In `Ca(OH)_(2)`, solution (aqueous), the molar concentration of `OH^(-)` is found to be x, the solubility of `Ca(OH)_(2)` in moles/litre is

Options

A. 2x
B. x
C. x/2
D. 4x

Answer

To find the solubility of calcium hydroxide, \( \text{Ca(OH)}_2 \), in moles per liter given that the molar concentration of \( \text{OH}^- \) ions is \( x \), we can follow these steps:

### Step 1: Write the dissociation equation
When calcium hydroxide dissolves in water, it dissociates according to the following equation:

\[ \text{Ca(OH)}_2 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + 2 \text{OH}^- (aq) \]

### Step 2: Define the solubility
Let the solubility of \( \text{Ca(OH)}_2 \) be \( S \) moles per liter. According to the dissociation equation:
- For every 1 mole of \( \text{Ca(OH)}_2 \) that dissolves, it produces 1 mole of \( \text{Ca}^{2+} \) and 2 moles of \( \text{OH}^- \).

### Step 3: Relate \( S \) to \( x \)
From the dissociation, we can see that:
- The concentration of \( \text{OH}^- \) ions produced is \( 2S \).
- We are given that the concentration of \( \text{OH}^- \) ions is \( x \).

Thus, we can set up the equation:
\[ 2S = x \]

### Step 4: Solve for \( S \)
To find the solubility \( S \), we rearrange the equation:
\[ S = \frac{x}{2} \]

### Conclusion
The solubility of \( \text{Ca(OH)}_2 \) in moles per liter is:
\[ S = \frac{x}{2} \]