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

Options

A. the pH of `1xx10^(-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 increases with temperature.
D. When a solution of a weak monoprotic acid is titrated against a strong base, at half-neutralisation point, `pH=1//2pK_(a)`.

Answer

To determine which statements are correct, let's analyze each statement one by one.

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

- HCl is a strong acid and completely dissociates in solution. Therefore, the concentration of H⁺ ions in a 10^-8 M HCl solution is 10^-8 M.
- The pH is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
- For a 10^-8 M solution:
\[ \text{pH} = -\log(10^{-8}) = 8 \]
- However, we must consider the contribution of H⁺ ions from water, which is 10^-7 M at 25°C. Therefore, the total concentration of H⁺ ions becomes:
\[ [H^+] = 10^{-8} + 10^{-7} = 1.1 \times 10^{-7} \text{ M} \]
- Now, calculating the pH:
\[ \text{pH} = -\log(1.1 \times 10^{-7}) \approx 6.96 \]
- Since the pH is less than 7, the statement is **incorrect**.

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

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

### Step 3: Analyze the third statement
**Statement 3:** "At 25 degrees Celsius, K_w of water is 10^-24."

- The value of K_w (ion product of water) at 25°C is actually 1.0 x 10^-14, not 10^-24.
- However, the statement mentions that at 90 degrees Celsius, K_w increases to 10^-13, which is true.
- Since the first part of the statement is incorrect, the entire statement is **incorrect**.

### Step 4: Analyze the fourth statement
**Statement 4:** "At half-neutralization point, pH = 1/2 pK_a."

- The half-neutralization point of a weak monoprotic acid (HA) titrated with a strong base (like NaOH) is defined as the point where half of the acid has been neutralized.
- At this point, the concentration of the acid ([HA]) equals the concentration of its conjugate base ([A⁻]), leading to the relationship:
\[ \text{pH} = \text{pK}_a \]
- Therefore, the statement that pH = 1/2 pK_a is **incorrect**.

### Summary of the Analysis
- **Statement 1:** Incorrect
- **Statement 2:** Correct
- **Statement 3:** Incorrect
- **Statement 4:** Incorrect

### Final Answer
Only **Statement 2** is correct.

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