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

Options

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

Answer

To solve the question regarding which statements are correct, we will analyze each statement step by step.

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

**Solution:**
- The pH of a solution is calculated using the formula:
\[ \text{pH} = -\log [\text{H}^+] \]
- For a 10^-8 M HCl solution, we must also consider the contribution of H⁺ ions from water, which is 10^-7 M at 25°C.
- Therefore, the total concentration of H⁺ ions in the solution is:
\[ [\text{H}^+] = 10^{-8} + 10^{-7} = 1.1 \times 10^{-7} \text{ M} \]
- Now, calculating the pH:
\[ \text{pH} = -\log(1.1 \times 10^{-7}) \approx 6.95 \]
- Since the pH is less than 7, this statement is **incorrect**.

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

**Solution:**
- To find the conjugate base, we remove one H⁺ ion from the acid:
\[ \text{H}_2\text{PO}_4^- \rightarrow \text{HPO}_4^{2-} + \text{H}^+ \]
- This is correct. Therefore, this statement is **correct**.

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

**Solution:**
- The auto-protolysis of water can be represented as:
\[ 2 \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^- \]
- The equilibrium constant for this reaction, K_w, does indeed increase with temperature. Therefore, this statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement:** When a solution of a weak monoprotic acid is titrated against a strong base at the half-neutralization point, pH will be equal to half pK.

**Solution:**
- At the half-neutralization point, the concentration of the salt (A⁻) is equal to the concentration of the acid (HA).
- The Henderson-Hasselbalch equation is:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
- At half-neutralization, \([\text{A}^-] = [\text{HA}]\), so:
\[ \text{pH} = \text{pK}_a + \log(1) = \text{pK}_a \]
- The statement claims pH = 1/2 pK, which is incorrect. Therefore, this statement is **incorrect**.

### Conclusion
- The correct statements are:
- Statement 2: Correct
- Statement 3: Correct
- Therefore, the correct option is **B and C**.