What is the minimum concentration of sulphuric acid required to initiate the precipitation of `BaSO_4` from a solution containing `7xx10^(-8) mol L^(-1)` of `BaCl_2` ? `[K_(sp)(BaSO_4)=1.4xx10^(-10)]`

Explanation

To find the minimum concentration of sulfuric acid required to initiate the precipitation of BaSO₄ from a solution containing 7 x 10⁻⁸ mol L⁻¹ of BaCl₂, we can follow these steps:

### Step 1: Understand the precipitation condition
The precipitation of BaSO₄ occurs when the ionic product of Ba²⁺ and SO₄²⁻ ions exceeds the solubility product constant (Ksp) of BaSO₄. The Ksp for BaSO₄ is given as 1.4 x 10⁻¹⁰.

### Step 2: Write the expression for Ksp
The Ksp expression for BaSO₄ can be written as:
\[ K_{sp} = [Ba^{2+}][SO_4^{2-}] \]

### Step 3: Identify the concentration of Ba²⁺
From the given information, the concentration of BaCl₂ is 7 x 10⁻⁸ mol L⁻¹. Since BaCl₂ dissociates into Ba²⁺ and 2Cl⁻ ions, the concentration of Ba²⁺ ions will also be:
\[ [Ba^{2+}] = 7 x 10^{-8} \, \text{mol L}^{-1} \]

### Step 4: Set up the Ksp equation
To find the minimum concentration of sulfate ions ([SO₄²⁻]), we can rearrange the Ksp expression:
\[ [SO_4^{2-}] = \frac{K_{sp}}{[Ba^{2+}]} \]

### Step 5: Substitute the values into the equation
Substituting the known values into the equation:
\[ [SO_4^{2-}] = \frac{1.4 x 10^{-10}}{7 x 10^{-8}} \]

### Step 6: Perform the calculation
Calculating the above expression:
\[ [SO_4^{2-}] = \frac{1.4}{7} x 10^{-10 + 8} = \frac{1.4}{7} x 10^{-2} \]
\[ [SO_4^{2-}] = 0.2 x 10^{-2} = 2 x 10^{-3} \, \text{mol L}^{-1} \]

### Step 7: Conclusion
Thus, the minimum concentration of sulfuric acid (H₂SO₄) required to initiate the precipitation of BaSO₄ is:
\[ [H_2SO_4] = 2 x 10^{-3} \, \text{mol L}^{-1} \]

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