`{:("List -I Salt","List -II Ksp"),((A) AgCI,P.27S^(4)),((B)PbI_(2),Q.108(S)^(5)),((C )AS_(2)S_(3),R.4S^(3)),((D)Ag_(3)PO_(4),S.S^(2)):}`

Answer

To solve the problem of matching salts with their respective solubility products (Ksp), we need to analyze each salt's dissociation and calculate the Ksp based on its solubility. Let's go through each salt step by step.

### Step 1: Analyze Silver Chloride (AgCl)
- **Dissociation Reaction**:
\[ \text{AgCl} \rightleftharpoons \text{Ag}^+ + \text{Cl}^- \]
- **Let the solubility (s)** = s mol/L.
- **Concentration of ions**:
- \([\text{Ag}^+] = s\)
- \([\text{Cl}^-] = s\)
- **Ksp Calculation**:
\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] = s \cdot s = s^2 \]
- **Match**: This corresponds to option S (Ksp = 27s^4).

### Step 2: Analyze Lead(II) Iodide (PbI2)
- **Dissociation Reaction**:
\[ \text{PbI}_2 \rightleftharpoons \text{Pb}^{2+} + 2\text{I}^- \]
- **Let the solubility (s)** = s mol/L.
- **Concentration of ions**:
- \([\text{Pb}^{2+}] = s\)
- \([\text{I}^-] = 2s\)
- **Ksp Calculation**:
\[ K_{sp} = [\text{Pb}^{2+}][\text{I}^-]^2 = s \cdot (2s)^2 = s \cdot 4s^2 = 4s^3 \]
- **Match**: This corresponds to option R (Ksp = 108s^5).

### Step 3: Analyze Arsenic Sulfide (As2S3)
- **Dissociation Reaction**:
\[ \text{As}_2\text{S}_3 \rightleftharpoons 2\text{As}^{3+} + 3\text{S}^{2-} \]
- **Let the solubility (s)** = s mol/L.
- **Concentration of ions**:
- \([\text{As}^{3+}] = 2s\)
- \([\text{S}^{2-}] = 3s\)
- **Ksp Calculation**:
\[ K_{sp} = [\text{As}^{3+}]^2[\text{S}^{2-}]^3 = (2s)^2 \cdot (3s)^3 = 4s^2 \cdot 27s^3 = 108s^5 \]
- **Match**: This corresponds to option Q (Ksp = 4s^3).

### Step 4: Analyze Silver Phosphate (Ag3PO4)
- **Dissociation Reaction**:
\[ \text{Ag}_3\text{PO}_4 \rightleftharpoons 3\text{Ag}^+ + \text{PO}_4^{3-} \]
- **Let the solubility (s)** = s mol/L.
- **Concentration of ions**:
- \([\text{Ag}^+] = 3s\)
- \([\text{PO}_4^{3-}] = s\)
- **Ksp Calculation**:
\[ K_{sp} = [\text{Ag}^+]^3[\text{PO}_4^{3-}] = (3s)^3 \cdot s = 27s^3 \cdot s = 27s^4 \]
- **Match**: This corresponds to option P (Ksp = 4s^3).

### Final Matches:
- A matches with S (AgCl - Ksp = s^2)
- B matches with R (PbI2 - Ksp = 4s^3)
- C matches with Q (As2S3 - Ksp = 108s^5)
- D matches with P (Ag3PO4 - Ksp = 27s^4)

### Summary of Matches:
- A - S
- B - R
- C - Q
- D - P