WOLFRAM|DEMONSTRATIONS PROJECT

Osmotic Pressure

solute

sucrose

NaCl

unknown

concentration (mg/L)

temperature (°C)

molecular weight

Osmosis involves the selective passage of certain components of a solution through a semipermeable membrane, with exclusion of other components. It is, of course, of central significance in biological processes. Consider in this Demonstration a membrane permeable only to water, but impermeable to the solute in a water solution. The membrane is represented by a blue disk at the bottom of the U-tube, separating the pure solvent on the left from the solution on the right. Solvent will spontaneously flow through the membrane into the solution, in a (vain) attempt to equalize the concentrations on the two sides. This gives rise to an osmotic pressure, designated

. For dilute solutions, the osmotic pressure, in atm, is well approximated by the van 't Hoff equation

Π=i[X]RT

, where

[X]

is the solute concentration in mol/L,

R=0.82057

L atm

-1

mol

, the ideal-gas constant, and

, the absolute temperature in K. The van 't Hoff factor

represents the number of ions per molecule for a dissociated solute. For example, for NaCl,

i=2

, giving the total number of

and

ions. All other solutes we consider are undissociated with

i=1

. The van 't Hoff equation can be written in a form remarkably analogous to the ideal gas law:

ΠV=

, but the underlying mechanisms for the two phenomena are completely different. Osmotic measurements provide a very sensitive method for determining molecular weights

, particularly for polymers. For a solute concentration of

g/L, the molar concentration

[X]

is equal to

An osmotic pressure of 1 atm would cause a rise of 1033.26 cm for the solution in a U-tube. To keep magnitudes to a more manageable laboratory scale, solute concentrations are limited to the range of 1-50 mg/L; 1 cm corresponds to

9.6781×

-4

atm or 0.73554 torr. You can measure solutions of sugar, table salt, or a random unknown. You have sufficient data then to calculate the molecular weight of the solute or, by marking the checkbox, let the program do the calculation.