The solubility product of `CaSO_(4)` is `2.4xx10^(-5)`. When 100 mL of `0.01M CaCl_(2)` and 100 mL of `0.002M Na_(2)SO_(4)` are mixed, then :

Options

A. `Na_(2)SO_(4)` will precipitate
B. Both will precipitate
C. `CaSO_(4)` will precipitate
D. None will precipitate

Explanation

To solve the problem, we need to determine whether a precipitate will form when mixing the two solutions of calcium chloride (CaCl₂) and sodium sulfate (Na₂SO₄). We will follow these steps:

### Step 1: Calculate the concentrations of ions after mixing
When we mix 100 mL of 0.01 M CaCl₂ with 100 mL of 0.002 M Na₂SO₄, we need to find the final concentrations of Ca²⁺ and SO₄²⁻ ions in the total volume of the solution (200 mL).

1. **Calculate the concentration of Ca²⁺ ions:**
- Initial concentration of CaCl₂ = 0.01 M
- Volume of CaCl₂ solution = 100 mL = 0.1 L
- Moles of Ca²⁺ from CaCl₂ = 0.01 M × 0.1 L = 0.001 moles
- Total volume after mixing = 100 mL + 100 mL = 200 mL = 0.2 L
- Final concentration of Ca²⁺ = moles / total volume = 0.001 moles / 0.2 L = 0.005 M

2. **Calculate the concentration of SO₄²⁻ ions:**
- Initial concentration of Na₂SO₄ = 0.002 M
- Volume of Na₂SO₄ solution = 100 mL = 0.1 L
- Moles of SO₄²⁻ from Na₂SO₄ = 0.002 M × 0.1 L = 0.0002 moles
- Final concentration of SO₄²⁻ = moles / total volume = 0.0002 moles / 0.2 L = 0.001 M

### Step 2: Calculate the ionic product (Q) for CaSO₄
The ionic product (Q) for the precipitation of CaSO₄ can be calculated using the formula:
\[ Q = [Ca^{2+}][SO_4^{2-}] \]

Substituting the concentrations we found:
\[ Q = (0.005)(0.001) = 5 \times 10^{-6} \]

### Step 3: Compare Q with Ksp
The solubility product (Ksp) of CaSO₄ is given as \( 2.4 \times 10^{-5} \).

Now we compare Q and Ksp:
- Q = \( 5 \times 10^{-6} \)
- Ksp = \( 2.4 \times 10^{-5} \)

Since \( Q < Ksp \), this indicates that the solution is unsaturated with respect to CaSO₄, meaning no precipitate will form.

### Conclusion
Since the ionic product (Q) is less than the solubility product (Ksp), no precipitation of CaSO₄ will occur when the two solutions are mixed.

### Final Answer
**No precipitate will form.**

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