statement-1: If water is heated of `50^(@)C` then pH will increase.
STATEMENT-2: `K_(w)` increases with increase in temperature.

Options

A. If both the statements are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B. If both the statements are TRUE AND STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C. If STATEMENT-1 is TRUE and STATEMETN-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To solve the given question, we will analyze both statements step by step.

### Step 1: Analyze Statement 1
**Statement 1:** If water is heated to 50°C, then pH will increase.

- At room temperature (25°C), water dissociates into hydrogen ions (H⁺) and hydroxide ions (OH⁻). The equilibrium can be represented as:
\[ H_2O \rightleftharpoons H^+ + OH^- \]
- The pH of pure water at 25°C is 7, which corresponds to a concentration of \( [H^+] = 1 \times 10^{-7} \, \text{mol/L} \).
- When the temperature increases, the dissociation of water also increases, leading to a higher concentration of both H⁺ and OH⁻ ions.

### Step 2: Effect of Temperature on pH
- As the temperature increases, the dissociation constant \( K_w \) (the ionic product of water) increases. This means that the concentration of H⁺ ions increases.
- Since pH is defined as:
\[ \text{pH} = -\log[H^+] \]
- If the concentration of H⁺ ions increases, the pH value will actually decrease, not increase.

**Conclusion for Statement 1:** Therefore, Statement 1 is **false**.

### Step 3: Analyze Statement 2
**Statement 2:** \( K_w \) increases with an increase in temperature.

- The dissociation of water is an endothermic process, which means that as the temperature increases, the equilibrium shifts to favor the formation of more H⁺ and OH⁻ ions.
- Thus, the value of \( K_w \), which is defined as:
\[ K_w = [H^+][OH^-] \]
- will increase with temperature.

**Conclusion for Statement 2:** Therefore, Statement 2 is **true**.

### Final Conclusion
- Statement 1 is false, and Statement 2 is true. Hence, the correct answer is that Statement 1 is incorrect and Statement 2 is correct.

### Summary of Results
- **Statement 1:** False
- **Statement 2:** True