 \text{ L} \]
Now, calculate the total amount of \( H_2SO_4 \) needed for 0.25 L:
\[ \text{Total } H_2SO_4 = 15 \text{ mmoles L}^{-1} \times 0.25 \text{ L} = 3.75 \text{ mmoles} \]

**Hint**: Always convert mL to L when working with concentrations.

4. **Convert Millimoles to Moles**:
Convert the amount from millimoles to moles:
\[ 3.75 \text{ mmoles} = 3.75 \times 10^{-3} \text{ moles} \]

**Hint**: Remember that 1 mole = 1000 mmoles.

5. **Calculate the Molar Mass of \( H_2SO_4 \)**:
The molar mass of \( H_2SO_4 \) can be calculated as follows:
\[ \text{Molar mass of } H_2SO_4 = (2 \times 1) + 32 + (4 \times 16) = 2 + 32 + 64 = 98 \text{ g/mol} \]

**Hint**: Be careful to add the atomic masses correctly to find the molar mass.

6. **Calculate the Mass of \( H_2SO_4 \)**:
Now, use the number of moles and the molar mass to find the mass:
\[ \text{Mass of } H_2SO_4 = \text{moles} \times \text{molar mass} = (3.75 \times 10^{-3} \text{ moles}) \times (98 \text{ g/mol}) = 0.3675 \text{ grams} \]

**Hint**: The mass can be found by multiplying the number of moles by the molar mass.

### Final Answer:
The mass of \( H_2SO_4 \) required for 250 mL of the sol is **0.3675 grams**.