Which of the following expression is not true ?

Options

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

Explanation

To determine which of the following expressions is not true regarding the ionic equilibrium of water, we can analyze each statement based on the principles of ionic equilibrium and the properties of water.

### Step-by-Step Solution:

1. **Understanding Kw**:
- The ionic product of water (Kw) is defined as the product of the molar concentrations of H⁺ and OH⁻ ions in pure water at a given temperature.
- At 25°C, Kw = [H⁺][OH⁻] = 1 × 10⁻¹⁴.

2. **Neutral Solution**:
- In a neutral solution, the concentrations of H⁺ and OH⁻ ions are equal.
- Let [H⁺] = [OH⁻] = x. Thus, x² = Kw = 1 × 10⁻¹⁴.
- Therefore, x = √(1 × 10⁻¹⁴) = 1 × 10⁻⁷ M.
- This means that in a neutral solution at 25°C, [H⁺] = [OH⁻] = 1 × 10⁻⁷ M.

3. **Acidic Solution**:
- In an acidic solution, the concentration of H⁺ ions is greater than 1 × 10⁻⁷ M, and the concentration of OH⁻ ions is less than 1 × 10⁻⁷ M.
- This maintains the relationship [H⁺][OH⁻] = Kw = 1 × 10⁻¹⁴.

4. **Temperature Dependence**:
- Kw is temperature-dependent. As the temperature increases, the value of Kw increases due to the endothermic nature of water ionization.
- Therefore, the statement that [H⁺] = [OH⁻] = 1 × 10⁻⁷ M for a neutral solution at all temperatures is incorrect.

5. **Evaluating the Statements**:
- **Statement 1**: H⁺ = OH⁻ = √Kw for a neutral solution. (True)
- **Statement 2**: H⁺ > √Kw and OH⁻ < √Kw for an acidic solution. (True)
- **Statement 3**: H⁺ < √Kw and OH⁻ > √Kw for a basic solution. (True)
- **Statement 4**: H⁺ = OH⁻ = 1 × 10⁻⁷ M for a neutral solution at all temperatures. (Not true)

### Conclusion:
The expression that is not true is **Statement 4**: H⁺ = OH⁻ = 1 × 10⁻⁷ M for a neutral solution at all temperatures.

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