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 determine the solubility product (Ksp) of the salt \( A_xB_y \) in terms of its solubility \( S \), 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. The dissociation can be represented as:
\[ A_xB_y (s) \rightleftharpoons x A^{+} (aq) + y B^{-} (aq) \]

### Step 2: Define the Solubility
Let the solubility of the salt \( A_xB_y \) be represented by \( S \). At equilibrium, the concentrations of the ions will be:
- The concentration of \( A^{+} \) will be \( xS \)
- The concentration of \( B^{-} \) will be \( yS \)

### Step 3: Write the Expression for Ksp
The solubility product \( K_{sp} \) is defined as the product of the concentrations of the ions, each raised to the power of their respective stoichiometric coefficients:
\[ K_{sp} = [A^{+}]^x [B^{-}]^y \]
Substituting the equilibrium concentrations:
\[ K_{sp} = (xS)^x (yS)^y \]

### Step 4: Simplify the Expression
Now, simplify the expression:
\[ K_{sp} = x^x S^x \cdot y^y S^y \]
Combining the terms gives:
\[ K_{sp} = x^x y^y S^{x+y} \]

### Final Expression
Thus, the solubility product \( K_{sp} \) of the salt \( A_xB_y \) can be represented as:
\[ K_{sp} = x^x y^y S^{x+y} \]

### Conclusion
The correct representation of the solubility product in terms of solubility \( S \) is:
\[ K_{sp} = x^x y^y S^{x+y} \]