Osmotic Pressure

Separate two solutions of different strength with a membrane that lets the solvent through but not the solute, and solvent moves from the dilute side to the concentrated one. The pressure that must be applied to the concentrated side to stop it is the osmotic pressure.

• $\Pi$ is the osmotic pressure
• $i$ is the number of particles each formula unit breaks into
• $C$ is the molar concentration
• $R$ is the gas constant
• $T$ is the absolute temperature

This is the van 't Hoff equation. Rewriting the ideal gas law as $P = \dfrac{n}{V}RT$ reveals an identical shape, because dissolved particles behave much as gas molecules do.

Example

The default input dissolves 9 g of salt in a litre of water and measures at body temperature, 37 °C. That is essentially physiological saline.

The concentration is $9 \div 58.44$, about 0.154 mol/L, and salt splits in two, doubling the particle count.

The osmotic pressure comes to about 794 kPa, or about 7.84 atm, which is 5958 mmHg.

Larger than it sounds

Almost eight atmospheres is a serious pressure. In terms of depth it matches the pressure at the bottom of 80 m of water, and it arises from a solution that is only 0.9 percent salt.

Intravenous fluids are fixed at 0.9 percent precisely so their osmotic pressure matches blood. Get it wrong and red blood cells either take on water until they burst or give up water and shrivel.

The same physics explains why reverse osmosis desalination needs such high pressures. Pushing water back against its osmotic pressure requires exceeding that pressure.

Points to watch

Against the calculated 7.84 atm, blood's actual osmotic pressure is about 7.6 atm. Salt does not dissociate completely in water, and its effective $i$ is nearer 1.86. Entering 1.86 instead of 2 brings the answer closer to measurement.

The equation is an approximation for dilute solutions and drifts as concentration rises.

Temperature enters as an absolute temperature. This calculator accepts degrees Celsius and converts to kelvin internally.