Eucaryotic Cell Index Glossary
Osmosis and Hydrostatic Pressure Simulator
The flow of water across a membrane in response to differing concentrations of solutes on either side - osmosis - generates a pressure across the membrane called osmotic pressure. Osmotic pressure is defined as the hydrostatic pressure required to stop the flow of water, and thus, osmotic and hydrostatic pressures are, for all intents and purposes, equivalent. The membrane being referred to here can be an artifical lipid bilayer, a plasma membrane or a layer of cells.
The osmotic pressure P of a dilute solution is approximated by the following:
P = RT (C1 + C2 + .. + Cn)
where R is the gas constant (0.082 liter-atmosphere/degree-mole), T is the absolute temperature, and C1 ... Cn are the molar concentrations of all solutes (ions and molecules).
Similarly, the osmotic pressure across of membrane separating two solutions is:
P = RT (delta C)
where delta C is the difference in solute concentration between the two solutions. Thus, if the membrane is permeable to water and not solutes, osmotic pressure is proportional to the difference in solute concentration across the membrane (the proportionality factor is RT).
To get an appreciation for these equations, try the pressure simulator below. You can enter concentrations either as molarity or grams/liter. The choices of solute are:
- NaCl: molecular weight 58.44; dissociates in solution into sodium and chloride ions
- Sucrose (table sugar): molecular weight = 342.3; does not dissociate
- Albumin: molecular weight approximately 66,000; a single protein
Note: you can easily enter "impossible" solutions in the simulator, for example, 1 M albumin, which would require dissolving 66 kg of albumin in a liter! The simulator will notify you if the pressure is either less than 1 cm or above 10000 cm. P>
Suggestion: Determine the pressure generated when 8.5 grams/liter NaCl (0.145 M) is on one side and water on the other - this is pretty close to the situation of having blood on one side and water on the other. You should also investigate the question of how much large macromolecules like albumin contribute to osmotic pressure (blood serum contains roughly 3% albumin).
Assumed temperature is 20C or 293K
A note for the sophisticate: In the discussion and simulator above, it was assumed that each NaCl fully dissociates into two free ions, which is essentially the case for very dilute solutions. However, in more concentrated, physiologic solutions, these two ions attract one another and the "osmotically effective" concentration of solute is less than twice the molarity of NaCl (roughly 0.93X for NaCl). The Van't Hoff equation described above can be modified for additional accuracy by incorporation of an osmotic coefficient I (0.93 for NaCl):
P = I RT (C1 + C2 + .. + Cn)
Did you try the blood-water comparision? You should have found that "physiological saline" generates sufficient osmotic pressure to support a column roughly 70 meters high! The calculation performed (without accounting for effective concentration) was:
P = 0.082 liter-atm/mole-degree * 997.9 cm/atm * 293 degrees * 0.29 moles of solute/liter
Back to Osmosis
Last updated on July 9, 2000
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