The solubility product for a salt of the type AB is `4xx10^(-8)`. What is the molarity of its standard solution?

Options

A. `2xx10^(-4)mol//L`
B. `16xx10^(-16)mol//L`
C. `2xx10^(-16)mol//L`
D. `4xx10^(-4)mol//L`

Answer

To find the molarity of the standard solution of the salt AB with a given solubility product (Ksp) of \( 4 \times 10^{-8} \), we can follow these steps:

### Step 1: Write the Dissociation Equation
The salt AB dissociates in water as follows:
\[ AB \rightleftharpoons A^+ + B^- \]

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

### Step 3: Write the Expression for Ksp
The solubility product \( Ksp \) is given by:
\[ Ksp = [A^+][B^-] \]
Since both ions are produced in equal amounts, we can substitute:
\[ Ksp = S \times S = S^2 \]

### Step 4: Substitute the Given Ksp Value
We know that:
\[ Ksp = 4 \times 10^{-8} \]
Thus, we can write:
\[ S^2 = 4 \times 10^{-8} \]

### Step 5: Solve for S
To find \( S \), we take the square root of both sides:
\[ S = \sqrt{4 \times 10^{-8}} \]
\[ S = \sqrt{4} \times \sqrt{10^{-8}} \]
\[ S = 2 \times 10^{-4} \]

### Step 6: Conclusion
The molarity of the standard solution of the salt AB is:
\[ S = 2 \times 10^{-4} \, \text{mol/L} \]

### Final Answer
The molarity of the standard solution is \( 2 \times 10^{-4} \, \text{M} \).

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