The freezing point of 11% aquous solution of calcium nitrate will be:

Options

A. `0^(@)` C
B. above `0^(@) C`
C. `1 ^(@) C`
D. below `0^(@)C`

Answer

To find the freezing point of an 11% aqueous solution of calcium nitrate, we can follow these steps:

### Step 1: Understand the Composition of the Solution
An 11% aqueous solution of calcium nitrate means that there are 11 grams of calcium nitrate (Ca(NO₃)₂) dissolved in 100 mL of water.

### Step 2: Calculate the Molar Mass of Calcium Nitrate
To understand how many moles of calcium nitrate are in the solution, we first need to calculate its molar mass.
- Calcium (Ca) = 40.08 g/mol
- Nitrogen (N) = 14.01 g/mol (2 nitrogen atoms)
- Oxygen (O) = 16.00 g/mol (6 oxygen atoms)

Molar mass of Ca(NO₃)₂ = 40.08 + (2 × 14.01) + (6 × 16.00)
= 40.08 + 28.02 + 96.00
= 164.10 g/mol

### Step 3: Calculate the Number of Moles of Calcium Nitrate
Using the molar mass, we can find the number of moles of calcium nitrate in the solution:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
\[ \text{Number of moles} = \frac{11 \text{ g}}{164.10 \text{ g/mol}} \approx 0.067 moles \]

### Step 4: Determine the Van 't Hoff Factor (i)
Calcium nitrate dissociates in solution into three ions:
\[ \text{Ca(NO}_3\text{)}_2 \rightarrow \text{Ca}^{2+} + 2 \text{NO}_3^{-} \]
Thus, the van 't Hoff factor (i) for calcium nitrate is 3.

### Step 5: Calculate the Freezing Point Depression
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 (3 for Ca(NO₃)₂)
- \( K_f \) = freezing point depression constant for water (approximately 1.86 °C kg/mol)
- \( m \) = molality of the solution

First, we need to calculate the molality (m):
\[ \text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} \]
The mass of the solvent (water) in 100 mL is approximately 100 g or 0.1 kg.
\[ m = \frac{0.067 \text{ moles}}{0.1 \text{ kg}} = 0.67 \text{ mol/kg} \]

Now we can calculate the freezing point depression:
\[ \Delta T_f = 3 \cdot 1.86 \cdot 0.67 \approx 3.75 °C \]

### Step 6: Calculate the New Freezing Point
The freezing point of pure water is 0 °C. Therefore, the new freezing point will be:
\[ \text{New Freezing Point} = 0 °C - \Delta T_f = 0 °C - 3.75 °C = -3.75 °C \]

### Conclusion
The freezing point of the 11% aqueous solution of calcium nitrate will be approximately -3.75 °C, which is less than 0 °C.