The solubility product of CuS, Ag2S and HgS are `10^(-31),10^(-44),10^(-54)` respectively. The solubility of these sulphides are in the order
(a)`Ag2S gt HgS gt CuS`
(b)`HgS gt CdS gt CuS`
(c)`Ag2S gt CuS gt HgS`
(d)`CuS gt CdS gt HgS`

Options

A. `Ag2S gt HgS gt CuS`
B. `HgS gt CdS gt CuS`
C. `Ag2S gt CuS gt HgS`
D. `CuS gt CdS gt HgS`

Explanation

To determine the order of solubility of CuS, Ag2S, and HgS based on their solubility products (Ksp), we will first write the dissociation equations for each sulfide and then calculate their solubility (S) from the given Ksp values.

### Step 1: Write the dissociation equations and Ksp expressions

1. **For CuS:**
\[ \text{CuS} \rightleftharpoons \text{Cu}^+ + \text{S}^{2-} \]
The solubility product expression is:
\[ K_{sp} = [\text{Cu}^+][\text{S}^{2-}] = S \cdot S = S^2 \]

2. **For Ag2S:**
\[ \text{Ag}_2\text{S} \rightleftharpoons 2\text{Ag}^+ + \text{S}^{2-} \]
The solubility product expression is:
\[ K_{sp} = [\text{Ag}^+]^2[\text{S}^{2-}] = (2S)^2 \cdot S = 4S^3 \]

3. **For HgS:**
\[ \text{HgS} \rightleftharpoons \text{Hg}^{2+} + \text{S}^{2-} \]
The solubility product expression is:
\[ K_{sp} = [\text{Hg}^{2+}][\text{S}^{2-}] = S \cdot S = S^2 \]

### Step 2: Substitute Ksp values and solve for S

1. **For CuS:**
\[ K_{sp} = 10^{-31} = S^2 \implies S = \sqrt{10^{-31}} = 10^{-15.5} \]

2. **For Ag2S:**
\[ K_{sp} = 10^{-44} = 4S^3 \implies S^3 = \frac{10^{-44}}{4} = 2.5 \times 10^{-45} \implies S = \sqrt[3]{2.5 \times 10^{-45}} \approx 10^{-15} \text{ (approximately)} \]

3. **For HgS:**
\[ K_{sp} = 10^{-54} = S^2 \implies S = \sqrt{10^{-54}} = 10^{-27} \]

### Step 3: Compare the solubility values

Now we have the solubility values:
- **CuS:** \( S \approx 10^{-15.5} \)
- **Ag2S:** \( S \approx 10^{-15} \)
- **HgS:** \( S \approx 10^{-27} \)

### Step 4: Order of solubility

From the calculated solubility values, we can see that:
- Ag2S has the highest solubility,
- CuS has a moderate solubility,
- HgS has the lowest solubility.

Thus, the order of solubility is:
\[ \text{Ag}_2\text{S} > \text{CuS} > \text{HgS} \]

### Conclusion

The correct answer is option (c): **Ag2S > CuS > HgS**.

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