Which of the following metal sulphides have maximum solubility in water ?

Options

A. `HgS (K_(sp) = 10^(-54))`
B. `CdS (K_(sp) = 10^(-30))`
C. `FeS(K_(sp) = 10^(-20))`
D. `ZnS (K_(sp) = 10^(-22))`

Explanation

To solve the question regarding which metal sulfides have the maximum solubility in water, we need to analyze the solubility product constant (Ksp) values of the given metal sulfides. The solubility of a compound in water is directly related to its Ksp value; a higher Ksp indicates greater solubility.

### Step-by-Step Solution:

1. **Understand the Relationship Between Ksp and Solubility**:
- The solubility (S) of a salt in water can be expressed as:
\[ S = \sqrt{K_{sp}} \]
- Thus, if Ksp increases, solubility also increases.

2. **Identify the Ksp Values**:
- For the given metal sulfides, we need to identify their Ksp values. Let's assume we have the following metal sulfides with their respective Ksp values:
- FeS: \( Ksp = 10^{-20} \)
- Other metal sulfides (hypothetical values for illustration):
- ZnS: \( Ksp = 10^{-25} \)
- PbS: \( Ksp = 10^{-28} \)
- Ag2S: \( Ksp = 10^{-50} \)

3. **Compare the Ksp Values**:
- From the values given:
- FeS has the highest Ksp value of \( 10^{-20} \).
- ZnS has a Ksp of \( 10^{-25} \).
- PbS has a Ksp of \( 10^{-28} \).
- Ag2S has a Ksp of \( 10^{-50} \).
- Clearly, \( 10^{-20} > 10^{-25} > 10^{-28} > 10^{-50} \).

4. **Determine the Maximum Solubility**:
- Since FeS has the highest Ksp value, it will have the maximum solubility in water compared to the other metal sulfides.

5. **Conclusion**:
- Therefore, the metal sulfide with the maximum solubility in water is **FeS**.

### Final Answer:
**FeS** has the maximum solubility in water among the given metal sulfides.

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