Solutions and Colligative Properties ❮ 185sucrose solution are related to the properties of those solutes. However, some solution
properties simply depend on the number of solute particles, not the type of solute. These
properties are called colligative properties and include:
● (^) vapor pressure lowering
● (^) freezing-point depression
● (^) boiling-point elevation
● (^) osmotic pressure
Vapor 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 pressure of
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
lowering is proportional to the number of solute particles added and is thus a col-
ligative 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 deter-
mines 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 equation
DTf = iKf molality
where DTf is the number of degrees that the freezing point has been lowered (the dif-
ference in the freezing point of the pure solvent and the solution); Kf is the freezing-
point depression constant (a constant of the individual solvent); the molality is the
molality of the solute; and i is the van’t Hoff factor—the ratio of the number of moles
of particles 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 freezing point of the solution.