The freezing point of 1% of lead nitrate solution in water will be :

Options

A. Below `0^@C`
B. `0^@C`
C. `1^@C`
D. `2^@C`

Answer

To determine the freezing point of a 1% lead nitrate (Pb(NO3)2) solution in water, we can follow these steps:

### Step 1: Understand the Freezing Point Depression
The freezing point of a solution is lower than that of the pure solvent due to the presence of solute particles. This phenomenon is known as freezing point depression.

### Step 2: Identify the Freezing Point of Pure Water
The freezing point of pure water is 0°C. When a solute is added, the freezing point will decrease.

### Step 3: Calculate the Molality of the Solution
To find the freezing point depression, we first need to calculate the molality of the lead nitrate solution.

- **1% w/v solution** means there are 1 gram of lead nitrate in 100 mL of solution.
- The molar mass of lead nitrate (Pb(NO3)2) is approximately 331.2 g/mol (207.2 g/mol for Pb + 2 × 14.01 g/mol for N + 6 × 16.00 g/mol for O).

Calculating the number of moles of lead nitrate in 1 gram:
\[ \text{Moles of Pb(NO3)2} = \frac{1 \text{ g}}{331.2 \text{ g/mol}} \approx 0.00302 \text{ mol} \]

### Step 4: Calculate the Molality
Assuming the density of the solution is close to that of water (1 g/mL), the mass of the solvent (water) in 100 mL of solution is approximately 100 g or 0.1 kg.

\[ \text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{0.00302 \text{ mol}}{0.1 \text{ kg}} = 0.0302 \text{ mol/kg} \]

### Step 5: Use the Freezing Point Depression Formula
The freezing point depression can be calculated using the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
Where:
- \( \Delta T_f \) = freezing point depression
- \( i \) = van 't Hoff factor (for Pb(NO3)2, it dissociates into 3 ions: Pb²⁺ and 2 NO3⁻, so \( i = 3 \))
- \( K_f \) = freezing point depression constant for water (approximately 1.86 °C kg/mol)

Calculating the freezing point depression:
\[ \Delta T_f = 3 \cdot 1.86 \text{ °C kg/mol} \cdot 0.0302 \text{ mol/kg} \approx 0.168 \text{ °C} \]

### Step 6: Calculate the New Freezing Point
The new freezing point of the solution is:
\[ \text{New Freezing Point} = 0°C - \Delta T_f \approx 0°C - 0.168°C \approx -0.168°C \]

### Conclusion
The freezing point of a 1% lead nitrate solution in water will be below 0°C.

### Final Answer
The correct option is: **below 0°C**.

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