# Osmotic Pressure definition clarification

currently reading Legninger's Principles of Biochemistry (8th edition if you absolutely needed to know) and under "Osmotic Pressure" it gives the definition to be:

Osmotic pressure, $$\Pi$$, [is] measured as the force necessary to resist water movement...

I find this way of thinking a little confusing, why should I care about resisting the water's force across a membrane? I want to know if it's equivalent for me to interpret this as the force the water EXERTS as it passes through a membrane. Learning from Mr. Isaac Newton, I would take this to be a safe assumption. Please let me know if I am wrong!

• *SIR Isaac Newton, forgive me
– Joël
Aug 17, 2022 at 18:36

Rather as "...the pressure necessary...", not force.

The full speed osmosis means zero differential pressure on the membrane. The non zero water net flow is caused by differences of water molecule collision frequencies and therefore of water diffusion rates in both directions.

Applying pressure ( externally or hydrostatically ) on the membrane from the side of the (more concentrated) solution compensates lower diffusion speed by counteracting pressure gradient flow.

The particular value of the counteracting pressure, that would cause the zero net water flow, is called the osmotic pressure of the solution.

If the pressure is high enough, it may cause a rupture of the membrane. One of possible demonstrations can be putting a tomato in deionized water.

OTOH, if no such pressure is applied and there is full osmotic water(or other solvent) flow, there is no unidirectional mechanical pressure on the membrane.

In summary, osmosis is the flow of solvent across a semipermeable membrane from a region of lower to higher solute concentration. Thermodynamically the process is driven by the increase in entropy on mixing more solvent with the solute. In solution, the solvent passes both ways through the semipermeable membrane but the solute cannot. Osmosis is not restricted to solution and can occur in the gas phase.

Using the word 'force' is confusing as is 'resistance'. A pressure difference exists across the semi-permeable membrane. This is balanced by applying external pressure, such as from a vertical capillary tube into which the solution moves as its volume increases, and equilibrium thereby restored. The external pressure produced by gravity acting on the vertical column of solution is equal to the osmotic pressure. The thermodynamic description was first given by Gibbs in 1897 but this does not explain anything at a molecular level. In fact many textbooks avoid this aspect completely.

One experimental observation is that the flow due to osmosis is greater than that possible from diffusion and is due to hydrodynamic flow through the membrane. This would be damped out very quickly so there has to be a process that keeps this going. Kramers et al. (Kramers & Myers, Am. J. Phys. v80,p694 2012) suggest the following. The solute collides with the membrane and is repelled, its momentum (now away from the membrane) is then dispersed between the solvent molecules, these being in greatest numbers, and this produces an effective potential barrier to solvent flow which by Boltzmann distribution means that fewer solvent molecules enter the membrane from the solution side, i.e. the membrane partly repels solvent molecules. This does not happen on the pure solvent side so more solvent flows into the solution than flows out increasing the hydrostatic pressure in the solution.

Another explanation based on MD simulations (Lion et Al. J. Chem. Phys. v137, p244911, 2012) is that osmosis is due to the density imbalance of solvent particles across the membrane. They write

'the density imbalance of solvent particles across the membrane is maintained by a balance between an outward force-driven flux (due to the higher total density in the solution) and an inward diffusive flux (due to the lower solvent density in the solution). We show that a simple calculation, based on the mechanics of hopping of solvent molecules across the membrane, can be used to derive the same relation between the solvent density gradient and the osmotic pressure as is obtained by standard thermodynamic arguments.'

So it seems that although osmosis is well studied its actual mechanism is still in dispute and much remains unresolved.