Which will have largest `Delta T_(b)`

Options

A. 65 g urea in 1 kg water
B. 18 g glucose in 100 g water
C. 342 g sucrose in 1000 g water
D. 180 g glucose in 1 kg water

Explanation

To determine which solution will have the largest ΔT_b (elevation in boiling point), we need to calculate the molality of each solution, as ΔT_b is directly proportional to molality (ΔT_b = k_b * m, where k_b is the molal elevation constant and m is the molality).

### Step-by-Step Solution:

1. **Understanding Molality**:
- Molality (m) is defined as the number of moles of solute per kilogram of solvent.
- Formula: \( m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} \)

2. **Calculate Molality for Each Solution**:

**Option 1: Urea in Water**
- Given: 65 grams of urea and 1 kg of water.
- Molar mass of urea (NH₂CONH₂) = 60 g/mol.
- Moles of urea = \( \frac{65 \text{ g}}{60 \text{ g/mol}} = 1.0833 \text{ mol} \).
- Molality (m) = \( \frac{1.0833 \text{ mol}}{1 \text{ kg}} = 1.0833 \text{ mol/kg} \).

**Option 2: Glucose in Water**
- Given: 18 grams of glucose and 100 grams of water.
- Molar mass of glucose (C₆H₁₂O₆) = 180 g/mol.
- Moles of glucose = \( \frac{18 \text{ g}}{180 \text{ g/mol}} = 0.1 \text{ mol} \).
- Mass of water = 100 g = 0.1 kg.
- Molality (m) = \( \frac{0.1 \text{ mol}}{0.1 \text{ kg}} = 1.0 \text{ mol/kg} \).

**Option 3: Sucrose in Water**
- Given: 342 grams of sucrose and 1000 grams of water.
- Molar mass of sucrose (C₁₂H₂₂O₁₁) = 342 g/mol.
- Moles of sucrose = \( \frac{342 \text{ g}}{342 \text{ g/mol}} = 1.0 \text{ mol} \).
- Mass of water = 1000 g = 1 kg.
- Molality (m) = \( \frac{1.0 \text{ mol}}{1.0 \text{ kg}} = 1.0 \text{ mol/kg} \).

**Option 4: Glucose in Water**
- Given: 18 grams of glucose and 1 kg of water.
- Molar mass of glucose = 180 g/mol.
- Moles of glucose = \( \frac{18 \text{ g}}{180 \text{ g/mol}} = 0.1 \text{ mol} \).
- Mass of water = 1 kg.
- Molality (m) = \( \frac{0.1 \text{ mol}}{1 \text{ kg}} = 0.1 \text{ mol/kg} \).

3. **Compare the Molalities**:
- Urea: 1.0833 mol/kg
- Glucose (100 g water): 1.0 mol/kg
- Sucrose: 1.0 mol/kg
- Glucose (1 kg water): 0.1 mol/kg

4. **Conclusion**:
- The solution with the highest molality is the one with urea, which has a molality of approximately 1.0833 mol/kg.
- Therefore, the solution that will have the largest ΔT_b is the one containing urea.

### Final Answer:
**Option 1: Urea in Water will have the largest ΔT_b.**