Which has maximum freezing point?

Options

A. `6g` urea solution in `100g H_(2)O`
B. `6g` acetic acid solution in `100gH_(2)O`
C. `6g` sodium chloride in `100g H_(2)O`
D. All have equal freezing point

Explanation

To determine which solution has the maximum freezing point among the given options, we need to analyze the freezing point depression caused by each solute. The freezing point depression can be calculated using the formula:

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

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

### Step 1: Calculate the molality of each solution

1. **Urea solution**:
- Mass of urea = 6 g
- Molar mass of urea (NH₂CONH₂) = 60 g/mol
- Moles of urea = \( \frac{6 \text{ g}}{60 \text{ g/mol}} = 0.1 \text{ mol} \)
- Mass of water = 100 g = 0.1 kg
- Molality (m) = \( \frac{0.1 \text{ mol}}{0.1 \text{ kg}} = 1 \text{ mol/kg} \)

2. **Acetic acid solution**:
- Mass of acetic acid = 6 g
- Molar mass of acetic acid (CH₃COOH) = 60 g/mol
- Moles of acetic acid = \( \frac{6 \text{ g}}{60 \text{ g/mol}} = 0.1 \text{ mol} \)
- Mass of water = 100 g = 0.1 kg
- Molality (m) = \( \frac{0.1 \text{ mol}}{0.1 \text{ kg}} = 1 \text{ mol/kg} \)

3. **Sodium chloride solution**:
- Mass of sodium chloride = 6 g
- Molar mass of sodium chloride (NaCl) = 58.5 g/mol
- Moles of sodium chloride = \( \frac{6 \text{ g}}{58.5 \text{ g/mol}} \approx 0.102 \text{ mol} \)
- Mass of water = 100 g = 0.1 kg
- Molality (m) = \( \frac{0.102 \text{ mol}}{0.1 \text{ kg}} \approx 1.02 \text{ mol/kg} \)

### Step 2: Determine the van't Hoff factor (i)

- For urea (non-electrolyte): \( i = 1 \)
- For acetic acid (weak electrolyte): \( i \approx 1.1 \) (it partially dissociates)
- For sodium chloride (strong electrolyte): \( i = 2 \) (it dissociates into Na⁺ and Cl⁻)

### Step 3: Calculate the freezing point depression for each solution

1. **Urea solution**:
\[ \Delta T_f = i \cdot K_f \cdot m = 1 \cdot K_f \cdot 1 \]

2. **Acetic acid solution**:
\[ \Delta T_f = 1.1 \cdot K_f \cdot 1 \]

3. **Sodium chloride solution**:
\[ \Delta T_f = 2 \cdot K_f \cdot 1.02 \]

### Step 4: Compare the freezing point depressions

Since \( K_f \) is constant for water, we can compare the values of \( \Delta T_f \):

- Urea: \( \Delta T_f = K_f \)
- Acetic acid: \( \Delta T_f = 1.1 K_f \)
- Sodium chloride: \( \Delta T_f = 2.04 K_f \)

### Conclusion

The solution with the least depression in freezing point will have the maximum freezing point. Since urea has the lowest \( \Delta T_f \), it will have the maximum freezing point.

Thus, the answer is **Option A: 6 gram urea solution in 100 gram H₂O**.