Osmotic Pressure

Osmosis is a process where solvent molecules move toward a solution through a semipermeable membrane. As the solution dilutes due to the entry of solvent, it expands. This expansion increases the hydrostatic pressure of the solution. When the hydrostatic pressure equals the osmotic pressure, osmosis stops.

Osmotic pressure, denoted by Π, is the minimum pressure needed to prevent the solvent from passing into the solution by osmosis. The van 't Hoff equation calculates the osmotic pressure of an ideal solution where the interactions between the solute and solvent are the same as those among the solvent molecules.

However, solutions of macromolecules like polymers are not ideal because of excluded volume effects, which is the space a polymer chain cannot occupy due to unfavorable chain overlapping, which causes the polymer to be more spread out than an ideal polymer chain, and interactions between the solute and solvent differ from those among the solvent molecules. This means their molar masses (M) are calculated using the expanded van 't Hoff equation, which involves the osmotic virial coefficient (B). This equation is further simplified by dividing both sides by the molar concentration of polymer J ([J]).

Now, by plotting the osmotic pressure divided by mass concentration (Π/c_mass,J) versus mass concentration (c_mass,J) for various concentrations of polymer J, the molar mass (M) can be determined from the y-intercept of the graph. The B value can be deduced from the slope of the line. This method provides a practical approach for determining the molar mass of polymers in solution.