The volume of the water needed to dissolve `1 g` of `BaSO_(4) (K_(SP)=1.1xx10^(-10))` at `25^(@) C` is:

Options

A. `280 litre`
B. `410 litre`
C. `205 litre`
D. None of these

Explanation

To find the volume of water needed to dissolve 1 g of BaSO₄ at 25°C, we will follow these steps:

### Step 1: Determine the solubility of BaSO₄ using Ksp.
The dissociation of BaSO₄ in water can be represented as:
\[ \text{BaSO}_4 (s) \rightleftharpoons \text{Ba}^{2+} (aq) + \text{SO}_4^{2-} (aq) \]

The solubility product (Ksp) expression for this equilibrium is:
\[ K_{sp} = [\text{Ba}^{2+}][\text{SO}_4^{2-}] \]

Let the solubility of BaSO₄ be \( S \) mol/L. Therefore, at equilibrium:
\[ [\text{Ba}^{2+}] = S \]
\[ [\text{SO}_4^{2-}] = S \]

Thus, we can write:
\[ K_{sp} = S \cdot S = S^2 \]

Given \( K_{sp} = 1.1 \times 10^{-10} \):
\[ S^2 = 1.1 \times 10^{-10} \]
\[ S = \sqrt{1.1 \times 10^{-10}} \]
\[ S \approx 1.05 \times 10^{-5} \text{ mol/L} \]

### Step 2: Calculate the molar mass of BaSO₄.
The molar mass of BaSO₄ can be 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

So, the molar mass of BaSO₄ is:
\[ 137.33 + 32.07 + 64.00 = 233.40 \text{ g/mol} \]

### Step 3: Calculate the mass of BaSO₄ that can be dissolved in 1 L of water.
Using the solubility \( S \):
\[ \text{Mass of BaSO}_4 = S \times \text{Molar mass} \]
\[ \text{Mass of BaSO}_4 = (1.05 \times 10^{-5} \text{ mol/L}) \times (233.40 \text{ g/mol}) \]
\[ \text{Mass of BaSO}_4 \approx 2.45 \times 10^{-3} \text{ g/L} \]

### Step 4: Calculate the volume of water needed to dissolve 1 g of BaSO₄.
To find the volume of water required to dissolve 1 g of BaSO₄, we set up the following proportion:
If 2.45 mg of BaSO₄ can dissolve in 1 L of water, then:
\[ \text{Volume} = \frac{1 \text{ g}}{2.45 \times 10^{-3} \text{ g/L}} \]
\[ \text{Volume} = \frac{1 \text{ g}}{0.00000245 \text{ g/L}} \]
\[ \text{Volume} \approx 408.16 \text{ L} \]

Thus, the volume of water needed to dissolve 1 g of BaSO₄ is approximately **410 L**.

### Summary of Steps:
1. Calculate solubility \( S \) using \( K_{sp} \).
2. Determine the molar mass of BaSO₄.
3. Calculate the mass of BaSO₄ that can dissolve in 1 L of water.
4. Use the mass to find the volume of water needed for 1 g of BaSO₄.