0.05 mole of NaOH is added to 5 liters of water What will be the pH of the solution ?

Options

A. 12
B. 7
C. 2
D. 10

Explanation

To find the pH of a solution when 0.05 moles of NaOH is added to 5 liters of water, we can follow these steps:

### Step 1: Determine the concentration of NaOH
NaOH dissociates completely in water to give Na⁺ and OH⁻ ions. Therefore, the concentration of OH⁻ ions will be equal to the concentration of NaOH.

- **Formula for concentration (C)**:
\[ C = \frac{\text{Number of moles}}{\text{Volume in liters}} \]
- **Given**:
- Number of moles of NaOH = 0.05 moles
- Volume of water = 5 liters

- **Calculation**:
\[ C = \frac{0.05 \text{ moles}}{5 \text{ liters}} = 0.01 \text{ M} \]

### Step 2: Find the concentration of OH⁻ ions
Since NaOH completely dissociates, the concentration of OH⁻ ions in the solution is also 0.01 M.

### Step 3: Use the ionic product of water to find [H⁺]
The ionic product of water (Kw) at 25°C is:
\[ K_w = [H^+][OH^-] = 1 \times 10^{-14} \]

We can rearrange this to find the concentration of H⁺ ions:
\[ [H^+] = \frac{K_w}{[OH^-]} \]
- **Substituting the values**:
\[ [H^+] = \frac{1 \times 10^{-14}}{0.01} = 1 \times 10^{-12} \text{ M} \]

### Step 4: Calculate the pH
The pH is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
- **Substituting the value of [H⁺]**:
\[ \text{pH} = -\log(1 \times 10^{-12}) = 12 \]

### Conclusion
The pH of the solution is 12.

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