Assertion: pH of water increases with increases in temperature .
Reason : With increase in temperature, `K_w` of water increases.

Options

A. Assertion and reason both are correct statements and Reason is correct explanation for assertion.
B. Assertion and reason both are correct statement but reason is not correct explanation for assertion
C. Assertion is correct statement but reason is wrong statement.
D. Assertion is wrong statement but reason is correct statement

Answer

To analyze the assertion and reason provided in the question, we can follow these steps:

### Step 1: Understand the Assertion
The assertion states that the pH of water increases with an increase in temperature.

### Step 2: Understand the Reason
The reason given is that with an increase in temperature, the ion product of water, \( K_w \), increases.

### Step 3: Analyze the Ion Product of Water
The ion product of water (\( K_w \)) is defined as:
\[ K_w = [H^+][OH^-] \]
At higher temperatures, \( K_w \) increases, meaning that the concentrations of both \( H^+ \) and \( OH^- \) ions in pure water increase.

### Step 4: Relationship Between \( H^+ \) Concentration and pH
The pH of a solution is defined as:
\[ pH = -\log[H^+] \]
When the concentration of \( H^+ \) ions increases, the pH value actually decreases.

### Step 5: Conclusion
Since the assertion states that the pH increases with temperature, but we have established that the pH actually decreases as \( H^+ \) concentration increases (due to the increase in \( K_w \)), the assertion is false. The reason provided is true because \( K_w \) does increase with temperature.

### Final Answer
- Assertion: False
- Reason: True