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 problem, we need to determine whether a solution with a pH of 7.5 at 4°C is acidic, basic, or neutral, given that the ionic product of water (K_w) is \(10^{-16}\) at this temperature.

### Step-by-Step Solution:

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

2. **Calculate the Concentration of H\(^+\) and OH\(^-\) at Neutral pH**:
At neutral pH, the concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) are equal. Let this concentration be \(x\).
\[ K_w = x^2 = 10^{-16} \]
Therefore, to find \(x\):
\[ x = \sqrt{10^{-16}} = 10^{-8} \, \text{mol/L} \]
This means that at neutral pH, \([H^+] = [OH^-] = 10^{-8} \, \text{mol/L}\).

3. **Determine the pH of the Neutral Solution**:
The pH is defined as:
\[ pH = -\log[H^+] \]
For the neutral solution:
\[ pH = -\log(10^{-8}) = 8 \]

4. **Compare the Given pH with Neutral pH**:
The pH of the solution given in the problem is 7.5. Since 7.5 is less than 8, this indicates that the solution is acidic.

5. **Conclusion**:
Since the pH of the solution (7.5) is less than the neutral pH (8), we conclude that the solution is acidic.

### Final Answer:
The solution with a pH of 7.5 at 4°C is **acidic**.

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