Which of the following expression is not true ?

Options

A. `[H^+]=[OH^-]=sqrtK_w` for a neutral solution at all temperatures.
B. `[H^+] gt sqrtK_w and [OH^-] lt sqrtKw` for an acidic solution
C. `[H^+] lt sqrtK_w and [OH^-] gt sqrtKw` for an alkaline solution
D. `[H^+]=[OH^-]=10^(-7)` M for a neutral solution at all temperature.

Answer

To determine which of the following expressions is not true regarding ionic equilibrium, we will analyze each statement systematically.

### Step-by-Step Solution:

1. **Understanding the Ionic Product of Water (Kw)**:
- The ionic product of water (Kw) is defined as:
\[ K_w = [H^+][OH^-] \]
- At 25°C, \( K_w = 1.0 \times 10^{-14} \).

2. **Analyzing Statement A**:
- **Statement A**: \( [H^+] = [OH^-] = \sqrt{K_w} \) for neutral solutions at all temperatures.
- This statement is true at 25°C because:
\[ [H^+] = [OH^-] = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7} \, \text{M} \]
- However, this equality holds true only at 25°C. At other temperatures, \( K_w \) changes, and thus the concentrations will also change. Therefore, this statement is not universally true.

3. **Analyzing Statement B**:
- **Statement B**: \( [H^+] > \sqrt{K_w} \) and \( [OH^-] < \sqrt{K_w} \) for acidic solutions.
- This statement is true because in acidic solutions, the concentration of hydrogen ions increases, making \( [H^+] \) greater than \( \sqrt{K_w} \) and consequently \( [OH^-] \) must be less than \( \sqrt{K_w} \).

4. **Analyzing Statement C**:
- **Statement C**: \( [OH^-] > \sqrt{K_w} \) and \( [H^+] < \sqrt{K_w} \) for basic solutions.
- This statement is also true. In basic solutions, the concentration of hydroxide ions increases, leading to \( [OH^-] \) being greater than \( \sqrt{K_w} \) and \( [H^+] \) being less than \( \sqrt{K_w} \).

5. **Analyzing Statement D**:
- **Statement D**: \( [H^+] = [OH^-] \) at all neutral solutions.
- This statement is false because while \( [H^+] = [OH^-] \) at 25°C, this equality does not hold at all temperatures. As temperature changes, \( K_w \) changes, which affects the concentrations of \( H^+ \) and \( OH^- \).

### Conclusion:
The expression that is **not true** is **Statement D**: \( [H^+] = [OH^-] \) at all neutral solutions.