The volume of water needed to dissolve 1g of `BaSO_4 (K_(sp)= 1.1 xx 10^(-10))" at 25"^@C` is

Options

A. 820 litres
B. 450 litres
C. 205 litres
D. none of these

Answer

To solve the problem of how much water is needed to dissolve 1 g of barium sulfate (BaSO₄) given its solubility product constant (Ksp), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Dissociation of BaSO₄**:
When barium sulfate dissolves in water, it dissociates into barium ions (Ba²⁺) and sulfate ions (SO₄²⁻):
\[ \text{BaSO}_4 (s) \rightleftharpoons \text{Ba}^{2+} (aq) + \text{SO}_4^{2-} (aq) \]

2. **Set Up the Expression for Ksp**:
The solubility product constant (Ksp) is given by the equation:
\[ K_{sp} = [\text{Ba}^{2+}][\text{SO}_4^{2-}] \]
If we let the solubility of BaSO₄ be \( s \) (in moles per liter), then:
\[ K_{sp} = s \cdot s = s^2 \]

3. **Substitute the Given Ksp Value**:
Given \( K_{sp} = 1.1 \times 10^{-10} \):
\[ s^2 = 1.1 \times 10^{-10} \]

4. **Calculate the Solubility (s)**:
To find \( s \), take the square root of both sides:
\[ s = \sqrt{1.1 \times 10^{-10}} \approx 1.05 \times 10^{-5} \text{ moles/L} \]

5. **Calculate the Molar Mass of BaSO₄**:
The molar mass of BaSO₄ is calculated as follows:
- Barium (Ba): 137.33 g/mol
- Sulfur (S): 32.07 g/mol
- Oxygen (O): 16.00 g/mol × 4 = 64.00 g/mol
\[ \text{Molar mass of BaSO}_4 = 137.33 + 32.07 + 64.00 = 233.40 \text{ g/mol} \]

6. **Convert Solubility to Grams**:
Now, we can convert the solubility in moles to grams:
\[ \text{mass of BaSO}_4 = s \times \text{molar mass} = (1.05 \times 10^{-5} \text{ moles/L}) \times (233.40 \text{ g/mol}) \approx 2.45 \times 10^{-3} \text{ g/L} \]

7. **Calculate the Volume of Water Needed**:
To find the volume of water needed to dissolve 1 g of BaSO₄, we can use the relationship:
\[ \text{Volume} = \frac{\text{mass of BaSO}_4}{\text{mass concentration}} = \frac{1 \text{ g}}{2.45 \times 10^{-3} \text{ g/L}} \approx 408.16 \text{ L} \]

### Final Answer:
The volume of water needed to dissolve 1 g of BaSO₄ is approximately **410 liters**.