Calculate the boiling and freezing points of 0.22m glycerol in ethanol.
Normal BP ethanol: 78.4
Kb ethanol: 1.22
Normal Freezing Point ethanol: -114.6
Kf ethanol: 1.99
The Correct Answer and Explanation is :
To calculate the boiling and freezing points of a 0.22 m (mol/kg) glycerol solution in ethanol, we will use the following colligative properties formulas:
- Boiling point elevation formula:
[
\Delta T_b = K_b \times m
]
where:
- (\Delta T_b) is the boiling point elevation,
- (K_b) is the ebullioscopic constant (boiling point elevation constant) for ethanol,
- (m) is the molality of the solution.
- Freezing point depression formula:
[
\Delta T_f = K_f \times m
]
where:
- (\Delta T_f) is the freezing point depression,
- (K_f) is the cryoscopic constant (freezing point depression constant) for ethanol,
- (m) is the molality of the solution.
Boiling Point Elevation:
- Given:
- (K_b = 1.22) (boiling point elevation constant for ethanol),
- (m = 0.22) mol/kg (molality of the glycerol solution).
Using the formula:
[
\Delta T_b = 1.22 \times 0.22 = 0.2684 \, \text{°C}
]
The normal boiling point of ethanol is 78.4°C, so the new boiling point will be:
[
\text{New boiling point} = 78.4 + 0.2684 = 78.6684 \, \text{°C}
]
Freezing Point Depression:
- Given:
- (K_f = 1.99) (freezing point depression constant for ethanol),
- (m = 0.22) mol/kg (molality of the glycerol solution).
Using the formula:
[
\Delta T_f = 1.99 \times 0.22 = 0.438 \, \text{°C}
]
The normal freezing point of ethanol is -114.6°C, so the new freezing point will be:
[
\text{New freezing point} = -114.6 – 0.438 = -115.038 \, \text{°C}
]
Final Answer:
- Boiling point of the solution: 78.67°C
- Freezing point of the solution: -115.04°C
Explanation:
Colligative properties depend on the concentration of solute particles, not their identity. The presence of glycerol in ethanol causes changes in the boiling and freezing points due to these properties. By adding glycerol to ethanol, the boiling point increases because the ethanol molecules have more difficulty escaping into the vapor phase due to the presence of the solute. This is called boiling point elevation. Similarly, the addition of glycerol to ethanol lowers the freezing point because the solute disrupts the formation of the solid structure of the solvent, which results in freezing point depression. These shifts are directly proportional to the molality of the solution, and we calculated them using the known constants for ethanol’s colligative properties.