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.
Understanding Chemistry: Raoult's Law and Vapor Pressure
Vapor pressure is not a measure of how fast a liquid boils. It describes a balance between liquid molecules entering the gas and gas molecules returning to the liquid. In a closed container, this balance becomes steady after some time.
Faster-moving molecules are more likely to leave the liquid, so warming a sample raises its vapor pressure. The dissolved material changes the chance that solvent molecules occupy the surface.
This is why the effect is linked to composition. It is not caused by the solute physically trapping every solvent molecule.
Mole fraction is the most useful way to describe that composition because it compares particle amounts. A large mass of a substance does not always mean many particles. For example, a small mass of a light solute can contain more particles than the same mass of a heavier solute.
Students should first convert each amount to moles, then find the total number of moles, then calculate each fraction. The fractions in a mixture must add up to one.
This provides a quick check on a calculation. A solvent-rich solution has a solvent mole fraction close to one, so its vapor pressure stays fairly close to that of the pure solvent.
The ideal model works best when unlike molecules attract each other about as strongly as like molecules do. Some real solutions do not behave this way. If solvent and solute molecules attract strongly, molecules have a harder time escaping into the gas.
The measured vapor pressure can be lower than the ideal prediction. This is called a negative deviation from Raoult's law. If unlike molecules attract weakly, escaping becomes easier and the measured pressure can be higher.
This is a positive deviation. Ethanol mixed with water is a useful example of a mixture that is not perfectly ideal because hydrogen bonding changes when the liquids are combined.
Electrolytes need extra care because they form several dissolved particles. Sodium chloride separates into sodium ions and chloride ions in water, so one formula unit can produce roughly two particles. More particles create a larger change in colligative properties than the same amount of a nonelectrolyte such as sugar.
The van't Hoff factor accounts for this difference, though real solutions may not reach the simple whole-number value because ions can attract each other. This idea matters in antifreeze, saline solutions, food preservation, and weather. Dissolved salts in road brine lower the freezing point, while dissolved substances in natural waters affect evaporation.
When solving problems, identify whether the solute is volatile, nonvolatile, or an electrolyte before choosing a model. Keep temperature units, pressure units, and amounts consistent, and remember that boiling point changes depend on the surrounding pressure as well as the solution composition.
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.