The solubility product of `CaSO_4` is `6.4xx10^(-5)` .The solubility of salt in moles/litre is :

Options

A. `8xx10^(-16)`
B. `8xx10^(-2)`
C. `8xx10^(-3)`
D. `1.6xx10^(-3)`

Explanation

To find the solubility of calcium sulfate (CaSO₄) given its solubility product (Ksp), we can follow these steps:

### Step 1: Write the dissociation equation for CaSO₄.
Calcium sulfate dissociates in water as follows:
\[ \text{CaSO}_4 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + \text{SO}_4^{2-} (aq) \]

### Step 2: Define the solubility (s).
Let the solubility of CaSO₄ in moles per liter be \( s \). When CaSO₄ dissolves, it produces \( s \) moles of \( \text{Ca}^{2+} \) and \( s \) moles of \( \text{SO}_4^{2-} \).

### Step 3: Write the expression for Ksp.
The solubility product (Ksp) expression for the dissociation of CaSO₄ can be written as:
\[ Ksp = [\text{Ca}^{2+}][\text{SO}_4^{2-}] \]

Substituting the concentrations in terms of solubility \( s \):
\[ Ksp = (s)(s) = s^2 \]

### Step 4: Substitute the given Ksp value.
We know that the Ksp of CaSO₄ is \( 6.4 \times 10^{-5} \):
\[ s^2 = 6.4 \times 10^{-5} \]

### Step 5: Solve for s.
To find the solubility \( s \), take the square root of both sides:
\[ s = \sqrt{6.4 \times 10^{-5}} \]

Calculating this gives:
\[ s \approx 8.0 \times 10^{-3} \text{ moles/liter} \]

### Conclusion:
The solubility of calcium sulfate (CaSO₄) is approximately \( 8.0 \times 10^{-3} \) moles/liter.

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