In 1 L saturated solution of `AgCl[K_(sp)(AgCl)=1.6xx10^(-19)], 0.1" mol of "CuCl[K_(sp)(CuCl)=1.0xx10^(-6)]`
is added. The resultant concentration of `Ag^(+)` in the solution is `1.6xx10^(-x)`. The value of ''x'' is

Answer

To solve the problem, we need to determine the concentration of \( Ag^+ \) ions in a saturated solution of \( AgCl \) after adding \( 0.1 \) mol of \( CuCl \). We will use the solubility product constants (\( K_{sp} \)) for both salts to find the answer.

### Step-by-Step Solution:

1. **Identify the Solubility Product Constants**:
- For \( AgCl \), \( K_{sp}(AgCl) = 1.6 \times 10^{-10} \).
- For \( CuCl \), \( K_{sp}(CuCl) = 1.0 \times 10^{-6} \).

2. **Dissociation of \( CuCl \)**:
- When \( CuCl \) dissolves, it dissociates into \( Cu^+ \) and \( Cl^- \) ions:
\[ CuCl \rightleftharpoons Cu^+ + Cl^- \]
- Since \( 0.1 \) mol of \( CuCl \) is added to \( 1 \) L of solution, the concentration of \( Cl^- \) ions from \( CuCl \) will be:
\[ [Cl^-] = 0.1 \, \text{mol/L} \]

3. **Calculate the Concentration of \( Cl^- \)**:
- The concentration of \( Cl^- \) from \( CuCl \) is \( 0.1 \, \text{mol/L} \).

4. **Use the \( K_{sp} \) Expression for \( AgCl \)**:
- The solubility product expression for \( AgCl \) is:
\[ K_{sp}(AgCl) = [Ag^+][Cl^-] \]
- Rearranging this gives:
\[ [Ag^+] = \frac{K_{sp}(AgCl)}{[Cl^-]} \]

5. **Substituting Values**:
- Substitute the known values into the equation:
\[ [Ag^+] = \frac{1.6 \times 10^{-10}}{0.1} \]
- Calculate:
\[ [Ag^+] = 1.6 \times 10^{-10} \times 10 = 1.6 \times 10^{-9} \, \text{mol/L} \]

6. **Expressing in the Required Form**:
- The problem states that the resultant concentration of \( Ag^+ \) is \( 1.6 \times 10^{-x} \).
- From our calculation, we have:
\[ 1.6 \times 10^{-9} = 1.6 \times 10^{-x} \]
- Therefore, \( x = 9 \).

### Final Answer:
The value of \( x \) is \( 9 \).