Match the column I with column II and mark the appropriate choice.
`{:(,"Column I",,"Column II",),((A),Fe(OH)_(3),(i),K_(sp)=s^(2),),((B),Ag_(2)CrO_(4),(ii),K_(sp)=27s^(4),),((C),CH_(3)COOAg,(iii),K_(sp)=108s^(5),),((D),Ca_(3)(PO_(4)),(iv),K_(sp)=4s^(3),):}`

Options

A. `(A)to(iii),(B)to(ii),(C)to(iv),(D)to(i)`
B. `(A)to(ii),(B)to(iv),(C)to(i),(D)to(iii)`
C. `(A)to(i),(B)to(iii),(C)to(ii),(D)to(iv)`
D. `(A)to(iv),(B)to(i),(C)to(iii),(D)to(ii)`

Explanation

To solve the problem of matching Column I with Column II based on the solubility products (Ksp) of the given compounds, we will analyze each compound step-by-step.

### Step 1: Analyze Fe(OH)₃
- **Dissociation**: Fe(OH)₃ ⇌ Fe³⁺ + 3OH⁻
- **Let the solubility of Fe(OH)₃ be S**.
- At equilibrium, [Fe³⁺] = S and [OH⁻] = 3S.
- **Ksp Calculation**:
\[ Ksp = [Fe^{3+}][OH^-]^3 = S(3S)^3 = S \cdot 27S^3 = 27S^4 \]
- **Match**: Ksp = 27s⁴ (ii)

### Step 2: Analyze Ag₂CrO₄
- **Dissociation**: Ag₂CrO₄ ⇌ 2Ag⁺ + CrO₄²⁻
- **Let the solubility of Ag₂CrO₄ be S**.
- At equilibrium, [Ag⁺] = 2S and [CrO₄²⁻] = S.
- **Ksp Calculation**:
\[ Ksp = [Ag^+]^2[CrO_4^{2-}] = (2S)^2(S) = 4S^3 \]
- **Match**: Ksp = 4s³ (iv)

### Step 3: Analyze CH₃COOAg
- **Dissociation**: CH₃COOAg ⇌ CH₃COO⁻ + Ag⁺
- **Let the solubility of CH₃COOAg be S**.
- At equilibrium, [CH₃COO⁻] = S and [Ag⁺] = S.
- **Ksp Calculation**:
\[ Ksp = [CH_3COO^-][Ag^+] = S \cdot S = S^2 \]
- **Match**: Ksp = s² (i)

### Step 4: Analyze Ca₃(PO₄)₂
- **Dissociation**: Ca₃(PO₄)₂ ⇌ 3Ca²⁺ + 2PO₄³⁻
- **Let the solubility of Ca₃(PO₄)₂ be S**.
- At equilibrium, [Ca²⁺] = 3S and [PO₄³⁻] = 2S.
- **Ksp Calculation**:
\[ Ksp = [Ca^{2+}]^3[PO_4^{3-}]^2 = (3S)^3(2S)^2 = 27S^3 \cdot 4S^2 = 108S^5 \]
- **Match**: Ksp = 108s⁵ (iii)

### Summary of Matches:
- A (Fe(OH)₃) matches with (ii) Ksp = 27s⁴
- B (Ag₂CrO₄) matches with (iv) Ksp = 4s³
- C (CH₃COOAg) matches with (i) Ksp = s²
- D (Ca₃(PO₄)₂) matches with (iii) Ksp = 108s⁵

### Final Answer:
- A - (ii)
- B - (iv)
- C - (i)
- D - (iii)