If the temperature of water is increased from `25^@C" to "45^@C`, the pH of water at `45^@C` will be

Options

A. 7
B. slightly greater than 7
C. `lt 7`
D. 8

Answer

To determine the pH of water at 45°C, we need to understand how temperature affects the ionization of water and the pH scale.

### Step-by-Step Solution:

1. **Understand the Ionization of Water**:
Water undergoes self-ionization according to the equation:
\[ 2H_2O \rightleftharpoons H_3O^+ + OH^- \]
At 25°C, the ion product of water (K_w) is \(1.0 \times 10^{-14}\), which gives a neutral pH of 7.

2. **Effect of Temperature on K_w**:
As the temperature increases, the ion product of water (K_w) also increases. At 45°C, K_w is higher than at 25°C. This means that the concentrations of \(H_3O^+\) and \(OH^-\) ions will also increase.

3. **Calculate the New pH**:
At 45°C, the pH of pure water will no longer be 7 because the increase in \(H_3O^+\) concentration means that the solution is more acidic. The exact value of K_w at 45°C is approximately \(3.5 \times 10^{-14}\).

To find the new pH:
\[ K_w = [H_3O^+][OH^-] \]
Since water is neutral, we have:
\[ [H_3O^+] = [OH^-] = x \]
Therefore:
\[ K_w = x^2 \]
Solving for \(x\):
\[ x = \sqrt{K_w} = \sqrt{3.5 \times 10^{-14}} \approx 5.92 \times 10^{-7} \, \text{M} \]

4. **Calculate pH**:
The pH is calculated using the formula:
\[ pH = -\log[H_3O^+] \]
Substituting the value of \(x\):
\[ pH = -\log(5.92 \times 10^{-7}) \approx 6.23 \]

5. **Conclusion**:
Therefore, the pH of water at 45°C is approximately 6.23, which is less than 7, indicating that the water is slightly acidic at this temperature.

### Final Answer:
The pH of water at 45°C will be approximately **6.23**.