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 regarding the dissociation of acids and bases, we will analyze each statement step by step.

### Step 1: Analyze the first statement regarding H2SO4
- **Given**: 2 liters of H2SO4 solution contains 0.1 moles.
- **Dissociation**: H2SO4 dissociates completely into 2 H⁺ ions and 1 SO₄²⁻ ion.
- **Calculation**:
- Moles of H⁺ produced = 2 × 0.1 = 0.2 moles.
- Concentration of H⁺ = Moles of H⁺ / Volume = 0.2 moles / 2 L = 0.1 M.
- **pH Calculation**:
- pH = -log[H⁺] = -log(0.1) = 1.
- **Conclusion**: The statement regarding the pH being 1 is correct.

### Step 2: Analyze the second statement regarding HNO3
- **Given**: 0.005 molar HNO3.
- **Dissociation**: HNO3 dissociates into H⁺ and NO₃⁻.
- **Calculation**:
- Concentration of H⁺ = 0.005 M.
- Using the ion product of water (Kw = 1 × 10⁻¹⁴):
- [OH⁻] = Kw / [H⁺] = 1 × 10⁻¹⁴ / 0.005 = 2 × 10⁻¹² M.
- **Conclusion**: The statement regarding the concentration of OH⁻ ions is correct.

### Step 3: Analyze the third statement regarding KOH
- **Given**: 0.01 molar KOH.
- **Dissociation**: KOH dissociates into K⁺ and OH⁻.
- **Calculation**:
- Concentration of OH⁻ = 0.01 M.
- pOH = -log(0.01) = 2.
- pH = 14 - pOH = 14 - 2 = 12.
- **Conclusion**: The statement regarding the pH being 12 is correct.

### Step 4: Analyze the fourth statement regarding NaOH
- **Given**: 0.001 molar NaOH.
- **Dissociation**: NaOH dissociates into Na⁺ and OH⁻.
- **Calculation**:
- Concentration of OH⁻ = 0.001 M.
- Using the ion product of water (Kw = 1 × 10⁻¹⁴):
- [H⁺] = Kw / [OH⁻] = 1 × 10⁻¹⁴ / 0.001 = 1 × 10⁻¹¹ M.
- **Conclusion**: The statement that the concentration of H⁺ ions is 10⁻³ M is incorrect. The correct concentration is 10⁻¹¹ M.

### Final Conclusion
The false statement is the one regarding the concentration of H⁺ ions in a 0.001 molar solution of NaOH, which is stated to be 10⁻³ moles per liter, but it is actually 10⁻¹¹ moles per liter.

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