Correct order of freezing point of given solution
I. 0.1 M glucose II. 0.2 M urea III.0.1 M NaCl IV. `0.05 M CaCl_2`

Options

A. `I lt II lt III lt IV`
B. `I gt II gt III gt IV`
C. `III=II lt IV lt I`
D. `IV gt II gt III gt I`

Answer

To determine the correct order of freezing points for the given solutions, we will analyze the depression in freezing point (ΔTf) for each solution. The freezing point depression is given by the formula:

\[ \Delta Tf = i \cdot Kf \cdot M \]

Where:
- \( \Delta Tf \) is the depression in freezing point,
- \( i \) is the van 't Hoff factor (the number of particles the solute dissociates into),
- \( Kf \) is the freezing point depression constant (which is constant for a given solvent),
- \( M \) is the molarity of the solution.

Since \( Kf \) is constant for all solutions, we can focus on the product \( i \cdot M \) to compare the freezing point depressions.

### Step-by-step Solution:

1. **Calculate \( i \) and \( M \) for each solution:**
- **I. 0.1 M Glucose:**
- \( i = 1 \) (glucose does not dissociate)
- \( M = 0.1 \)
- \( i \cdot M = 1 \cdot 0.1 = 0.1 \)

- **II. 0.2 M Urea:**
- \( i = 1 \) (urea does not dissociate)
- \( M = 0.2 \)
- \( i \cdot M = 1 \cdot 0.2 = 0.2 \)

- **III. 0.1 M NaCl:**
- \( i = 2 \) (NaCl dissociates into Na⁺ and Cl⁻)
- \( M = 0.1 \)
- \( i \cdot M = 2 \cdot 0.1 = 0.2 \)

- **IV. 0.05 M CaCl₂:**
- \( i = 3 \) (CaCl₂ dissociates into Ca²⁺ and 2 Cl⁻)
- \( M = 0.05 \)
- \( i \cdot M = 3 \cdot 0.05 = 0.15 \)

2. **Determine the order of \( \Delta Tf \):**
- From the calculations:
- I. Glucose: \( 0.1 \)
- II. Urea: \( 0.2 \)
- III. NaCl: \( 0.2 \)
- IV. CaCl₂: \( 0.15 \)

- The order of \( i \cdot M \) values is:
- Urea (0.2) = NaCl (0.2) > CaCl₂ (0.15) > Glucose (0.1)

3. **Determine the order of freezing points (Tf):**
- Since \( \Delta Tf \) is directly proportional to \( i \cdot M \), a higher \( i \cdot M \) means a lower freezing point.
- Therefore, the order of freezing points (Tf) is the opposite of the order of \( \Delta Tf \):
- Glucose > CaCl₂ > Urea = NaCl

### Final Answer:
The correct order of freezing points for the given solutions is:
\[ \text{Glucose} > \text{CaCl}_2 > \text{Urea} = \text{NaCl} \]