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 of the given solutions, we need to calculate the depression in freezing point (ΔTf) for each solution using the formula:

\[ \Delta T_f = i \cdot K_f \cdot m \]

Where:
- \(i\) = van 't Hoff factor (number of particles the solute breaks into)
- \(K_f\) = freezing point depression constant (which is constant for a given solvent)
- \(m\) = molality of the solution (we'll use molarity here as a simplification since the problem gives us molarity)

Since \(K_f\) is constant for all solutions, we can compare the values of \(i \cdot m\) for each solution to determine the order of freezing points.

### Step 1: Calculate \(i \cdot m\) for each solution

1. **Glucose (0.1 M)**:
- Glucose does not dissociate in solution, so \(i = 1\).
- \(i \cdot m = 1 \cdot 0.1 = 0.1\)

2. **Urea (0.2 M)**:
- Urea also does not dissociate, so \(i = 1\).
- \(i \cdot m = 1 \cdot 0.2 = 0.2\)

3. **NaCl (0.1 M)**:
- NaCl dissociates into two ions: Na\(^+\) and Cl\(^-\), so \(i = 2\).
- \(i \cdot m = 2 \cdot 0.1 = 0.2\)

4. **CaCl₂ (0.05 M)**:
- CaCl₂ dissociates into three ions: Ca\(^{2+}\) and 2 Cl\(^-\), so \(i = 3\).
- \(i \cdot m = 3 \cdot 0.05 = 0.15\)

### Step 2: Summarize the results

- Glucose: \(i \cdot m = 0.1\)
- Urea: \(i \cdot m = 0.2\)
- NaCl: \(i \cdot m = 0.2\)
- CaCl₂: \(i \cdot m = 0.15\)

### Step 3: Determine the order of freezing points

The freezing point depression is directly related to the value of \(i \cdot m\):
- The larger the value of \(i \cdot m\), the greater the depression in freezing point (lower freezing point).
- Therefore, the order of freezing points from highest to lowest is:
- Glucose (0.1)
- CaCl₂ (0.15)
- Urea (0.2)
- NaCl (0.2)

Since Urea and NaCl have the same \(i \cdot m\), they will have the same freezing point.

### Final Order of Freezing Points:

1. Glucose (highest freezing point)
2. CaCl₂
3. Urea = NaCl (lowest freezing point)