Moreover, he recognized this linear relationship between pressure and solute concentration (at constant temperature) resembled the behavior of gas molecules (Giese, 1979), whose pressure and volume are related by the gas law:
where P is the pressure of a gas in atmospheres, V is its volume in liters, n is the number of moles of gas, R is the "gas constant" (0.082 liter-atmospheres per degree-mole) and T is is the absolute temperature. Rearranging this statement, segregating constants from variables and solving for pressure, produces:
The expression (n/V) is more complex for a solution of a solute in a solvent than it is for a gas, and the behavior of the particles is equally more complex. At low concentrations of solute, however (in the range of cellular concentrations!), the expression simplifies to the <<osmotic concentration>> of the solute. Finally, substituting pi for P produces the v'ant Hoff equation above. A 1 molar solution of an idealized, osmotically active non-electrolyte creates an osmotic pressure of 22.4 atmospheres!
Thus, appreciating the relationship between osmosis and solute concentration provides a basis for measuring the effects of osmosis on cell volume, for example, and for predicting whether a cell in any aqueous environment will swell or shrink. How might you derive an equation relating the velocity of osmosis between two compartments to the solute concentrations in those compartments? Are <<gaseous and osmotic pressures>> really equivalent?