Predict if there will be any precipitate by mixing 50 mL of 0.01 M NaCl and 50 mL of 0.01 M `AgNO_(3)` solution. The solubility product of AgCl is `1.5xx10^(-10)`.

Options

A. Since ionic product is greater than solubility product no precipitate will be formed.
B. Since ionic product is lesser than solubility product, precipitation will occur .
C. Since ionic product is greater than solubility product, precipitation will occur.
D. Since ionic product and solubility product are same, precipitation will not occur.

Explanation

To determine if a precipitate will form when mixing 50 mL of 0.01 M NaCl and 50 mL of 0.01 M AgNO₃, we will follow these steps:

### Step 1: Calculate the number of moles of Cl⁻ and Ag⁺ ions
1. **For NaCl:**
- Volume = 50 mL = 0.050 L
- Concentration = 0.01 M
- Moles of Cl⁻ = Volume × Concentration = 0.050 L × 0.01 mol/L = 0.0005 mol = 0.5 mmol

2. **For AgNO₃:**
- Volume = 50 mL = 0.050 L
- Concentration = 0.01 M
- Moles of Ag⁺ = Volume × Concentration = 0.050 L × 0.01 mol/L = 0.0005 mol = 0.5 mmol

### Step 2: Calculate the total volume after mixing
- Total volume = Volume of NaCl + Volume of AgNO₃ = 50 mL + 50 mL = 100 mL = 0.1 L

### Step 3: Calculate the concentrations of Cl⁻ and Ag⁺ in the mixed solution
1. **Concentration of Cl⁻:**
- Concentration = Moles / Total Volume = 0.0005 mol / 0.1 L = 0.005 M

2. **Concentration of Ag⁺:**
- Concentration = Moles / Total Volume = 0.0005 mol / 0.1 L = 0.005 M

### Step 4: Calculate the ionic product (IP) of AgCl
- The ionic product (IP) is given by:
\[ \text{IP} = [\text{Ag}^+] \times [\text{Cl}^-] = 0.005 \, \text{M} \times 0.005 \, \text{M} = 2.5 \times 10^{-5} \]

### Step 5: Compare the ionic product with the solubility product (Ksp) of AgCl
- Given Ksp of AgCl = \(1.5 \times 10^{-10}\)
- Since \( \text{IP} = 2.5 \times 10^{-5} \) is greater than \( Ksp = 1.5 \times 10^{-10} \), we conclude that the solution is supersaturated.

### Step 6: Conclusion
- Because the ionic product is greater than the solubility product, a precipitate of AgCl will form when the two solutions are mixed.

### Final Answer
- Yes, a precipitate will form.

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