1% solution of Ca`(NO_3)_2` has freezing point:

Options

A. `0^@C`
B. Less than `0^@C`
C. Greater than `0^@C`
D. None of these

Answer

To determine the freezing point of a 1% solution of calcium nitrate (Ca(NO₃)₂), we will follow these steps:

### Step 1: Understand the Composition of the Solution
A 1% solution of calcium nitrate means that in 100 g of the solution, there is 1 g of Ca(NO₃)₂ and 99 g of water (the solvent).

**Hint:** Remember that a 1% solution indicates the mass of solute per 100 g of solution.

### Step 2: Calculate the Molar Mass of Calcium Nitrate
The molar mass of calcium nitrate (Ca(NO₃)₂) can be calculated as follows:
- Calcium (Ca): 40.08 g/mol
- Nitrogen (N): 14.01 g/mol (2 nitrogen atoms)
- Oxygen (O): 16.00 g/mol (6 oxygen atoms)

Calculating the total:
\[ \text{Molar mass of Ca(NO₃)₂} = 40.08 + (2 \times 14.01) + (6 \times 16.00) = 164.1 \text{ g/mol} \]

**Hint:** Always ensure to add the contributions from all atoms in the compound to find the molar mass.

### Step 3: Calculate the Number of Moles of Calcium Nitrate
Using the mass of the solute (1 g) and its molar mass (164.1 g/mol):
\[ \text{Number of moles of Ca(NO₃)₂} = \frac{1 \text{ g}}{164.1 \text{ g/mol}} \approx 0.0061 \text{ moles} \]

**Hint:** The number of moles is calculated by dividing the mass of the solute by its molar mass.

### Step 4: Calculate the Molality of the Solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The mass of the solvent (water) is 99 g, which is 0.099 kg.
\[ \text{Molality (m)} = \frac{0.0061 \text{ moles}}{0.099 \text{ kg}} \approx 0.0616 \text{ mol/kg} \]

**Hint:** Convert grams to kilograms when calculating molality.

### Step 5: Determine the Van 't Hoff Factor (i)
Calcium nitrate dissociates in solution as follows:
\[ \text{Ca(NO₃)₂} \rightarrow \text{Ca}^{2+} + 2\text{NO₃}^- \]
This means that one formula unit of calcium nitrate produces three particles in solution (1 Ca²⁺ and 2 NO₃⁻). Therefore, the van 't Hoff factor (i) is 3.

**Hint:** The van 't Hoff factor indicates the number of particles produced from one formula unit of solute in solution.

### Step 6: Use the Freezing Point Depression Formula
The freezing point depression (ΔTf) can be calculated using the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
Where:
- \(K_f\) for water = 1.86 °C kg/mol
- \(i = 3\)
- \(m \approx 0.0616 \text{ mol/kg}\)

Substituting the values:
\[ \Delta T_f = 3 \cdot 1.86 \cdot 0.0616 \approx 0.344 \text{ °C} \]

**Hint:** The freezing point depression indicates how much the freezing point of the solvent is lowered.

### Step 7: Calculate the New Freezing Point
The normal freezing point of water is 0 °C. Therefore, the new freezing point will be:
\[ \text{New Freezing Point} = 0 - \Delta T_f = 0 - 0.344 \approx -0.344 \text{ °C} \]

**Hint:** The new freezing point is always lower than the original freezing point of the solvent.

### Final Answer
The freezing point of a 1% solution of calcium nitrate (Ca(NO₃)₂) is approximately -0.344 °C.

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