Solubility product of the salt `A_xB_y` will be represented most suitably, if the solubility is represented by S

Options

A. `K_(sp)=X^yY^x(S)^(X""xy)`
B. `K_(sp)=X^y+Y^x+S^(x+y)`
C. `K_(sp)=X^xy^y(s)^(x+y)`
D. `K_(sp)=X*S^(x+y)*Y`

Answer

To find the solubility product (Ksp) of the salt \( A_xB_y \) when its solubility is represented by \( S \), we can follow these steps:

### Step 1: Write the Dissociation Equation
When the salt \( A_xB_y \) dissolves in water, it dissociates into its ions:
\[ A_xB_y (s) \rightleftharpoons x A^{y+} (aq) + y B^{x-} (aq) \]

### Step 2: Define the Solubility
Let the solubility of the salt \( A_xB_y \) be \( S \). This means that at equilibrium:
- The concentration of \( A^{y+} \) ions will be \( xS \) (since there are \( x \) moles of \( A^{y+} \) produced for every mole of \( A_xB_y \) that dissolves).
- The concentration of \( B^{x-} \) ions will be \( yS \) (since there are \( y \) moles of \( B^{x-} \) produced for every mole of \( A_xB_y \) that dissolves).

### Step 3: Write the Expression for Ksp
The solubility product \( K_{sp} \) is given by the product of the concentrations of the ions, each raised to the power of their coefficients in the balanced dissociation equation:
\[ K_{sp} = [A^{y+}]^x \cdot [B^{x-}]^y \]

### Step 4: Substitute the Concentrations
Substituting the expressions for the concentrations of the ions:
\[ K_{sp} = (xS)^x \cdot (yS)^y \]

### Step 5: Simplify the Expression
Now, we can simplify this expression:
\[ K_{sp} = x^x \cdot S^x \cdot y^y \cdot S^y \]
\[ K_{sp} = x^x \cdot y^y \cdot S^{x+y} \]

### Final Expression
Thus, the solubility product \( K_{sp} \) for the salt \( A_xB_y \) is:
\[ K_{sp} = x^x \cdot y^y \cdot S^{x+y} \]

### Summary
The solubility product \( K_{sp} \) of the salt \( A_xB_y \) is represented as:
\[ K_{sp} = x^x \cdot y^y \cdot S^{x+y} \]