12.8:
Vapor Pressure Lowering
Some properties of a solution depend on the type of solute. An aqueous solution of hydrochloric acid turns a pH paper red, while a sodium hydroxide solution turns it blue.
Other properties of a solution depend only on the concentration or the number of particles of the solute rather than the type of solute. These are called colligative properties.
One such property is the vapor pressure of a solution. The vapor pressure of a liquid is the pressure of the gas above the liquid resulting from evaporation when the liquid and the gas are in a dynamic equilibrium in a closed container.
The vapor pressure of the solution is always less than that of the pure solvent.
Consider a solution made when a non-volatile solute, that is one with no measurable vapor pressure, is added to a volatile solvent.
In a pure solvent, the entire surface of the liquid is solvent particles. Some of these particles escape into the gaseous state to create vapor, while some of the gas molecules above condense back into a liquid state.
When the rate of vaporization equals the rate of condensation, a dynamic equilibrium is reached.
In a solution, the liquid surface has both solute and solvent particles. So, a smaller number of the surface solvent particles can vaporize.
The rate of condensation decreases to re-establish the dynamic equilibrium with the diminished rate of vaporization, now with a lower concentration of solvent particles in the gaseous state.
The vapor pressure of a solution can be calculated by Raoult’s law, which states that the partial pressure of a solution is equal to the mole fraction of the solvent, X, multiplied by the vapor pressure of the pure solvent, Pº.
For example, a solution contains 1.5 mol of a non-volatile solute such as glycerol and 3.5 mol of water at 25 °C. The mole fraction of the solvent is 0.70 and the vapor pressure of pure water is 23.8 torr.
The vapor pressure of the solution can be calculated using Raoult’s law to be 16.7 torr, 70% of the vapor pressure of the pure solvent.
An equation for vapor pressure lowering, ΔP, can also be derived from Raoult’s Law. Since the mole fraction of the solvent is equal to one minus the mole fraction of the solute, it can be substituted into Raoult’s Law.
This can be used to create an equation where vapor pressure lowering is directly proportional to the mole fraction of the solute.
Recalling the previous example, the mole fraction of the solute is 1 minus the mole fraction of the solvent. Plugging in the value, the mole fraction of the solute is 0.3.
Given that the vapor pressure of pure water is 23.8 torr, the lowering of vapor pressure is calculated to be 7.14 torr.
Adding ΔP and the vapor pressure of the solution, the vapor pressure of the pure solvent is obtained
12.8:
Vapor Pressure Lowering
The equilibrium vapor pressure of a liquid is the pressure exerted by its gaseous phase when vaporization and condensation are occurring at equal rates:
Dissolving a nonvolatile substance in volatile liquid results in a lowering of the liquid’s vapor pressure. This phenomenon can be explained by considering the effect of added solute molecules on the liquid's vaporization and condensation processes. To vaporize, solvent molecules must be present at the surface of the solution. The presence of solute decreases the surface area available to solvent molecules and thereby reduces the rate of solvent vaporization. Since the rate of condensation is unaffected by the presence of solute, the net result is that the vaporization-condensation equilibrium is achieved with fewer solvent molecules in the vapor phase (i.e., at a lower vapor pressure).
While this interpretation is useful, it does not account for several important aspects of the colligative nature of vapor pressure lowering. A more rigorous explanation involves the property of entropy. For purposes of understanding the lowering of a liquid's vapor pressure, it is adequate to note that the more dispersed nature of matter in a solution, compared to separate solvent and solute phases, serves to effectively stabilize the solvent molecules and hinder their vaporization. A lower vapor pressure results, and a correspondingly higher boiling point.
The relationship between the vapor pressures of solution components and the concentrations of those components is described by Raoult’s law: The partial pressure exerted by any component of an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.
where PA is the partial pressure exerted by component A in the solution, PºA is the vapor pressure of pure A, and XA is the mole fraction of A in the solution.
Recalling that the total pressure of a gaseous mixture is equal to the sum of partial pressures for all its components (Dalton’s law of partial pressures), the total vapor pressure exerted by a solution containing i components is
A nonvolatile substance is one whose vapor pressure is negligible (Pº ≈ 0), and so the vapor pressure above a solution containing only nonvolatile solutes is due only to the solvent:
This text is adapted from Openstax, Chemistry 2e, Section 11.4: Colligative Properties.
Suggested Reading
- Andrews, Frank C. "Colligative properties of simple solutions." Science 194, no. 4265 (1976): 567-571.
- Lindsay Jr, W. T., and Chu Tisin Liu. “Vapor pressure lowering of aqueous solutions at elevated temperatures.” Westinghouse Research Laboratories, Pittsburgh, Pennsylvania, 1968.
- Chinard, Francis P. "Colligative properties." Journal of Chemical Education 32, no. 7 (1955): 377.