The solubility product of `BaSO_4 ` is `4 xx 10^(-10)` . The solubility of `BaSO_4` in presence of 0.02 `N H_2SO_4` will be

Options

A. `4 xx 10^(-8)` M
B. `2 xx 10^(-8)` M
C. `2 xx 10^(-5) `M
D. `2 xx 10^(-4)` M

Answer

To solve the problem of finding the solubility of BaSO₄ in the presence of 0.02 N H₂SO₄, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Molarity of H₂SO₄:**
Given that the normality (N) of H₂SO₄ is 0.02 N, we can convert normality to molarity (M).
The relationship between normality and molarity for H₂SO₄ (which has an n-factor of 2, since it can donate two protons) is:
\[ \text{Molarity} = \frac{\text{Normality}}{\text{n-factor}} = \frac{0.02 \, \text{N}}{2} = 0.01 \, \text{M} \]

**Hint:** Remember that the n-factor represents the number of moles of H⁺ ions contributed by one mole of the acid.

2. **Set Up the Dissociation of BaSO₄:**
The dissociation of BaSO₄ in water can be represented as:
\[ \text{BaSO}_4 (s) \rightleftharpoons \text{Ba}^{2+} (aq) + \text{SO}_4^{2-} (aq) \]
Let the solubility of BaSO₄ be \( s \) mol/L. Therefore, at equilibrium:
- \([Ba^{2+}] = s\)
- \([SO_4^{2-}] = s\)

3. **Account for the Contribution of SO₄²⁻ from H₂SO₄:**
Since H₂SO₄ dissociates to give SO₄²⁻ ions as well, the concentration of SO₄²⁻ from H₂SO₄ is 0.01 M. Thus, the total concentration of SO₄²⁻ becomes:
\[ [SO_4^{2-}] = s + 0.01 \]

4. **Write the Expression for Ksp:**
The solubility product (Ksp) of BaSO₄ is given as \( 4 \times 10^{-10} \). The Ksp expression is:
\[ K_{sp} = [Ba^{2+}][SO_4^{2-}] = s \cdot (s + 0.01) \]
Substituting the value of Ksp:
\[ 4 \times 10^{-10} = s \cdot (s + 0.01) \]

5. **Neglect the Small Quantity:**
Since \( s \) is expected to be very small compared to 0.01, we can neglect \( s^2 \) in the equation:
\[ 4 \times 10^{-10} \approx s \cdot 0.01 \]

6. **Solve for s:**
Rearranging the equation gives:
\[ s = \frac{4 \times 10^{-10}}{0.01} = 4 \times 10^{-8} \, \text{M} \]

### Final Answer:
The solubility of BaSO₄ in the presence of 0.02 N H₂SO₄ is \( 4 \times 10^{-8} \, \text{M} \).

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