Depression in freezing point for 1 M urea, 1 M NaCl and 1 M `CaCl_(2)` are in the ratio of

Options

A. `1:2:3`
B. `1:1:1`
C. `3:2:1`
D. Data insufficient

Answer

To find the ratio of depression in freezing point for 1 M urea, 1 M NaCl, and 1 M CaCl₂, we need to understand how the depression in freezing point is calculated and the role of the van 't Hoff factor (i).

### Step-by-Step Solution:

1. **Understanding Depression in Freezing Point**:
The depression in freezing point (ΔTf) is given by the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \( \Delta T_f \) = depression in freezing point
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( K_f \) = freezing point depression constant (depends on the solvent)
- \( m \) = molality of the solution

Since we are comparing solutions of the same molarity (1 M), we can assume that the molality (m) and \( K_f \) are constant for all three solutions.

2. **Determining the van 't Hoff Factor (i)**:
- **For Urea (NH₂CONH₂)**: Urea is a non-electrolyte and does not dissociate in solution. Thus, \( i = 1 \).
- **For Sodium Chloride (NaCl)**: NaCl dissociates into two ions: Na⁺ and Cl⁻. Therefore, \( i = 2 \).
- **For Calcium Chloride (CaCl₂)**: CaCl₂ dissociates into three ions: Ca²⁺ and 2 Cl⁻. Hence, \( i = 3 \).

3. **Calculating the Depression in Freezing Point**:
Since the depression in freezing point is directly proportional to \( i \), we can express the depression in freezing point for each solute as follows:
- For Urea: \( \Delta T_f \) (urea) = \( 1 \cdot K_f \cdot 1 = K_f \)
- For NaCl: \( \Delta T_f \) (NaCl) = \( 2 \cdot K_f \cdot 1 = 2K_f \)
- For CaCl₂: \( \Delta T_f \) (CaCl₂) = \( 3 \cdot K_f \cdot 1 = 3K_f \)

4. **Finding the Ratio**:
The ratio of the depression in freezing points for urea, NaCl, and CaCl₂ can be expressed as:
\[ \Delta T_f \text{ (urea)} : \Delta T_f \text{ (NaCl)} : \Delta T_f \text{ (CaCl₂)} = K_f : 2K_f : 3K_f \]
Simplifying this gives us:
\[ 1 : 2 : 3 \]

### Final Answer:
The depression in freezing point for 1 M urea, 1 M NaCl, and 1 M CaCl₂ are in the ratio **1 : 2 : 3**.