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

Options

A. (a) `CdS (K_(sp) = 36 xx 10^(-30))`
B. (b) `FeS (K_(sp) = 11 xx 10^(-20))`
C. (c) `HgS(K_(sp) = 32 xx 10^(-54))`
D. (d) `ZnS(K_(sp) = 11 xx 10^(-22))`

Explanation

To determine which metal sulfide has the maximum solubility in water, we can follow these steps:

### Step 1: Understand the Dissolution of Metal Sulfides
When a metal sulfide (MS) dissolves in water, it dissociates into metal ions (M²⁺) and sulfide ions (S²⁻):
\[ \text{MS} \rightleftharpoons \text{M}^{2+} + \text{S}^{2-} \]

### Step 2: Write the Expression for Solubility Product (Ksp)
The solubility product (Ksp) for this dissociation can be expressed as:
\[ K_{sp} = [\text{M}^{2+}][\text{S}^{2-}] \]
Where \([\text{M}^{2+}]\) is the molar solubility of the metal ion and \([\text{S}^{2-}]\) is the molar solubility of the sulfide ion.

### Step 3: Compare Ksp Values
We are given the Ksp values for the following metal sulfides:
- CdS: \( K_{sp} = 36 \times 10^{-30} \)
- FeS: \( K_{sp} = 11 \times 10^{-20} \)
- HgS: \( K_{sp} = 32 \times 10^{-54} \)
- ZnS: \( K_{sp} = 11 \times 10^{-22} \)

### Step 4: Identify the Highest Ksp
To find out which metal sulfide has the maximum solubility, we need to identify the highest Ksp value among the given options:
- CdS: \( 36 \times 10^{-30} \)
- FeS: \( 11 \times 10^{-20} \)
- HgS: \( 32 \times 10^{-54} \)
- ZnS: \( 11 \times 10^{-22} \)

### Step 5: Conclusion
From the comparison:
- FeS has the highest Ksp value of \( 11 \times 10^{-20} \), which indicates it has the maximum solubility in water.

### Final Answer
**FeS (Iron(II) sulfide) has the maximum solubility in water.**

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