Which of the following statement(s) is(are) correct?

Options

A. The pH of `1.0xx10^(-8)M` solution of HCl is 8
B. The conjugate base of `H_(2)PO_(4)^(-)` is `HPO_(4)^(2-)`
C. Autoprotolysis constant of water increase with temperature
D. When a solution of a weak monoprotic acid is titrated against a strong base, at half neutralisation point `pH=(1/2) pK_(a)`

Explanation

To determine which of the statements are correct, we will analyze each option step by step.

### Step 1: Analyze Option A
**Statement:** The pH of a 1.0 × 10⁻⁸ M HCl solution is 8.

- **Solution:**
- The concentration of H⁺ ions in the solution is given as 1.0 × 10⁻⁸ M.
- To find the pH, we use the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
- Substituting the value:
\[ \text{pH} = -\log(1.0 \times 10^{-8}) = 8 \]
- However, HCl is a strong acid, and the pH of strong acids should be less than 7. Therefore, this statement is incorrect.

### Step 2: Analyze Option B
**Statement:** The conjugate base of H₂PO₄⁻ is HPO₄²⁻.

- **Solution:**
- The conjugate base is formed by removing one H⁺ ion from the acid.
- Starting with H₂PO₄⁻:
\[ \text{H}_2\text{PO}_4^- \rightarrow \text{HPO}_4^{2-} + \text{H}^+ \]
- This confirms that the conjugate base of H₂PO₄⁻ is indeed HPO₄²⁻. Thus, this statement is correct.

### Step 3: Analyze Option C
**Statement:** The autoprotolysis constant of water increases with temperature.

- **Solution:**
- The autoprotolysis of water refers to the self-ionization of water:
\[ 2 \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^- \]
- As temperature increases, the ionization of water increases, leading to a higher concentration of H₃O⁺ and OH⁻ ions.
- Therefore, the autoprotolysis constant (Kw) increases with temperature. This statement is correct.

### Step 4: Analyze Option D
**Statement:** When a solution of weak monoprotic acid is titrated against a strong base at half-neutralization point, pH is equal to half pKa.

- **Solution:**
- At the half-neutralization point, the concentration of the weak acid and its conjugate base are equal. According to the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
- At half-neutralization, \([\text{A}^-] = [\text{HA}]\), thus:
\[ \text{pH} = \text{pKa} \]
- Therefore, the statement that pH is equal to half pKa is incorrect. This statement is wrong.

### Conclusion
The correct statements are:
- Option B: The conjugate base of H₂PO₄⁻ is HPO₄²⁻.
- Option C: The autoprotolysis constant of water increases with temperature.

### Final Answer
**Correct Options:** B and C.

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