You are given a `10^(-5)` M NaCl solution and `10^(-8)M AgNO_3` solution . They are mixed in 1:1 volume ratio . `K_(sp)(AgCl)=10^(-5) M^(2)` Choose the correct statement.

Options

A. Precipitation will take place
B. Precipitation will not take place
C. Cannot be determined
D. After 1 hour precipitation will take place

Answer

To solve the problem, we need to determine whether a precipitate of AgCl will form when mixing the given solutions. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Components
We have two solutions:
- **NaCl**: 10^(-5) M
- **AgNO3**: 10^(-8) M

When mixed in a 1:1 volume ratio, we need to find the concentrations of Ag^+ and Cl^- ions in the resulting solution.

### Step 2: Calculate the Concentration of Cl⁻ Ions
Since NaCl is a strong electrolyte, it completely dissociates in solution:
\[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]

In a 1:1 volume ratio, the concentration of Cl⁻ after mixing will be:
\[ \text{Concentration of Cl}^- = \frac{10^{-5} \, \text{M} \times V}{2V} = \frac{10^{-5}}{2} = 5 \times 10^{-6} \, \text{M} \]

### Step 3: Calculate the Concentration of Ag⁺ Ions
AgNO3 also dissociates completely:
\[ \text{AgNO}_3 \rightarrow \text{Ag}^+ + \text{NO}_3^- \]

In a 1:1 volume ratio, the concentration of Ag⁺ after mixing will be:
\[ \text{Concentration of Ag}^+ = \frac{10^{-8} \, \text{M} \times V}{2V} = \frac{10^{-8}}{2} = 5 \times 10^{-9} \, \text{M} \]

### Step 4: Calculate the Ionic Product (IP) for AgCl
The ionic product (IP) for the precipitation reaction of AgCl is given by:
\[ \text{IP} = [\text{Ag}^+][\text{Cl}^-] = (5 \times 10^{-9})(5 \times 10^{-6}) = 25 \times 10^{-15} = 2.5 \times 10^{-14} \]

### Step 5: Compare IP with Ksp
The solubility product constant (Ksp) for AgCl is given as:
\[ K_{sp}(\text{AgCl}) = 10^{-5} \]

### Step 6: Determine if Precipitate Forms
For a precipitate to form, the ionic product must be greater than the Ksp:
\[ \text{IP} = 2.5 \times 10^{-14} \quad \text{and} \quad K_{sp} = 10^{-5} \]

Since \( 2.5 \times 10^{-14} < 10^{-5} \), the condition for precipitation is not met.

### Conclusion
No precipitate of AgCl will form when the two solutions are mixed.

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