Which of the following statements is//are correct?

Options

A. The `pH` of `1.0 xx 10^(-8)M` solution of `HCI` is `8`.
B. The conjugate base of `H_(2)PO_(4)^(Theta)` is `HPO_(4)^(-2)`.
C. The autoprotolysis constant of water increases with temperature.
D. When a solution of a weak monoprotic acid is trated against a strong base, at half-neutralisation point, `pH = (1//2) pK_(a)`.

Explanation

To determine which statements are correct, we will analyze each statement one by one.

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

**Solution:**
- HCl is a strong acid and completely dissociates in water.
- A 1 x 10^-8 M solution of HCl will contribute H⁺ ions from the acid itself and also from the autoionization of water.
- The concentration of H⁺ from water is 1 x 10^-7 M.
- Therefore, the total concentration of H⁺ ions in the solution is:
\[ [H^+] = 1 \times 10^{-8} + 1 \times 10^{-7} = 1.1 \times 10^{-7} \, \text{M} \]
- The pH is calculated as:
\[ pH = -\log(1.1 \times 10^{-7}) \approx 6.96 \]
- Since the pH is approximately 6.96, which is less than 7, the statement that the pH is 8 is incorrect.

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

**Solution:**
- The conjugate base is formed by removing one proton (H⁺) from the acid.
- Removing one H⁺ from H₂PO₄⁻ gives HPO₄²⁻.
- Therefore, this statement is correct.

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

**Solution:**
- The autoprotolysis constant of water (Kw) is defined as:
\[ K_w = [H^+][OH^-] \]
- As temperature increases, the ionization of water increases, leading to a higher concentration of H⁺ and OH⁻ ions.
- Therefore, Kw increases with temperature, making this statement correct.

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

**Solution:**
- At the half-neutralization point, the pH of the solution is equal to the pKa of the weak acid, not half of it.
- Therefore, this statement is incorrect.

### Conclusion
- The correct statements are:
- Statement 2: Correct
- Statement 3: Correct
- The incorrect statements are:
- Statement 1: Incorrect
- Statement 4: Incorrect

Thus, the correct options for this question are **B and C**.

---