Which of the following solutions will have highest boiling point:- (Assume M=m)

Options

A. `34.2% (w//V)` sugar
B. `18%(w//V)` Glucose
C. `6.00%(w//V)` Urea
D. All will have same b.p.

Answer

To determine which solution will have the highest boiling point among sugar, glucose, and urea, we need to analyze the colligative properties of these solutions. The boiling point elevation can be calculated using the formula:

\[ \Delta T_b = i \cdot K_b \cdot m \]

Where:
- \(\Delta T_b\) = elevation in boiling point
- \(i\) = van 't Hoff factor (number of particles the solute breaks into)
- \(K_b\) = ebullioscopic constant (depends on the solvent)
- \(m\) = molality of the solution

### Step-by-Step Solution:

1. **Identify the Solutes and Their Molecular Weights:**
- Sugar (C₁₂H₂₂O₁₁): Molecular weight = 342 g/mol
- Glucose (C₆H₁₂O₆): Molecular weight = 180 g/mol
- Urea (NH₂CONH₂): Molecular weight = 60 g/mol

2. **Calculate the Moles of Each Solute in 1 Liter of Solution:**
- For sugar:
\[ \text{Moles of sugar} = \frac{34.2 \text{ g}}{342 \text{ g/mol}} = 0.1 \text{ moles} \]
- For glucose:
\[ \text{Moles of glucose} = \frac{18 \text{ g}}{180 \text{ g/mol}} = 0.1 \text{ moles} \]
- For urea:
\[ \text{Moles of urea} = \frac{6 \text{ g}}{60 \text{ g/mol}} = 0.1 \text{ moles} \]

3. **Determine the van 't Hoff Factor (i):**
- Sugar (non-electrolyte): \(i = 1\)
- Glucose (non-electrolyte): \(i = 1\)
- Urea (non-electrolyte): \(i = 1\)

4. **Calculate the Molality (m) for Each Solution:**
Since we are considering 1 liter of solution, and assuming the density of the solution is close to that of water, the mass of the solvent (water) is approximately 1 kg. Therefore, the molality (m) for each solution is:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{0.1 \text{ moles}}{1 \text{ kg}} = 0.1 \text{ mol/kg} \]

5. **Calculate the Boiling Point Elevation for Each Solution:**
Since \(K_b\) is the same for all solutions (assuming they are in the same solvent), and \(i\) and \(m\) are the same for all three solutions, the elevation in boiling point (\(\Delta T_b\)) will also be the same for all solutions:
\[ \Delta T_b = i \cdot K_b \cdot m = 1 \cdot K_b \cdot 0.1 \]

6. **Conclusion:**
Since the boiling point elevation is the same for all three solutions, they will all have the same boiling point.

### Final Answer:
All solutions (sugar, glucose, and urea) will have the same boiling point.

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