2
represented by Eq. 1. This equation includes the molar gas law
constant (R) that takes int account volume, temperature, and
pressure, and the solvent activity (a1), which mostly depend on
concentration and thus is usually taken as unity (one) for the
pure solvent and as the mole fraction (x1) for ideal solutions.
R, is the molar gas law constant, is 8.314 J mole -1 K -1. The pres-
sure required to prevent the movement of solvent through the
semi-permeable membrane must be equal to the free energy
of the pure solvent and is called osmotic pressure (π). The
osmotic pressure is related to the molar volume of the solvent
(V1) in Eq. 2, which describes the fundamental relationship
between osmotic pressure and solution thermodynamics.
For dilute solutions, the solvent activity (a1) can be approxi-
mated as (1 - x2), where x2 is the mole fraction of the solute. In
this case, Eq. 2 becomes Eq. 3, which is similar to the ideal gas
law and is known as the van't Hoff equation.
Measurements of osmotic pressure made early in the twentieth
century on dilute sucrose solutions using copper ferrocyanide
membranes confirmed the applicability of Eq. 3. For example, a
0.0291 molar aqueous sucrose solution at 15.6°C exhibited an
osmotic pressure of 0.684 atm compared with the calculated
value of 0.689 atm. Osmotic pressure is a sensitive property
that changes with the concentration of the solute. It can be
used to determine the molar mass of a polymer by measur-
ing the osmotic pressure when the polymer is dissolved in
a solvent. The osmotic pressure is measured using a special
device called an osmometer. There are limitations to measur-
ing osmotic pressure due to the requirements of specialized
membranes. However, synthetic polymeric films can be used as
permeable membranes in aqueous solutions to study interac-
tions between substances. By understanding osmotic pressure
and using specific equations, scientists can gather important
data about solutes and study solution thermodynamics.
Reverse Osmosis
Just as the osmotic pressure is that pressure which when
applied to the solution phase will prevent the solvent from
passing through a semipermeable membrane into the solution,
the application of greater pressure will cause solvent to pass
from the solution into the pure solvent, or reverse osmosis. The
versatility and efficiency of reverse osmosis make it a valuable
method for water purification, desalination, and wastewater
treatment. Its wide-ranging applications contribute to ad-
dressing water scarcity, promoting sustainability, and ensuring
access to clean water resources.
Osmosis (continued)
Fig. 2: Concept of osmotic pressure.
(Credit: McGraw Hill)
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