Which set is not correct for the solubility product `(K_(SP))`, solubility `(S g//litre)` of sparingly soluble salt `A_(3)B_(2)(mol.wt=M)` in watrer ?

Options

A. `K_(SP)=108S^(5)`
B. `K_(SP)=[(3S)/(M)]^(2)[2S)/(M)]^(2)`
C. `K_(SP)=[3a^(2+)]^(3)[2B^(3-)]^(2)`
D. `[B^(3-)]=(2S)/(M)`

Explanation

To determine which set is not correct for the solubility product (Ksp) and solubility (S in g/litre) of the sparingly soluble salt A₃B₂, we will follow these steps:

### Step 1: Write the Dissociation Equation
The dissociation of the salt A₃B₂ in water can be represented as:
\[ A_3B_2 (s) \rightleftharpoons 3A^{2+} (aq) + 2B^{3-} (aq) \]

### Step 2: Determine the Molar Concentrations
From the dissociation equation, we can see that:
- For every 1 mole of A₃B₂ that dissolves, it produces 3 moles of \( A^{2+} \) and 2 moles of \( B^{3-} \).
- If the solubility of A₃B₂ is \( S \) mol/L, then:
- The concentration of \( A^{2+} \) will be \( 3S \)
- The concentration of \( B^{3-} \) will be \( 2S \)

### Step 3: Write the Expression for Ksp
The solubility product (Ksp) expression for the salt is given by:
\[ K_{sp} = [A^{2+}]^3 [B^{3-}]^2 \]

### Step 4: Substitute the Concentrations into the Ksp Expression
Substituting the concentrations we found in Step 2 into the Ksp expression:
\[ K_{sp} = (3S)^3 (2S)^2 \]
\[ K_{sp} = 27S^3 \cdot 4S^2 \]
\[ K_{sp} = 108S^5 \]

### Step 5: Analyze the Given Sets
Now we need to analyze the sets provided in the question. We will check if they correctly relate to the Ksp and solubility derived above.

1. **Set 1**: Ksp = 108S^5, which is correct.
2. **Set 2**: Concentration of \( B^{3-} \) is \( 2S \), which is also correct.
3. **Set 3**: If any set states that the concentration of \( A^{2+} \) is \( 3S \) but does not relate it correctly to Ksp, it would be incorrect.

### Conclusion
The set that does not correctly represent the relationship between Ksp and solubility will be the answer.

### Final Answer
The incorrect set is the one that misrepresents the concentration of ions or the Ksp value.

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