Acetic acid, HC2H3O2, is the major component of vinegar. The boiling point of pure acetic acid is 118.5oC. The boiling point elevation constant of vinegar is 3.08 oC/m. What is the change in boiling point and the boiling point of a solution containing 31.5-g of glucose (C6H12O6) in 750 g of acetic acid?
The correct answer and explanation is :
To determine the change in boiling point ((\Delta T_b)) and the new boiling point of the solution, we use the boiling point elevation formula:
[
\Delta T_b = i \cdot K_b \cdot m
]
where:
- (i) = van’t Hoff factor (for glucose, (i = 1) since it does not dissociate in solution)
- (K_b = 3.08^\circ C/m) (boiling point elevation constant for acetic acid)
- (m) = molality of the solution (moles of solute per kilogram of solvent)
Step 1: Calculate Moles of Glucose
The molecular weight of glucose ((C_6H_{12}O_6)) is:
[
(6 \times 12.01) + (12 \times 1.008) + (6 \times 16.00) = 180.16 \text{ g/mol}
]
Moles of glucose:
[
\frac{31.5 \text{ g}}{180.16 \text{ g/mol}} = 0.175 \text{ moles}
]
Step 2: Calculate Molality
Molality ((m)) is given by:
[
m = \frac{\text{moles of solute}}{\text{kg of solvent}}
]
Mass of acetic acid solvent = 750 g = 0.750 kg
[
m = \frac{0.175 \text{ moles}}{0.750 \text{ kg}} = 0.233 \text{ m}
]
Step 3: Calculate Boiling Point Elevation
Using the boiling point elevation formula:
[
\Delta T_b = (1) \times (3.08^\circ C/m) \times (0.233 m)
]
[
\Delta T_b = 0.717^\circ C
]
Step 4: Determine New Boiling Point
The boiling point of pure acetic acid is (118.5^\circ C), so the new boiling point is:
[
118.5^\circ C + 0.717^\circ C = 119.2^\circ C
]
Final Answer:
- Change in boiling point = 0.717°C
- New boiling point of the solution = 119.2°C
Explanation:
Boiling point elevation occurs when a non-volatile solute (glucose) is dissolved in a solvent (acetic acid), increasing the boiling point. This is due to the presence of solute particles interfering with the ability of solvent molecules to escape as vapor, requiring more energy (higher temperature) to reach boiling. Since glucose does not dissociate into ions, its van’t Hoff factor is 1, meaning it contributes to the elevation only through the number of particles in solution. The final result shows a slight increase in boiling point due to the relatively small concentration of glucose in acetic acid.