Which statement is false ? (Assume complete dissociation in each case)

Options

A. If 2.0 L of a solution of `H_(2)SO_(4)` contains 0.1 mole, then pH of the solution is 1
B. The concentration of `OH^(-)` ions in 0.005 M HNO3 is `2.0xx10^(-12) (mol)/L`
C. The pH of 0.01 M KOH is 12
D. In a 0.001 M solution of NaOH the concentration of `H^(+)` ions is `10^(-3) (mol)/L`

Explanation

To determine which statement is false, we will analyze each option step by step.

### Step 1: Analyze Option 1
**Statement**: If 2.0 liters of a solution of H₂SO₄ contains 0.1 molar, then the pH of the solution is 1.

1. **Dissociation of H₂SO₄**: H₂SO₄ is a strong dibasic acid, meaning it dissociates completely into 2 moles of H⁺ ions for every mole of H₂SO₄.
- H₂SO₄ → 2 H⁺ + SO₄²⁻

2. **Calculate moles of H⁺**:
- Given concentration of H₂SO₄ = 0.1 M in 2.0 L.
- Moles of H₂SO₄ = 0.1 mol/L × 2 L = 0.2 moles.
- Therefore, moles of H⁺ = 0.2 moles × 2 = 0.4 moles.

3. **Calculate concentration of H⁺**:
- Concentration of H⁺ = moles of H⁺ / volume = 0.4 moles / 2 L = 0.2 M.

4. **Calculate pH**:
- pH = -log[H⁺] = -log(0.2) = 0.7 (approximately).

**Conclusion**: The statement that the pH is 1 is **false**.

### Step 2: Analyze Option 2
**Statement**: The concentration of OH⁻ ions in 0.005 molar HNO₃ is 2 x 10⁻¹² mole per liter.

1. **Dissociation of HNO₃**: HNO₃ is a strong acid and dissociates completely.
- HNO₃ → H⁺ + NO₃⁻

2. **Calculate concentration of H⁺**:
- Concentration of H⁺ = 0.005 M.

3. **Calculate concentration of OH⁻ using Kw**:
- Kw = [H⁺][OH⁻] = 1 x 10⁻¹⁴.
- [OH⁻] = Kw / [H⁺] = 1 x 10⁻¹⁴ / 0.005 = 2 x 10⁻¹² M.

**Conclusion**: This statement is **true**.

### Step 3: Analyze Option 3
**Statement**: The pH of 0.01 molar KOH is 12.

1. **Dissociation of KOH**: KOH is a strong base and dissociates completely.
- KOH → K⁺ + OH⁻

2. **Calculate concentration of OH⁻**:
- Concentration of OH⁻ = 0.01 M.

3. **Calculate pOH**:
- pOH = -log[OH⁻] = -log(0.01) = 2.

4. **Calculate pH**:
- pH = 14 - pOH = 14 - 2 = 12.

**Conclusion**: This statement is **true**.

### Step 4: Analyze Option 4
**Statement**: In a 0.001 molar solution of sodium hydroxide, the concentration of H⁺ ion is 10⁻³ mole per liter.

1. **Dissociation of NaOH**: NaOH is a strong base and dissociates completely.
- NaOH → Na⁺ + OH⁻

2. **Calculate concentration of OH⁻**:
- Concentration of OH⁻ = 0.001 M.

3. **Calculate pOH**:
- pOH = -log[OH⁻] = -log(0.001) = 3.

4. **Calculate pH**:
- pH = 14 - pOH = 14 - 3 = 11.

5. **Calculate concentration of H⁺**:
- pH = -log[H⁺] → [H⁺] = 10⁻¹¹ M.

**Conclusion**: The statement that the concentration of H⁺ is 10⁻³ M is **false**.

### Final Conclusion
The false statement is from **Option 1** and **Option 4**. However, since the question asks for which statement is false, we conclude that:

**The false statement is from Option 4**: "In a 0.001 molar solution of sodium hydroxide, the concentration of H⁺ ion is 10⁻³ mole per liter."