What is the pH of a solution obtained by dissolving 0.0005 mole of the strong electrolyte, calcium hydroxide, `Ca(OH)_(2)` , to form 100 ml of a saturated solution (aqueous)? `(K_(w)=1.0xx10^(-14) "mole"^(2) "litre"^(-2))`

Options

A. `9.8`
B. `11.7`
C. `12.0`
D. `3.0`

Answer

To find the pH of a solution obtained by dissolving 0.0005 moles of calcium hydroxide (Ca(OH)₂) in 100 mL of water, we can follow these steps:

### Step 1: Calculate the concentration of Ca(OH)₂
Since calcium hydroxide dissociates into one calcium ion (Ca²⁺) and two hydroxide ions (OH⁻), we need to calculate the concentration of hydroxide ions produced.

1. **Moles of Ca(OH)₂** = 0.0005 moles
2. **Volume of solution** = 100 mL = 0.1 L

The concentration of Ca(OH)₂ in the solution is:
\[ \text{Concentration of Ca(OH)₂} = \frac{\text{moles}}{\text{volume}} = \frac{0.0005 \text{ moles}}{0.1 \text{ L}} = 0.005 \text{ M} \]

### Step 2: Calculate the concentration of OH⁻ ions
Since each mole of Ca(OH)₂ produces 2 moles of OH⁻ ions:
\[ \text{Concentration of OH}^- = 2 \times \text{Concentration of Ca(OH)₂} = 2 \times 0.005 \text{ M} = 0.01 \text{ M} \]

### Step 3: Calculate the pOH of the solution
The pOH of the solution can be calculated using the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the concentration of OH⁻:
\[ \text{pOH} = -\log(0.01) = -\log(10^{-2}) = 2 \]

### Step 4: Calculate the pH of the solution
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
We can find the pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 2 = 12 \]

### Final Answer
The pH of the solution is **12**.

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