operates by the same principle.
BOILING-POINT ELEVATION
A liquid boils when its vapor pressure equals the atmospheric pressure. Since, as we have seen
above, the vapor pressure of a solution is lower than that of the pure solvent, more energy (and
consequently a higher temperature) will be required before its vapor pressure equals atmospheric
pressure. In other words, the boiling point of a solution is higher than that of the pure solvent. The
extent to which the boiling point of a solution is raised relative to that of the pure solvent is given by
the following formula:
∆Tb = K (^) bm
where ∆Tb is the boiling-point elevation, Kb is a proportionality constant characteristic of a
particular solvent, and m is the molality of the solution. Note how similar this equation is in form to
that for freezing-point depression: The only difference is that a solvent will have different values for
Kf and Kb, and that it is important to keep in mind that in one case the temperature is raised (∆T > 0),
while in the other case the temperature is lowered (∆T < 0).
OSMOTIC PRESSURE
Consider a container separated into two compartments by a semipermeable membrane (which, by
definition, selectively permits the passage of certain molecules). One compartment contains pure
water, while the other contains water with dissolved solute. The membrane allows water but not the
solute molecules to pass through. Because it is more favorable for the two compartments to
equalize their concentration, water will diffuse from the compartment containing pure water to the
compartment containing the water-solute mixture. This net flow will cause the water level in the
compartment containing the solution to rise above the level in the compartment containing pure
water.
Because the solute cannot pass through the membrane, the concentrations of solute in the two
compartments can never be equal. The pressure exerted by the water level in the solute-containing
compartment will eventually oppose the influx of water, and thus the water level will rise only to the
point at which it exerts a sufficient pressure to counterbalance the tendency of water to flow across