Osmotic Pressure

Osmosis

Osmosis is the net movement of water across a semipermeable membrane from a region of low solute concentration to high solute concentration. The pressure required to halt this flow is the osmotic pressure.

Van't Hoff Equation

$\Pi = i \cdot M \cdot R \cdot T$

Where:

• Π — osmotic pressure (Pa)
• i — van't Hoff factor (number of ions per formula unit)
• M — molar concentration (mol/m³; 1 mM = 1 mol/m³)
• R = 8.314 J·mol⁻¹·K⁻¹
• T — absolute temperature (K)

Van't Hoff Factors

Physiological Osmotic Pressure

Normal blood plasma osmolarity ≈ 308 mOsm/L, giving Π ≈ 5700–6000 mmHg (~7.8 atm) at body temperature.

Osmolarity

$\text{Osmolarity (Osm/L)} = i \times M \text{ (mol/L)}$

0.9% NaCl (physiological saline): 154 mM NaCl × i=2 = 308 mOsm/L.

Water Potential

In plant physiology, water potential:

$\Psi = \Psi_s + \Psi_p$

Where Ψ_s = −Π (solute potential) and Ψ_p is turgor pressure.

Unit Conversion

• 1 mmHg = 133.322 Pa
• 1 atm = 101,325 Pa = 760 mmHg

Functions to Implement

• osmotic_pressure_Pa(M_mol_m3, T_K=310, i=1) — osmotic pressure in Pascals
• osmotic_pressure_mmHg(M_mol_m3, T_K=310, i=1) — osmotic pressure in mmHg
• osmolarity_osmol_L(M_mol_L, i=1) — osmolarity in Osm/L