To solve the question regarding which of the statements is correct, we will analyze each statement one by one based on the information provided in the video transcript.
### Step-by-Step Solution:
1. **Statement 1: pH of HCl solution is 8 when its molarity is 1 × 10^-8 M.**
- **Analysis**: HCl is a strong acid and completely dissociates in solution. For a 1 × 10^-8 M HCl solution, the concentration of H⁺ ions from HCl is 1 × 10^-8 M. However, we must also consider the H⁺ ions contributed by water, which is 1 × 10^-7 M at neutral pH (25°C). Therefore, the total concentration of H⁺ ions is:
\[
[H^+] = 1 \times 10^{-8} + 1 \times 10^{-7} = 1.1 \times 10^{-7} \, \text{M}
\]
- The pH is calculated as:
\[
\text{pH} = -\log(1.1 \times 10^{-7}) \approx 6.95
\]
- Since the pH is approximately 7 (not 8), **this statement is incorrect**.
2. **Statement 2: The conjugate base of H₂PO₄⁻ is HPO₄²⁻.**
- **Analysis**: The conjugate base of an acid is formed by removing one proton (H⁺). Starting from H₃PO₄ (phosphoric acid):
- Removing one proton gives H₂PO₄⁻.
- Removing another proton gives HPO₄²⁻.
- Therefore, the conjugate base of H₂PO₄⁻ is indeed HPO₄²⁻, making **this statement correct**.
3. **Statement 3: The autoprotolysis constant of water increases with an increase in temperature.**
- **Analysis**: The autoprotolysis of water can be represented as:
\[
2H_2O \rightleftharpoons H_3O^+ + OH^-
\]
- As temperature increases, the equilibrium shifts to the right (according to Le Chatelier's principle), leading to an increase in the concentration of H₃O⁺ and OH⁻ ions. Thus, the autoprotolysis constant (K_w = [H₃O⁺][OH⁻]) increases with temperature. Therefore, **this statement is correct**.
4. **Statement 4: At the half-neutralization point of a weak monoprotic acid titrated with a strong base, pH = 1/2.**
- **Analysis**: At the half-neutralization point, the concentration of the weak acid and its conjugate base (salt) are equal. The pH at this point is given by:
\[
\text{pH} = pK_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right)
\]
- Since at half-neutralization, the concentrations of salt and acid are equal, the log term becomes 0, and thus:
\[
\text{pH} = pK_a
\]
- Therefore, the statement that pH = 1/2 is incorrect. **This statement is incorrect**.
### Conclusion:
The correct statements are:
- Statement 2: The conjugate base of H₂PO₄⁻ is HPO₄²⁻.
- Statement 3: The autoprotolysis constant of water increases with an increase in temperature.
### Final Answer:
**Correct Statements: 2 and 3.**
