Which of the following statements are correct?

Options

A. The pH of `1xx10^(-8)` M HCl solution is 8.
B. The conjugate base of `H_2PO_4^-` is `HPO_4^(2-)`
C. Autoprotolysis constant of water increases with temperature
D. When a solution of weak monoprotic acid is titrated ngninat a strong base, at half neutralisation point, pH=1/2 `pK_a`

Answer

To determine which statements are correct, let's analyze each statement step by step based on the information provided in the video transcript.

### Step 1: Analyze the first statement
**Statement:** The pH of 1 x 10^-8 molar HCl solution is 8.

**Analysis:**
- The concentration of H⁺ ions from HCl is 1 x 10^-8 M.
- However, pure water also contributes H⁺ ions with a concentration of 1 x 10^-7 M.
- Therefore, the total concentration of H⁺ ions in the solution is:
\[ [H^+] = 1 \times 10^{-8} + 1 \times 10^{-7} = 1.1 \times 10^{-7} \text{ M} \]
- Now, using the pH formula:
\[ \text{pH} = -\log[H^+] \]
\[ \text{pH} = -\log(1.1 \times 10^{-7}) \approx 7 - \log(1.1) \approx 7 - 0.041 = 6.96 \]
- Therefore, the pH is approximately 6.96, which is not 8. **This statement is incorrect.**

### Step 2: Analyze the second statement
**Statement:** The conjugate base of H₂PO₄⁻ is HPO₄²⁻.

**Analysis:**
- The conjugate base of an acid is formed when the acid donates a proton (H⁺).
- H₂PO₄⁻ can donate a proton to form HPO₄²⁻:
\[ \text{H₂PO₄}^- \rightarrow \text{HPO₄}^{2-} + \text{H}^+ \]
- Therefore, this statement is correct. **This statement is correct.**

### Step 3: Analyze the third statement
**Statement:** The auto-protolysis constant of water increases with temperature.

**Analysis:**
- As temperature increases, the dissociation of water into H⁺ and OH⁻ ions increases.
- This means that the equilibrium constant for the auto-protolysis of water (Kw) increases with temperature.
- Therefore, this statement is correct. **This statement is correct.**

### Step 4: Analyze the fourth statement
**Statement:** At the half-neutralization point of a monoprotic acid titrated against a strong base, pH = half pKa.

**Analysis:**
- At the half-neutralization point, the concentrations of the acid (HA) and its conjugate base (A⁻) are equal.
- The Henderson-Hasselbalch equation states:
\[ \text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
- At half-neutralization, \([\text{A}^-] = [\text{HA}]\), so:
\[ \text{pH} = \text{pKa} + \log(1) = \text{pKa} \]
- Therefore, the statement that pH = half pKa is incorrect. **This statement is incorrect.**

### Summary of Statements
1. **Incorrect** - The pH of 1 x 10^-8 molar HCl solution is not 8.
2. **Correct** - The conjugate base of H₂PO₄⁻ is HPO₄²⁻.
3. **Correct** - The auto-protolysis constant of water increases with temperature.
4. **Incorrect** - At the half-neutralization point, pH = pKa, not half pKa.

### Final Answer
The correct statements are:
- The conjugate base of H₂PO₄⁻ is HPO₄²⁻.
- The auto-protolysis constant of water increases with temperature.