A saturated solution of `Ag_(2)SO_(4) is 2.5 xx 10^(-2)M`. The value of its solubility product is

Options

A. `62.5 xx 10^(-6)`
B. `6.25 xx 10^(-4)`
C. `15.625 xx 10^(-10)`
D. `3.125 xx 10^(-6)`

Explanation

To find the solubility product (Ksp) of a saturated solution of Ag2SO4 with a concentration of 2.5 x 10^(-2) M, we can follow these steps:

### Step 1: Write the Dissociation Equation
Ag2SO4 dissociates in water according to the following equation:
\[ \text{Ag}_2\text{SO}_4 (s) \rightleftharpoons 2 \text{Ag}^+ (aq) + \text{SO}_4^{2-} (aq) \]

### Step 2: Define Molar Solubility
Let the molar solubility of Ag2SO4 be \( S \). From the dissociation equation, we can see that:
- For every 1 mole of Ag2SO4 that dissolves, it produces 2 moles of Ag+ and 1 mole of SO4^2-.
- Therefore, the concentration of Ag+ will be \( 2S \) and the concentration of SO4^2- will be \( S \).

### Step 3: Write the Expression for Ksp
The solubility product constant (Ksp) is given by the expression:
\[ Ksp = [\text{Ag}^+]^2 [\text{SO}_4^{2-}] \]
Substituting the concentrations from Step 2:
\[ Ksp = (2S)^2 (S) \]
This simplifies to:
\[ Ksp = 4S^3 \]

### Step 4: Substitute the Given Solubility
We are given that the molar solubility \( S \) is \( 2.5 \times 10^{-2} \) M. Substituting this value into the Ksp expression:
\[ Ksp = 4(2.5 \times 10^{-2})^3 \]

### Step 5: Calculate Ksp
Now we calculate \( (2.5 \times 10^{-2})^3 \):
\[ (2.5 \times 10^{-2})^3 = 15.625 \times 10^{-6} \]
Now, substituting this back into the Ksp equation:
\[ Ksp = 4 \times 15.625 \times 10^{-6} \]
Calculating this gives:
\[ Ksp = 62.5 \times 10^{-6} \]

### Step 6: Final Answer
Thus, the value of the solubility product \( Ksp \) for Ag2SO4 is:
\[ Ksp = 6.25 \times 10^{-5} \]