Which of the following statements (s) 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. Autoprotoysis constant of water increases with temperature.
D. When a solution of weak monoprotic acid is titrated against a strong base, at half-neutralisation, point `pH =(1//2) pK_(a)`.

Answer

To determine which of the statements regarding ionic equilibrium are correct, we will analyze each statement one by one.

### Step 1: Analyze the first statement
**Statement:** The pH of a 1.0 x 10^-8 molar solution of HCl is 8.

- HCl is a strong acid and dissociates completely in solution:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
- Therefore, the concentration of \(\text{H}^+\) ions from HCl is \(1.0 \times 10^{-8}\) M.
- However, we also need to consider the \(\text{H}^+\) ions contributed by water, which is \(1.0 \times 10^{-7}\) M.
- The total concentration of \(\text{H}^+\) ions in the solution is:
\[ [\text{H}^+] = 1.0 \times 10^{-8} + 1.0 \times 10^{-7} = 1.1 \times 10^{-7} \text{ M} \]
- Now, we calculate the pH:
\[ \text{pH} = -\log(1.1 \times 10^{-7}) \approx 6.95 \]
- Since the statement claims the pH is 8, this statement is **incorrect**.

### Step 2: Analyze the second statement
**Statement:** The conjugate base of \( \text{H}_2\text{PO}_4^- \) is \( \text{HPO}_4^{2-} \).

- The conjugate base is formed by removing one \(\text{H}^+\) ion from the acid:
\[ \text{H}_2\text{PO}_4^- \rightarrow \text{HPO}_4^{2-} + \text{H}^+ \]
- This statement is **correct**.

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

- The auto-protovysis constant of water (\(K_w\)) is defined as:
\[ K_w = [\text{H}^+][\text{OH}^-] \]
- It is known that \(K_w\) increases with an increase in temperature.
- Therefore, this statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement:** When a solution of weak monoprotic acid is titrated against a base, at the half-neutralization point, the pH is equal to half of \(pK_a\).

- At the half-neutralization point, the concentration of the weak acid is equal to the concentration of its conjugate base (salt).
- The pH at this point is given by:
\[ \text{pH} = \text{p}K_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
- Since at half-neutralization, \([\text{Salt}] = [\text{Acid}]\), the log term becomes 0:
\[ \text{pH} = \text{p}K_a \]
- The statement claims that pH equals half of \(pK_a\), which is **incorrect**.

### Conclusion
- **Correct Statements:** 2 and 3
- **Incorrect Statements:** 1 and 4