Understanding the Concepts
* Boiling Point Elevation: When a solute (like glucose) is dissolved in a solvent (like water), the boiling point of the solution increases compared to the pure solvent.
* Freezing Point Depression: Similarly, the freezing point of the solution decreases compared to the pure solvent.
* Colligative Properties: These changes in boiling and freezing points are examples of colligative properties, which depend only on the concentration of solute particles, not their identity.
Calculations
1. Moles of Glucose:
* Molar mass of glucose (C6H12O6) = 180.156 g/mol
* Moles of glucose = 45 g / 180.156 g/mol ≈ 0.25 mol
2. Molality (m):
* Molality is moles of solute per kilogram of solvent.
* Mass of water (solvent) = 500 g = 0.5 kg
* Molality (m) = 0.25 mol / 0.5 kg = 0.5 mol/kg
3. Boiling Point Elevation (ΔTb):
* ΔTb = Kb * m
* Kb (ebullioscopic constant for water) = 0.512 °C/m
* ΔTb = 0.512 °C/m * 0.5 mol/kg = 0.256 °C
4. Freezing Point Depression (ΔTf):
* ΔTf = Kf * m
* Kf (cryoscopic constant for water) = 1.86 °C/m
* ΔTf = 1.86 °C/m * 0.5 mol/kg = 0.93 °C
Results:
* Change in Boiling Point: The boiling point of the water will increase by 0.256 °C.
* Change in Freezing Point: The freezing point of the water will decrease by 0.93 °C.
Important Note: These calculations assume that glucose does not dissociate in water. If the solute were an ionic compound (like NaCl), it would dissociate into multiple ions, leading to a larger change in boiling and freezing points.
