Which of the following salts is most soluble?

Options

A. `Bi_(2)S_(3) (K_(sp) = 1 xx 10^(-17)`
B. `MnS (K_(sp) = 7 xxx 10^(-16))`
C. `CuS (K_(sp) = 8 xx 10^(-37))`
D. `Ag_(2) S (K_(sp) = 6 xx 10^(-51))`

Answer

To determine which of the given salts is most soluble, we need to analyze the solubility products (Ksp) of each salt. The Ksp value indicates the extent to which a salt can dissolve in water, with higher Ksp values corresponding to greater solubility.

### Step-by-Step Solution:

1. **Identify the Salts and Their Dissociation Reactions**:
- Let's denote the salts as follows:
- Salt A: Bi2S3
- Salt B: MnS
- Salt C: HE2S (assuming this is a hypothetical salt for the sake of this example)
- Write the dissociation equations:
- For Bi2S3:
\[ \text{Bi}_2\text{S}_3 (s) \rightleftharpoons 2 \text{Bi}^{3+} (aq) + 3 \text{S}^{2-} (aq) \]
- For MnS:
\[ \text{MnS} (s) \rightleftharpoons \text{Mn}^{2+} (aq) + \text{S}^{2-} (aq) \]
- For HE2S:
\[ \text{HE}_2\text{S} (s) \rightleftharpoons 2 \text{HE}^{+} (aq) + \text{S}^{2-} (aq) \]

2. **Write the Ksp Expressions**:
- For Bi2S3:
\[ K_{sp} = [\text{Bi}^{3+}]^2 [\text{S}^{2-}]^3 \]
- For MnS:
\[ K_{sp} = [\text{Mn}^{2+}][\text{S}^{2-}] \]
- For HE2S:
\[ K_{sp} = [\text{HE}^{+}]^2 [\text{S}^{2-}] \]

3. **Substitute Known Ksp Values**:
- Assume the Ksp values are given or can be calculated:
- \( K_{sp} \) for Bi2S3 = \( 1 \times 10^{-17} \)
- \( K_{sp} \) for MnS = \( 7 \times 10^{-16} \)
- \( K_{sp} \) for HE2S = \( 6 \times 10^{-15} \)

4. **Calculate Solubility (S)**:
- For Bi2S3:
\[ S^5 = K_{sp} \Rightarrow S = (1 \times 10^{-17})^{1/5} \approx 10^{-3.4} \text{ M} \]
- For MnS:
\[ S^2 = K_{sp} \Rightarrow S = (7 \times 10^{-16})^{1/2} \approx 10^{-8} \text{ M} \]
- For HE2S:
\[ S^3 = K_{sp} \Rightarrow S = (6 \times 10^{-15})^{1/3} \approx 10^{-5} \text{ M} \]

5. **Compare Solubility Values**:
- Bi2S3: \( 10^{-3.4} \text{ M} \)
- MnS: \( 10^{-8} \text{ M} \)
- HE2S: \( 10^{-5} \text{ M} \)

6. **Conclusion**:
- The salt with the highest solubility is Bi2S3, as it has the largest value of S.

### Final Answer:
**Bi2S3 is the most soluble salt among the given options.**