If ionic product of water is `K_w=10^(-16)` at `4^@C` , then a solution with pH =7.5 at `4^@C` will

Options

A. Turn blue litmus red
B. Turn red litmus blue
C. Be neutral to litmus
D. Be alkaline

Answer

To solve the question, we need to analyze the given information and determine the nature of the solution with a pH of 7.5 at 4°C, where the ionic product of water (K_w) is given as \( K_w = 10^{-16} \).

### Step-by-Step Solution:

1. **Understanding the Ionic Product of Water**:
The ionic product of water at a given temperature is defined as:
\[ K_w = [H^+][OH^-] \]
At 4°C, we are given \( K_w = 10^{-16} \).

2. **Calculating the Concentration of Ions**:
At neutrality (pH = 7), the concentration of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) are equal. Therefore, we can express:
\[ [H^+] = [OH^-] = \sqrt{K_w} = \sqrt{10^{-16}} = 10^{-8} \text{ M} \]

3. **Calculating pH**:
The pH is calculated using the formula:
\[ pH = -\log[H^+] \]
For pure water at 4°C:
\[ pH = -\log(10^{-8}) = 8 \]
This indicates that at 4°C, pure water is neutral with a pH of 8.

4. **Analyzing the Given pH**:
The solution in question has a pH of 7.5. Since the neutral pH at 4°C is 8, a pH of 7.5 is lower than the neutral pH. This means the solution is acidic.

5. **Effect on Litmus Paper**:
- **Blue Litmus Paper**: Turns red in acidic solutions.
- **Red Litmus Paper**: Remains red in acidic solutions.

Since the solution is acidic (pH 7.5), blue litmus paper will turn red.

### Conclusion:
The solution with a pH of 7.5 at 4°C will turn blue litmus red.

### Final Answer:
The correct option is: **turn blue litmus red**.

---