💧 Colligative Properties & Membrane Thermodynamics
Osmotic Pressure Calculator ($\Pi = iMRT$)
Compute equilibrium osmotic pressure across semipermeable membranes, calculate total solution osmolarity, and evaluate cellular tonicity (Isotonic, Hypotonic, Hypertonic).
💉 0.9% Normal Saline (NaCl, i=2)
🍬 5% Dextrose D5W (i=1)
🧪 CaCl₂ Solution (i=3)
🌊 Seawater (~27 atm)
Osmotic Parameters
Glucose/Sucrose = 1, NaCl = 2, CaCl₂/Na₂SO₄ = 3
mol/L (M)
Calculated Osmotic Pressure (Π)
7.84 atm
Osmolarity
308 mOsm/L
Tonicity vs Blood
Isotonic 🟢
Water Column Height
81.0 meters
💡 Biological Tonicity Impact:
At 308 mOsm/L, this solution is isotonic with human erythrocytes (red blood cells), resulting in zero net osmotic water flux and preventing cell lysis or crenation.
The Morse Equation of Osmotic Pressure
Jacobus Henricus van 't Hoff showed that solute molecules in dilute solutions exert an osmotic pressure equivalent to ideal gas pressure:
$$\Pi = i \cdot M \cdot R \cdot T$$
- Gas Constant ($R$): $0.082057\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K}) = 8.31446\text{ J}/(\text{mol}\cdot\text{K})$.
- Osmolarity: $\text{Osmolarity} = i \times M$ (expressed in $\text{Osm/L}$ or $\text{mOsm/L}$).
- Human Blood Osmolarity: Normal physiological osmolarity is $\sim 285 - 300\text{ mOsm/L}$ ($\Pi \approx 7.3 - 7.7\text{ atm}$ at $37^\circ\text{C}$).