Raoult's law explains how the vapor pressure of a liquid changes when another substance is dissolved in it. Vapor pressure comes from solvent molecules escaping from the liquid surface into the gas phase. When a nonvolatile solute is added, fewer solvent molecules are at the surface, so fewer can escape.
This lowering of vapor pressure is a key colligative property, meaning it depends mainly on the number of dissolved particles, not their identity.
For an ideal solution, the partial vapor pressure of each volatile component equals its mole fraction times its pure vapor pressure. For a solution with a nonvolatile solute, the solvent vapor pressure is Psolvent = Xsolvent P°solvent. Because the vapor pressure is lower, the solution must be heated to a higher temperature before its vapor pressure equals atmospheric pressure, causing boiling-point elevation.
Raoult's law is used to predict solution behavior in chemistry, distillation, antifreeze mixtures, and many laboratory calculations.
Key Facts
- Raoult's law for a volatile solvent: Psolvent = Xsolvent P°solvent
- For an ideal mixture of volatile liquids: Ptotal = PA + PB = XA P°A + XB P°B
- Mole fraction of solvent: Xsolvent = nsolvent / (nsolvent + nsolute)
- Vapor pressure lowering for a nonvolatile solute: ΔP = P°solvent - Psolvent = Xsolute P°solvent
- Boiling occurs when vapor pressure equals external pressure: Pvapor = Patm
- Boiling-point elevation: ΔTb = i Kb m, where i is the van't Hoff factor, Kb is the boiling-point constant, and m is molality
Vocabulary
- Vapor pressure
- The pressure exerted by vapor in equilibrium with its liquid at a given temperature.
- Raoult's law
- A law stating that the vapor pressure of a component in an ideal solution equals its mole fraction times its pure vapor pressure.
- Mole fraction
- The fraction of total moles in a mixture that belong to one component.
- Nonvolatile solute
- A dissolved substance that has little tendency to evaporate into the gas phase.
- Ideal solution
- A solution in which attractions between unlike particles are similar to attractions between like particles, so Raoult's law is followed closely.
Common Mistakes to Avoid
- Using mass fraction instead of mole fraction is wrong because Raoult's law depends on the number of particles in moles, not their masses.
- Forgetting that a nonvolatile solute has essentially no vapor pressure is wrong because only the solvent contributes significantly to the vapor above the solution.
- Assuming vapor pressure lowering depends on the solute's chemical identity is wrong for ideal colligative behavior because the main factor is the number of dissolved particles.
- Thinking boiling-point elevation means the solution has a higher vapor pressure at the same temperature is wrong because the solution actually has a lower vapor pressure and must be heated more to boil.
Practice Questions
- 1 At 25°C, pure water has a vapor pressure of 23.8 torr. A solution has Xwater = 0.920 and contains a nonvolatile solute. Calculate the vapor pressure of the solution.
- 2 A solution contains 3.00 mol of ethanol and 2.00 mol of water. If P°ethanol = 59.0 torr and P°water = 23.8 torr at the same temperature, assume ideal behavior and calculate the total vapor pressure.
- 3 Explain why adding salt to water lowers the vapor pressure but raises the boiling point, using particle behavior at the liquid surface.