Osmotic Pressure Formula
Reference for osmotic pressure pi = iMRT covering van't Hoff factor, molarity, and temperature.
Applications in IV fluids, dialysis, and reverse osmosis.
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The Formula
π = iMRT
Osmotic pressure drives water across a semipermeable membrane from low to high solute concentration. It is vital for understanding cell function, kidney filtration, and IV fluid preparation.
Variables
| Symbol | Meaning |
|---|---|
| π | Osmotic pressure (atm) |
| i | Van 't Hoff factor (number of particles per formula unit) |
| M | Molarity of the solution (mol/L) |
| R | Gas constant (0.0821 L⋅atm/mol⋅K) |
| T | Temperature (Kelvin) |
Example 1
Find the osmotic pressure of 0.1 M glucose (non-electrolyte) at 37°C
i = 1 (glucose does not dissociate), T = 310 K
π = 1 × 0.1 × 0.0821 × 310
π ≈ 2.55 atm
Example 2
Find the osmotic pressure of 0.15 M NaCl at 25°C
i = 2 (NaCl → Na⁺ + Cl⁻), T = 298 K
π = 2 × 0.15 × 0.0821 × 298
π ≈ 7.33 atm
When to Use It
Use the osmotic pressure formula when:
- Preparing IV solutions that are isotonic with blood
- Understanding water movement in plant and animal cells
- Designing reverse osmosis water purification systems
- Determining the molecular weight of unknown solutes
Key Notes
- The van't Hoff factor i assumes complete dissociation — at concentrations above ~0.1 M, ion pairing reduces i; more precise calculations require activity coefficients (Debye-Hückel theory)
- Normal blood osmolarity is ~285–295 mOsm/L; IV solutions outside ~270–310 mOsm/L cause cells to swell (hypotonic solution) or shrink and crenate (hypertonic solution)
- Reverse osmosis requires applied pressure exceeding the osmotic pressure of the feed water — seawater at ~35 g/L salinity has an osmotic pressure of about 27 atm, setting the minimum pump pressure
- The formula is structurally identical to the ideal gas law (PV = nRT) because dissolved solute particles create pressure against a membrane just as gas molecules create pressure against a container wall
Key Notes
- van't Hoff equation: π = iMRT: π is osmotic pressure (atm), i is the van't Hoff factor (particles per formula unit), M is molarity (mol/L), R = 0.08206 L·atm/(mol·K), and T is temperature (K). A 1 M glucose solution at 25°C: π = 1 × 1 × 0.08206 × 298 ≈ 24.4 atm.
- Osmosis direction — water moves to equalize concentration: Water moves across a semipermeable membrane from low solute concentration (high water activity) to high solute concentration (low water activity). Osmotic pressure is the pressure needed to stop this flow — it resists osmosis.
- Isotonic, hypertonic, hypotonic relative to cells: Isotonic solution (~285 mOsm/L for blood): no net water movement. Hypertonic: cells lose water and shrink (crenation in red blood cells). Hypotonic: water enters cells, causing swelling and potentially lysis. This is why IV fluids must be isotonic.
- Reverse osmosis: apply pressure > π to force pure water through: Seawater osmotic pressure ≈ 27 atm. Reverse osmosis desalination applies 55–80 atm. The membrane allows water but blocks ions, producing fresh water from seawater or brackish water.
- Applications: Osmotic pressure is central to kidney dialysis (controlled osmosis to remove waste products), IV fluid formulation, food preservation by osmotic dehydration (salt-curing, jam-making), desalination technology, plant nutrient uptake (root osmotic pressure drives water absorption), and capillary oncotic pressure in physiology.