If for a binary weak electrolyte the solubility product is `4xx10^(-10) ` at 298K.Calculate its solubility is mol `dm^(-3)` at the same temperature

Options

A. `4xx10^(-5)`
B. `2xx10^(-5)`
C. `8xx10^(-10)`
D. `16xx10^(-20)`

Answer

To solve the problem, we need to calculate the solubility of a binary weak electrolyte given its solubility product (Ksp) at a specific temperature. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Electrolyte
A binary weak electrolyte can be represented as AB, which dissociates into its ions:
\[ AB \rightleftharpoons A^+ + B^- \]

### Step 2: Define Solubility
Let the solubility of the electrolyte AB be \( S \) mol/dm³. When it dissolves, it produces \( S \) mol/dm³ of \( A^+ \) ions and \( S \) mol/dm³ of \( B^- \) ions.

### Step 3: Write the Expression for Ksp
The solubility product constant (Ksp) is defined as:
\[ Ksp = [A^+][B^-] \]
Since both ions are produced in equal amounts from the dissociation of AB, we can express this as:
\[ Ksp = S \times S = S^2 \]

### Step 4: Substitute the Given Ksp Value
We are given that:
\[ Ksp = 4 \times 10^{-10} \]

So we can set up the equation:
\[ S^2 = 4 \times 10^{-10} \]

### Step 5: Solve for S
To find the solubility \( S \), we take the square root of both sides:
\[ S = \sqrt{4 \times 10^{-10}} \]
\[ S = 2 \times 10^{-5} \text{ mol/dm}^3 \]

### Final Answer
Thus, the solubility of the binary weak electrolyte at 298 K is:
\[ S = 2 \times 10^{-5} \text{ mol/dm}^3 \]