solution are related to the properties of those solutes. However, some solution properties
simply depend on the numberof solute particles, not the type of solute. These properties
are called colligative propertiesand include:
vapor pressure lowering
freezing-point depression
boiling-point elevation
osmotic pressureVapor Pressure Lowering
If a liquid is placed in a sealed container, molecules will evaporate from the surface of
the liquid and eventually establish a gas phase over the liquid that is in equilibrium
with the liquid phase. The pressure generated by this gas is the vapor pressureof the
liquid. Vapor pressure is temperature-dependent; the higher the temperature, the
higher the vapor pressure. If the liquid is made a solvent by adding a nonvolatile solute,
the vapor pressure of the resulting solution is always less than that of the pure liquid.
The vapor pressure has been lowered by the addition of the solute; the amount of low-
ering is proportional to the number of solute particles added and is thus a colligative
property.
Solute particles are evenly distributed throughout a solution, even at the surface. Thus,
there are fewer solvent particles at the gas–liquid interface where evaporation takes place.
Fewer solvent particles escape into the gas phase, and so the vapor pressure is lower. The
higher the concentration of solute particles, the less solvent is at the interface and the lower
the vapor pressure. This relationship is referred to as Raoult’s law.Freezing-Point Depression
The freezing point of a solution of a nonvolatile solute is always lower than the freezing
point of the pure solvent. It is the number of solute particles that determines the
amount of the lowering of the freezing point. The amount of lowering of the freezing
point is proportional to the molality of the solute and is given by the equationΔTf=iKfmolalitywhere ΔTfis the number of degrees that the freezing point has been lowered (the differ-
ence in the freezing point of the pure solvent and the solution); Kfis the freezing-point
depression constant (a constant of the individual solvent); the molalityis the molality
of the solute; and iis the van’t Hoff factor––the ratio of the number of moles of parti-
cles released into solution per mole of solute dissolved. For a nonelectrolyte, such as
sucrose, the van’t Hoff factor would be 1. For an electrolyte, such as sodium chloride,
you must take into consideration that if 1 mol of NaCl dissolves, 2 mol of particles
would result (1 mol Na+, 1 mol Cl−). Therefore, the van’t Hoff factor should be 2.
However, because sometimes there is a pairing of ions in solution, the observed van’t
Hoff factor is slightly less (for example, it is 1.9 for a 0.05 m NaCl solution). The more
dilute the solution, the closer the observed van’t Hoff factor should be to the expected
factor. If you can calculate the molality of the solution, you can also calculate the freez-
ing point of the solution.184 Step 4. Review the Knowledge You Need to Score High
KEY IDEA