Equal volume of the following `Ca^(+2)` and `F^(-)` solutions are mixed. In which case will percipitation occur? (`K_(sp)` of `CaF_(2) = 7 xx 10^(-10)`).

Options

A. `10^(-2) M Ca^(+2) + 10^(-5)MF^(-)`
B. `10^(-3) M Ca^(+2) + 10^(-5)MF^(-)`
C. `10^(-4) M Ca^(+2) + 10^(-2)MF^(-)`
D. `10^(-2) M Ca^(+2) + 10^(-6)MF^(-)`

Explanation

To determine whether precipitation occurs when equal volumes of `Ca^(+2)` and `F^(-)` solutions are mixed, we need to apply the solubility product constant (Ksp) for calcium fluoride (CaF2). The Ksp for CaF2 is given as \( 7 \times 10^{-10} \).

### Step-by-step Solution:

1. **Understanding the Reaction**:
The dissolution of calcium fluoride can be represented as:
\[ CaF_2 (s) \rightleftharpoons Ca^{2+} (aq) + 2F^{-} (aq) \]
The solubility product expression is:
\[ K_{sp} = [Ca^{2+}][F^{-}]^2 \]

2. **Condition for Precipitation**:
Precipitation occurs when the product of the ion concentrations exceeds the Ksp value:
\[ [Ca^{2+}][F^{-}]^2 > K_{sp} \]

3. **Analyzing Each Case**:
We will analyze each option provided in the question to see if precipitation occurs.

**Option 1**: \( [Ca^{2+}] = 10^{-2} \, M \) and \( [F^{-}] = 10^{-5} \, M \)
\[ [Ca^{2+}][F^{-}]^2 = (10^{-2})(10^{-5})^2 = (10^{-2})(10^{-10}) = 10^{-12} \]
Since \( 10^{-12} < 7 \times 10^{-10} \), precipitation does not occur.

**Option 2**: \( [Ca^{2+}] = 10^{-3} \, M \) and \( [F^{-}] = 10^{-5} \, M \)
\[ [Ca^{2+}][F^{-}]^2 = (10^{-3})(10^{-5})^2 = (10^{-3})(10^{-10}) = 10^{-13} \]
Since \( 10^{-13} < 7 \times 10^{-10} \), precipitation does not occur.

**Option 3**: \( [Ca^{2+}] = 10^{-4} \, M \) and \( [F^{-}] = 10^{-2} \, M \)
\[ [Ca^{2+}][F^{-}]^2 = (10^{-4})(10^{-2})^2 = (10^{-4})(10^{-4}) = 10^{-8} \]
Since \( 10^{-8} > 7 \times 10^{-10} \), precipitation occurs.

**Option 4**: \( [Ca^{2+}] = 10^{-2} \, M \) and \( [F^{-}] = 10^{-6} \, M \)
\[ [Ca^{2+}][F^{-}]^2 = (10^{-2})(10^{-6})^2 = (10^{-2})(10^{-12}) = 10^{-14} \]
Since \( 10^{-14} < 7 \times 10^{-10} \), precipitation does not occur.

4. **Conclusion**:
Precipitation occurs only in **Option 3** where \( [Ca^{2+}] = 10^{-4} \, M \) and \( [F^{-}] = 10^{-2} \, M \).