Which one of the following is most soluble ?

Options

A. `CuS(K_("sp") = 8 xx 10^(-37))`
B. `MnS (K_("sp") = 7 xx 10^(-16))`
C. `Bi_(2)S_(3)(K_("sp") = 1 xx 10^(-70))`
D. `Ag_(2)S(K_("sp") = 6 xx 10^(-51))`

Answer

To determine which ionic compound is the most soluble among the given options, we need to analyze their solubility products (Ksp). Here’s a step-by-step solution:

### Step 1: Identify the Ionic Compounds
We are given the following ionic compounds:
1. CuS (Copper(II) sulfide)
2. MnS (Manganese(II) sulfide)
3. Bi2S3 (Bismuth(III) sulfide)
4. Ag2S (Silver sulfide)

### Step 2: Write the Dissociation Equations
For each compound, we can write the dissociation equations to find the ions produced:
- CuS → Cu²⁺ + S²⁻
- MnS → Mn²⁺ + S²⁻
- Bi2S3 → 2Bi³⁺ + 3S²⁻
- Ag2S → 2Ag⁺ + S²⁻

### Step 3: Write the Ksp Expressions
The solubility product (Ksp) expression for each compound can be written as follows:
- For CuS: Ksp = [Cu²⁺][S²⁻]
- For MnS: Ksp = [Mn²⁺][S²⁻]
- For Bi2S3: Ksp = [Bi³⁺]²[S²⁻]³
- For Ag2S: Ksp = [Ag⁺]²[S²⁻]

### Step 4: Determine the Relationship Between Ksp and Solubility (S)
Let’s denote the molar solubility of each compound as S:
- For CuS: Ksp = S²
- For MnS: Ksp = S²
- For Bi2S3: Ksp = (2S)²(3S)³ = 108S⁵
- For Ag2S: Ksp = (2S)²(S) = 4S³

### Step 5: Compare Ksp Values
We need the Ksp values for each compound to find the most soluble one. The Ksp values are:
- CuS: Ksp = 8.9 × 10⁻¹⁹
- MnS: Ksp = 7.0 × 10⁻¹⁶
- Bi2S3: Ksp = 3.9 × 10⁻¹⁵
- Ag2S: Ksp = 1.14 × 10⁻¹⁷

### Step 6: Identify the Highest Ksp Value
From the Ksp values:
- CuS: 8.9 × 10⁻¹⁹
- MnS: 7.0 × 10⁻¹⁶
- Bi2S3: 3.9 × 10⁻¹⁵
- Ag2S: 1.14 × 10⁻¹⁷

The highest Ksp value is for MnS (7.0 × 10⁻¹⁶).

### Step 7: Conclusion
Since the solubility is directly proportional to Ksp, the compound with the highest Ksp value is the most soluble. Therefore, **MnS is the most soluble compound among the given options.**