Which one has the minimum solubility product ?

Options

A. `AgCI`
B. `AICI_(3)`
C. `BaCI_(2)`
D. `NH_(4)CI`

Answer

To determine which compound has the minimum solubility product (Ksp) among the given options (AgCl, AlCl3, BaCl2, and NH4Cl), we can follow these steps:

### Step 1: Understand the concept of solubility product (Ksp)
The solubility product (Ksp) is an equilibrium constant that applies to the solubility of ionic compounds. It is defined for a saturated solution of a sparingly soluble ionic compound.

### Step 2: Write the Ksp expressions for each compound
For a general ionic compound \( AB \) that dissociates into \( A^n \) and \( B^m \):
\[ Ksp = [A^n]^m \times [B^m]^n \]

- **AgCl**: Dissociates into \( Ag^+ \) and \( Cl^- \)
\[ Ksp = [Ag^+][Cl^-] \]

- **AlCl3**: Dissociates into \( Al^{3+} \) and \( 3Cl^- \)
\[ Ksp = [Al^{3+}][Cl^-]^3 \]

- **BaCl2**: Dissociates into \( Ba^{2+} \) and \( 2Cl^- \)
\[ Ksp = [Ba^{2+}][Cl^-]^2 \]

- **NH4Cl**: Dissociates into \( NH4^+ \) and \( Cl^- \)
\[ Ksp = [NH4^+][Cl^-] \]

### Step 3: Analyze the charges of ions
The solubility product is influenced by the charges of the ions. Higher charges lead to a greater Ksp value because they require more ions to be present in solution to reach saturation.

- **AgCl**: \( Ag^+ \) (1+) and \( Cl^- \) (1-)
- **AlCl3**: \( Al^{3+} \) (3+) and \( 3Cl^- \) (1-)
- **BaCl2**: \( Ba^{2+} \) (2+) and \( 2Cl^- \) (1-)
- **NH4Cl**: \( NH4^+ \) (1+) and \( Cl^- \) (1-)

### Step 4: Compare Ksp values qualitatively
- **AgCl** has a low Ksp because it is sparingly soluble and forms a precipitate.
- **AlCl3** and **BaCl2** have higher Ksp values due to the presence of higher charged ions.
- **NH4Cl** is soluble in water but does not form a precipitate, indicating a higher Ksp than AgCl.

### Step 5: Conclusion
Based on the analysis, **AgCl** has the minimum solubility product (Ksp) among the given options because it is the least soluble and forms a precipitate.

### Final Answer
The compound with the minimum solubility product is **AgCl**.

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