Among the following statements
a) If two salts have equal solubility then their solubility products are equal.
b) `BaSO_(4)` , in more soluble in water than in dil. `H_(2),SO_(4)`
( c)When KI is added to `Pbl_(2)`, then the`[Pb^(2+)]` decreases
d) In any solution containing AgCI, the value of `[Ag^(+)] [CI^(-)]` is constant at constant temperature.

Options

A. All are correct
B. a, b and d are correct
C. a, c andd are correct
D. b, c and d are correct

Answer

To solve the question regarding the correctness of the given statements, we will analyze each statement one by one.

### Step 1: Analyze Statement A
**Statement A:** If two salts have equal solubility, then their solubility products are equal.

**Solution:**
- Let’s consider two salts: \( BaCl_2 \) and \( MgSO_4 \).
- For \( BaCl_2 \):
- Dissociation: \( BaCl_2 \rightarrow Ba^{2+} + 2Cl^{-} \)
- If the solubility is \( s \), then:
- \( [Ba^{2+}] = s \)
- \( [Cl^{-}] = 2s \)
- Solubility product \( K_{sp} = [Ba^{2+}][Cl^{-}]^2 = s(2s)^2 = 4s^3 \).

- For \( MgSO_4 \):
- Dissociation: \( MgSO_4 \rightarrow Mg^{2+} + SO_4^{2-} \)
- If the solubility is \( s \), then:
- \( [Mg^{2+}] = s \)
- \( [SO_4^{2-}] = s \)
- Solubility product \( K_{sp} = [Mg^{2+}][SO_4^{2-}] = s \cdot s = s^2 \).

- Since \( K_{sp} \) for \( BaCl_2 \) is \( 4s^3 \) and for \( MgSO_4 \) is \( s^2 \), they are not equal even if the solubility \( s \) is the same.

**Conclusion:** Statement A is **incorrect**.

### Step 2: Analyze Statement B
**Statement B:** \( BaSO_4 \) is more soluble in water than in dilute \( H_2SO_4 \).

**Solution:**
- \( BaSO_4 \) dissociates in water to form \( Ba^{2+} \) and \( SO_4^{2-} \) ions.
- In dilute \( H_2SO_4 \), there is a common ion \( SO_4^{2-} \) present.
- The presence of a common ion decreases the solubility of \( BaSO_4 \) due to the common ion effect.

**Conclusion:** Statement B is **correct**.

### Step 3: Analyze Statement C
**Statement C:** When KI is added to \( PbI_2 \), then the \( [Pb^{2+}] \) decreases.

**Solution:**
- \( PbI_2 \) dissociates into \( Pb^{2+} \) and \( 2I^{-} \).
- Adding KI introduces more \( I^{-} \) ions into the solution.
- The increased concentration of \( I^{-} \) will shift the equilibrium to the left (according to Le Chatelier's principle), thus decreasing the concentration of \( Pb^{2+} \).

**Conclusion:** Statement C is **correct**.

### Step 4: Analyze Statement D
**Statement D:** In any solution containing \( AgCl \), the value of \( [Ag^{+}][Cl^{-}] \) is constant at constant temperature.

**Solution:**
- \( AgCl \) is a sparingly soluble salt that dissociates into \( Ag^{+} \) and \( Cl^{-} \).
- The solubility product \( K_{sp} \) is defined as \( K_{sp} = [Ag^{+}][Cl^{-}] \).
- At a constant temperature, \( K_{sp} \) remains constant regardless of the concentrations of \( Ag^{+} \) and \( Cl^{-} \).

**Conclusion:** Statement D is **correct**.

### Final Conclusion
- **Correct Statements:** B, C, and D.
- **Incorrect Statement:** A.