Consider a U-tube in which a pure solvent such as water in the right arm is brought into contact with an aqueous solution made with a nonvolatile solute such as glucose (or any other soluble substance) in the left arm, and the two arms are separated by a semipermeable membrane (e.g., a selective membrane), permeable only to water, that is, solvent molecules. The two sides or arms of the U-tube are initially at the same height. It is observed that a pressure develops across the membrane that drives solvent molecules from the right arm into the left arm in an effort to dilute the solution and try to equalize concentrations in both arms. This pressure is called osmotic pressure, П, and the process is known as osmosis (Figure 1.2). It is given by the equation:
i = the van’t Hoff factor, which is equal to 1.00 since glucose is a nonelectrolyte,
M = the molarity of the solution,
R = the universal gas constant, 0.0821 Latm/Kmol,
T = the absolute temperature in Kelvins.
Sometime later, the system in the U-tube reaches equilibrium, and a height differential, AH, between the solution level on the left and pure solvent level on the right is observed. Because of this height differential, a hydrostatic pressure, AP, develops and remains, and is given by the equation
where p = the density of the glucose solution, and g = the acceleration constant due to gravity.
In fact, the final hydrostatic pressure is equal to the initial osmotic pressure. Note the basic difference between osmosis and diffusion. Although both processes are driven by concentration gradients, a semipermeable membrane is present as a barrier in osmosis. No barrier is present in the process of diffusion.
Osmosis is a commonly occurring biological process, regulating and maintaining the proper concentrations of electrolytes in the cells of the human body. Osmometry is often used to find the molar mass (MM) of an unknown substance dissolved in solution through its molarity, M, when the other quantities—mass of unknown substance, volume of solution, temperature, and osmotic pressure—can be measured experimentally.
A calculation of osmotic pressure is shown in the following example.
A very dilute sucrose solution of concentration 0.010 M in water is separated from pure water by an osmotic (i.e., semipermeable) membrane. Find the osmotic pressure that develops at 25 °C (298 K).
Use П = iMRr, where i = 1 for sugar and all other nonelectrolytes.
So П = (1)(0.010 M)(0.0821 L-atm/K-mol)(298 K) = 0.24 atm.
This result can also be converted into units of torr, if desired, since 1.0 atm = 760 Torr.
In that case, the osmotic pressure would be 182 Torr.