Which statements 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 2
B. The concentration of OH in 0.005 M `HNO_(3)` is `2.0 xx 10^(-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^(+)` is `10^(-3)` mol/L

Answer

To determine which statement is false, we will analyze each statement based on the information provided in the video transcript.

### Step-by-Step Solution:

1. **Statement 1: pH of a 0.1 M H2SO4 solution is 2.**
- Given: 0.1 moles of H2SO4 in 2 liters of solution.
- H2SO4 is a strong acid and dissociates completely:
\[ H2SO4 \rightarrow 2H^+ + SO4^{2-} \]
- From 0.1 moles of H2SO4, we get:
\[ 0.1 \text{ moles H2SO4} \times 2 = 0.2 \text{ moles H}^+ \]
- Molarity of \( H^+ \):
\[ \text{Molarity} = \frac{0.2 \text{ moles}}{2 \text{ L}} = 0.1 \text{ M} \]
- pH calculation:
\[ pH = -\log[H^+] = -\log(0.1) = 1 \]
- **Conclusion:** The statement that pH is 2 is **false**.

2. **Statement 2: Concentration of \( H^- \) in 0.05 M HNO3 is \( 2 \times 10^{-12} \) M.**
- HNO3 is also a strong acid and dissociates completely:
\[ HNO3 \rightarrow H^+ + NO3^- \]
- Molarity of \( H^+ \) is 0.05 M.
- Using the water ion product \( K_w = 10^{-14} \):
\[ [OH^-] = \frac{K_w}{[H^+]} = \frac{10^{-14}}{0.05} = 2 \times 10^{-13} \text{ M} \]
- Therefore, the concentration of \( H^- \) is not \( 2 \times 10^{-12} \) M.
- **Conclusion:** This statement is **false**.

3. **Statement 3: pH of 0.01 M KOH is 12.**
- KOH is a strong base and dissociates completely:
\[ KOH \rightarrow K^+ + OH^- \]
- Molarity of \( OH^- \) is 0.01 M.
- Calculate \( pOH \):
\[ pOH = -\log(0.01) = 2 \]
- Calculate pH:
\[ pH = 14 - pOH = 14 - 2 = 12 \]
- **Conclusion:** This statement is **true**.

4. **Statement 4: In a 0.001 M NaOH solution, the concentration of \( H^+ \) is 3 moles per liter.**
- NaOH is a strong base and dissociates completely:
\[ NaOH \rightarrow Na^+ + OH^- \]
- Molarity of \( OH^- \) is 0.001 M.
- Calculate \( H^+ \) concentration:
\[ [H^+] = \frac{K_w}{[OH^-]} = \frac{10^{-14}}{0.001} = 10^{-11} \text{ M} \]
- **Conclusion:** This statement is **false**.

### Summary of Findings:
- The false statements are:
- Statement 1: pH of 0.1 M H2SO4 is 2.
- Statement 2: Concentration of \( H^- \) in 0.05 M HNO3 is \( 2 \times 10^{-12} \) M.
- Statement 4: In 0.001 M NaOH, the concentration of \( H^+ \) is 3 moles per liter.