Appreciating the relationship between osmosis and solute concentration provides a basis
for predicting whether a cell in any aqueous environment will swell or shrink and for
measuring and regulating the effects of osmosis on cell volume. Often, however, measuring
cell volume is difficult and it's more useful to consider the pressure produced *by*
osmosis or alternatively, the **osmotic pressure **necessary to prevent such
a change in volume.

What is the relationship between osmotic pressure and solute concentration? Specifically, considering the simulation on the right, how might you derive an equation relating the pressure necessary to prevent the barrier movement to the solute concentrations in the two compartments?

Over 100 years ago, Jacob v'ant Hoff, who won the first Nobel Prize in Chemistry,
derived a precise relationship between the osmotic pressure or potential of a solution (**p**, **pi**) and solute concentration (**C)**, a
proportionality constant (**R**) and the absolute temperature (**T**):

**p**** = CRT**

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**:

**PV = nRT**

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:

**P = (n/V) **x** RT**

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 **p****
**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!

Are** gaseous and osmotic pressures **really

The van't Hoff expression allows you to calculate the theoretical osmotic pressure of
any single compartment (against a reference compartment containing distilled water).
How can you use the van't Hoff relationship to predict and calculate the osmotic
pressure between two compartments (such as a cell and its environment)? To address
this question and explore the relationship between osmotic pressure and solute
concentration further, consider the **following
simulation** that has been expanded to include plotting and curve-fitting
functions.