The solubility of AgCI is

Options

A. `sqrt(K_(sp))`
B. `(K_(sp))^(1//3)`
C. `( (K_(sp))/4)^(1//3)`
D. `(8K_(sp))^(1//2)`

Answer

To solve the question regarding the solubility of AgCl (Silver Chloride), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Solubility (S)**:
Let the solubility of AgCl be denoted as \( S \) mol/L. This means that in a saturated solution, the concentration of AgCl that can dissolve is \( S \).

2. **Dissociation of AgCl**:
When AgCl dissolves in water, it dissociates into its ions:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]
For every mole of AgCl that dissolves, one mole of Ag\(^+\) and one mole of Cl\(^-\) are produced.

3. **Concentration of Ions**:
Since the solubility is \( S \), at equilibrium:
- The concentration of Ag\(^+\) ions = \( S \) mol/L
- The concentration of Cl\(^-\) ions = \( S \) mol/L

4. **Write the Solubility Product Expression (Ksp)**:
The solubility product constant \( K_{sp} \) for AgCl is given by:
\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] \]
Substituting the concentrations from step 3:
\[ K_{sp} = (S)(S) = S^2 \]

5. **Relate Solubility to Ksp**:
From the expression derived, we can express the solubility \( S \) in terms of \( K_{sp} \):
\[ S = \sqrt{K_{sp}} \]

6. **Conclusion**:
Thus, the solubility of AgCl can be expressed as:
\[ S = \sqrt{K_{sp}} \]

### Final Answer:
The solubility of AgCl is given by \( S = \sqrt{K_{sp}} \).

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