The solubility product of AgCI is `K_(sp)`. Then the solubility of AgCI in xM KCI is

Options

A. `K_(sp)xx X^2`
B. `x/(K_(sp))`
C. `(K_(sp))/(X^2)`
D. `(K_(sp))/(X)`

Answer

To solve the problem of finding the solubility of AgCl in xM KCl, we will follow these steps:

### Step 1: Write the dissociation equation for AgCl
AgCl dissociates in water as follows:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]

### Step 2: Define the solubility product (Ksp)
The solubility product \( K_{sp} \) for AgCl can be expressed as:
\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] \]
If we assume the solubility of AgCl in pure water is \( S \), then at equilibrium:
\[ [\text{Ag}^+] = S \quad \text{and} \quad [\text{Cl}^-] = S \]
Thus, we can write:
\[ K_{sp} = S \cdot S = S^2 \]

### Step 3: Consider the presence of KCl
When KCl is added to the solution, it dissociates completely:
\[ \text{KCl (s)} \rightleftharpoons \text{K}^+ (aq) + \text{Cl}^- (aq) \]
In a solution of xM KCl, the concentration of Cl⁻ ions will be:
\[ [\text{Cl}^-] = S + x \]
where \( S \) is the solubility of AgCl and \( x \) is the concentration of Cl⁻ from KCl.

### Step 4: Write the expression for Ksp in the presence of KCl
Now we can write the expression for \( K_{sp} \) in the presence of KCl:
\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] = S(S + x) \]

### Step 5: Neglect the \( S^2 \) term
Since AgCl is sparingly soluble, \( S \) is very small compared to \( x \). Therefore, we can neglect the \( S^2 \) term in the equation:
\[ K_{sp} \approx S \cdot x \]

### Step 6: Solve for S
Rearranging the equation gives us:
\[ S = \frac{K_{sp}}{x} \]

### Conclusion
Thus, the solubility of AgCl in xM KCl is:
\[ S = \frac{K_{sp}}{x} \]