The solubility product of AgCl is `1.8xx10^(-10)`. Precipitation of AgCl will occur only when equal volumes of solutions of :

Options

A. `10^(-4)M" "Ag^(+) and 10^(-4)M" "Cl^(-)`
B. `10^(-7)M" "Ag^(+) and 10^(-7)"M "Cl^(-)`
C. `10^(-5)M" "Ag^(+) and 10^(-5)M" "Cl^(-)`
D. `10^(-10)" M "Ag^(+) and 10^(-10)" M "Cl^(-)`

Answer

To determine when precipitation of AgCl will occur upon mixing equal volumes of solutions, we need to analyze the solubility product (Ksp) of AgCl, which is given as \(1.8 \times 10^{-10}\). Precipitation occurs when the ionic product (the product of the concentrations of the ions) exceeds the Ksp.

### Step-by-Step Solution:

1. **Understanding the Ksp**:
The solubility product \(K_{sp}\) for AgCl can be represented as:
\[ K_{sp} = [Ag^+][Cl^-] \]
For precipitation to occur, the ionic product must be greater than \(K_{sp}\).

2. **Calculating Ionic Products for Given Solutions**:
We will calculate the ionic product for each solution provided in the options. The ionic product is calculated by multiplying the concentrations of \(Ag^+\) and \(Cl^-\) ions.

- **Option 1**: Concentration of \(Ag^+ = 10^{-4} \, M\) and \(Cl^- = 10^{-4} \, M\)
\[ Ionic \, Product = [Ag^+][Cl^-] = (10^{-4})(10^{-4}) = 10^{-8} \]

- **Option 2**: Concentration of \(Ag^+ = 10^{-7} \, M\) and \(Cl^- = 10^{-7} \, M\)
\[ Ionic \, Product = (10^{-7})(10^{-7}) = 10^{-14} \]

- **Option 3**: Concentration of \(Ag^+ = 10^{-5} \, M\) and \(Cl^- = 10^{-5} \, M\)
\[ Ionic \, Product = (10^{-5})(10^{-5}) = 10^{-10} \]

- **Option 4**: Concentration of \(Ag^+ = 10^{-10} \, M\) and \(Cl^- = 10^{-10} \, M\)
\[ Ionic \, Product = (10^{-10})(10^{-10}) = 10^{-20} \]

3. **Comparing Ionic Products with Ksp**:
Now we will compare each calculated ionic product with the given \(K_{sp} = 1.8 \times 10^{-10}\).

- **Option 1**: \(10^{-8} < 1.8 \times 10^{-10}\) (No precipitation)
- **Option 2**: \(10^{-14} < 1.8 \times 10^{-10}\) (No precipitation)
- **Option 3**: \(10^{-10} < 1.8 \times 10^{-10}\) (No precipitation)
- **Option 4**: \(10^{-20} < 1.8 \times 10^{-10}\) (No precipitation)

4. **Conclusion**:
None of the options yield an ionic product greater than the Ksp of AgCl. Therefore, precipitation of AgCl will not occur in any of the provided solutions.

### Final Answer:
Precipitation of AgCl will not occur in any of the given solutions.