Which of the following statements 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. Auto-protolysis constant of water increases with temperature
D. neutralization point ` pH =((1)/(2))pK_(a)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Given Information
We are given:
- A 1 molal aqueous solution of a salt.
- The elevation in boiling point (ΔTB) is equal to 3 times the molal elevation constant (Kb).
- Kb = 1.86 K kg/mol.
- We need to find the freezing point of the solution and the osmotic pressure at 27 degrees Celsius.

### Step 2: Calculate the Van't Hoff Factor (I)
The elevation in boiling point is given by the formula:
\[ \Delta T_B = I \cdot K_B \cdot M \]
Where:
- \( \Delta T_B = 3 \cdot K_B \)
- \( M = 1 \) (since it is a 1 molal solution)

Substituting the values:
\[ 3 \cdot K_B = I \cdot K_B \cdot 1 \]
This simplifies to:
\[ I = 3 \]

### Step 3: Calculate the Freezing Point Depression (ΔTf)
The depression in freezing point is given by the formula:
\[ \Delta T_F = I \cdot K_F \cdot M \]
Where:
- \( K_F = 1.86 \, \text{K kg/mol} \)
- \( M = 1 \)

Substituting the values:
\[ \Delta T_F = 3 \cdot 1.86 \cdot 1 = 5.58 \, \text{K} \]

Since the freezing point of pure water is 0°C, the freezing point of the solution (Tf) will be:
\[ T_F = 0 - \Delta T_F = 0 - 5.58 = -5.58 \, \text{°C} \]

### Step 4: Calculate the Osmotic Pressure (π)
The osmotic pressure is given by the formula:
\[ \pi = I \cdot C \cdot R \cdot T \]
Where:
- \( C \) (concentration) can be considered as molality (1 mol/kg).
- \( R = 0.081 \, \text{L atm/(mol K)} \)
- \( T = 27 + 273 = 300 \, \text{K} \)

Substituting the values:
\[ \pi = 3 \cdot 1 \cdot 0.081 \cdot 300 \]
Calculating this gives:
\[ \pi = 3 \cdot 0.081 \cdot 300 = 73.89 \, \text{atm} \]

### Final Results
- The freezing point of the solution is **-5.58 °C**.
- The osmotic pressure of the solution at 27 °C is **73.89 atm**.