For a reaction, `A_(x),B_(y)hArrxA^(y+)+yB^(x-),K_(sp)` xan be represented as

Options

A. `[A^(y+)]^(x)[B^(x-)]^(y)`
B. `[A]^(y)[B]^(x)`
C. `[A]^(x)[B]^(y)`
D. `[A]^(x+y)[B]^(x-y)`

Explanation

To find the expression for the solubility product constant (Ksp) for the given reaction \( AX_{y} \rightleftharpoons X A^{y+} + Y B^{x-} \), we can follow these steps:

### Step 1: Write the balanced dissociation reaction
The reaction shows the dissociation of the salt \( AX_{y} \) into its ions:
\[ AX_{y} \rightleftharpoons X A^{y+} + Y B^{x-} \]

### Step 2: Identify the stoichiometric coefficients
From the balanced equation, we can see:
- The coefficient for \( A^{y+} \) is \( X \).
- The coefficient for \( B^{x-} \) is \( Y \).

### Step 3: Write the expression for Ksp
The solubility product constant \( Ksp \) is defined as the product of the concentrations of the ions, each raised to the power of their respective coefficients from the balanced equation. Therefore, we can write:
\[ K_{sp} = [A^{y+}]^{X} \times [B^{x-}]^{Y} \]

### Step 4: Substitute the concentrations
Let:
- \( [A^{y+}] = a \)
- \( [B^{x-}] = b \)

Thus, we can rewrite the Ksp expression as:
\[ K_{sp} = [A^{y+}]^{X} \times [B^{x-}]^{Y} = a^{X} \times b^{Y} \]

### Final Expression
Thus, the final expression for \( K_{sp} \) is:
\[ K_{sp} = [A^{y+}]^{X} \times [B^{x-}]^{Y} \]