Properties of a solution determined only by the number of particles, regardless of the type of solute particles, are called colligative properties. There are four: vapor-pressure lowering, boiling-point elevation, freezing-point depression, and osmotic pressure.
Basic Knowledge
① Vapor-pressure lowering (Raoult's law): ΔP = P0·xsolute
② Boiling-point elevation: ΔTb = Kb·m
③ Freezing-point depression: ΔTf = Kf·m
④ Osmotic pressure (van't Hoff): π = cRT (πV=nRT)
For water, Kb=0.52 and Kf=1.86 K·kg/mol. For electrolytes, multiply by the van't Hoff factor i: NaCl→i≈2, CaCl2→i≈3.
Raoult's law（ΔP = P0·xsolute）
Boiling-point elevation（ΔTb = i·Kb·m）
Freezing-point depression（ΔTf = i·Kf·m）
Osmotic pressure（π = i·cRT、πV = nRT）
van't Hoff factor i（greater than 1 for electrolytes）
Semipermeable membrane（a membrane that allows only solvent to pass）
Further Study (Principles and Applications)
Colligative properties are used to determine the molar mass of unknown substances. Osmotic pressure is especially suitable for measuring the molar masses of proteins and polymers (M = mRT/(πV)). Road deicers used in winter, such as NaCl and CaCl2, are applications of freezing-point depression. Seawater has an osmotic pressure of approximately 25 atm, and reverse-osmosis membranes (RO membranes) using this principle are used in seawater desalination. In living organisms, physiological saline (0.9% NaCl) has the same osmotic pressure as blood plasma and is an isotonic solution.
- Colligative properties are proportional to the number of particles
- Electrolytes are corrected using the van't Hoff factor i
- NaCl: i=2、CaCl2: i=3
- For water, Kf=1.86, Kb=0.52
- πV=nRT has the same form as the ideal-gas equation
- Osmotic pressure is highly sensitive for determining molar mass
- Reverse-osmosis membranes ⇒ seawater desalination
Points of Caution (Common Confusions and Frequent Mistakes)
① Boiling-point elevation and freezing-point depression use molality, while osmotic pressure uses molarity. ② The factor i is required for electrolytes. ③ ΔT is an absolute value. ④ Osmotic pressure represents the direction in which water enters the solution.
Practice
- Find the freezing point of an aqueous solution made by dissolving 60 g of urea (M=60) in 1 kg of water (Kf=1.86).
- At 27℃, 4.0 g of a nonelectrolyte is dissolved in 1.0 L of water. If the osmotic pressure is 1.0×105 Pa, find its molar mass.
- At the same concentration of 0.10 mol/kg, which has the greatest freezing-point depression: glucose, NaCl, or CaCl2?