What is the value of `pK_w` of water?

Options

A. 7
B. 10
C. 12
D. 14

Answer

To find the value of \( pK_w \) of water, we need to understand the relationship between the ionic product of water (\( K_w \)) and its \( pK_w \).

### Step-by-Step Solution:

1. **Understand the Ionic Product of Water (\( K_w \))**:
The ionic product of water is defined as:
\[ K_w = [H^+][OH^-] \]
At 25°C (298 K), the value of \( K_w \) is:
\[ K_w = 1.0 \times 10^{-14} \]

2. **Calculate \( pK_w \)**:
The \( pK_w \) is calculated using the formula:
\[ pK_w = -\log K_w \]
Substituting the value of \( K_w \):
\[ pK_w = -\log(1.0 \times 10^{-14}) \]

3. **Simplify the Logarithm**:
Using the properties of logarithms:
\[ pK_w = -(-14) \log(10) = 14 \]
Since \( \log(10) = 1 \), we have:
\[ pK_w = 14 \]

### Final Answer:
The value of \( pK_w \) of water at 25°C is:
\[ pK_w = 14 \]