Assertion (A): `pH` of water increases with an increase in temperature.
Reason (R) : `K_(w)` or water increases with increase in temperature.

Options

A. If both (A) and (R) are correc, and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct but (R) is not the correct explanation of (A).
C. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect, but (R) is correct.

Explanation

To solve the question regarding the assertion and reason about the pH of water and the ion product constant of water (Kw), we will analyze both statements step by step.

### Step 1: Understand the Assertion
**Assertion (A):** The pH of water increases with an increase in temperature.

- pH is defined as the negative logarithm of the hydrogen ion concentration:
\[ \text{pH} = -\log[H^+] \]
- As the temperature increases, we need to consider how the dissociation of water is affected.

### Step 2: Analyze the Dissociation of Water
The dissociation of water can be represented as:
\[ H_2O \rightleftharpoons H^+ + OH^- \]
This reaction is endothermic, meaning it absorbs heat.

### Step 3: Apply Le Chatelier's Principle
According to Le Chatelier's Principle, if we increase the temperature of an endothermic reaction, the equilibrium will shift to the right to absorb the added heat. This means more \(H^+\) ions and \(OH^-\) ions will be produced.

### Step 4: Effect on pH
- As the concentration of \(H^+\) ions increases, the pH of the solution will decrease because:
\[ \text{pH} = -\log[H^+] \]
- Therefore, the assertion that the pH of water increases with an increase in temperature is **incorrect**.

### Step 5: Understand the Reason
**Reason (R):** The \(K_w\) of water increases with an increase in temperature.

- The ion product constant of water (\(K_w\)) is defined as:
\[ K_w = [H^+][OH^-] \]
- Since both \(H^+\) and \(OH^-\) concentrations increase with temperature, \(K_w\) also increases.

### Step 6: Conclusion
- The reason that \(K_w\) increases with temperature is **correct**.
- Therefore, the assertion is incorrect while the reason is correct.

### Final Answer
The correct option is **D**: Assertion is incorrect but Reason is correct.

---