How to calculate osmotic pressure
Osmotic pressure is the pressure needed to stop water from flowing into a solution across a membrane, and it depends on the number of dissolved particles, not what they are. First find osmolarity by multiplying the molarity by the van't Hoff factor i, the number of particles each formula unit splits into (glucose stays as 1, NaCl splits into Na⁺ and Cl⁻ for 2, CaCl₂ into 3). Then the van't Hoff equation gives the pressure: π = iMRT, with R = 0.08206 L·atm/mol·K and temperature in kelvin. Comparing to blood plasma (about 0.30 Osm, roughly 7.6 atm at body temperature) tells you the tonicity: a more concentrated solution is hypertonic and pulls water out of cells, a less concentrated one is hypotonic and pushes water in.
Assumes ideal, fully dissociating solutes. Real solutions deviate slightly (the osmotic coefficient), so measured values run a bit lower than the ideal i.
Osmolarity isn't the same thing as tonicity
Everything above computes osmolarity, the total concentration of dissolved particles. But whether those particles actually pull water across a real membrane depends on whether the membrane lets them through. A solute that crosses the membrane just as easily as water contributes to osmolarity but does almost nothing to tonicity, since it can't stay concentrated on one side long enough to hold water there.
This is captured by the reflection coefficient (σ), a value between 0 and 1 for each solute-membrane pair: σ = 1 means the membrane completely blocks the solute (fully "effective", real, sustained osmotic pressure); σ = 0 means the solute crosses as freely as water (fully "ineffective", no matter how concentrated, it can't hold water anywhere). Effective osmolarity = the sum of σ×i×M over every solute, and that number, not total osmolarity, is what actually predicts water movement.
Urea is the classic example. Cell membranes are meaningfully permeable to it, so a urea solution has real, calculable osmolarity by the math above, but doesn't hold water the way the same osmolarity of NaCl would. A solution that's "iso-osmotic" to blood using urea alone still lets water move freely across the membrane, cells don't actually experience it as isotonic.
Plasma proteins apply the same principle at a different membrane. Capillary walls are leaky to small solutes, ions, glucose, and urea all cross fairly freely there, so none of those create effective osmotic pressure at the capillary level. What does stay trapped inside capillaries is plasma protein (mainly albumin), too large to cross. That protein-driven pressure is oncotic (colloid osmotic) pressure, and it's the force pulling fluid back into capillaries that balances the hydrostatic pressure pushing fluid out, together, Starling forces.
One more distinction worth knowing: this tool computes osmolarity (particles per liter of solution). Clinically, osmolality (particles per kilogram of solvent) is what lab osmometers actually measure. For dilute aqueous solutions like these, the two are numerically almost identical, but they aren't defined the same way.
Related tools: Molar mass & molarity · Membrane transport explorer · all biochem tools.
Worked example 1: 0.15 M NaCl at body temperature
The tool's default: 0.15 M NaCl (i = 2, since it dissociates into Na⁺ and Cl⁻) at 37 °C.
0.15 M NaCl is physiological saline. It's isotonic with blood by design, which is exactly why this is the tool's default example.
Worked example 2: 0.05 M CaCl₂ at room temperature
CaCl₂ dissociates into one Ca²⁺ and two Cl⁻, so i = 3. At 0.05 M and 25 °C:
Half the osmolarity of blood means this solution would push water into cells if the two were separated by a semipermeable membrane, the cells would swell.
FAQ
What's the difference between osmolarity and molarity?
Molarity counts moles of formula units; osmolarity counts moles of dissolved particles. A dissociating solute like NaCl produces more particles than its molarity alone suggests. That's what the van't Hoff factor i corrects for.
Why kelvin instead of Celsius?
π = iMRT comes from the same ideal-gas relationship as PV = nRT, which only holds with absolute temperature. Celsius can be zero or negative at normal lab temperatures, which would make the equation meaningless.
Is blood plasma exactly 0.30 Osm?
0.30 Osm (300 mOsm/L) is the standard approximate value used in coursework; real plasma typically falls around 275-295 mOsm/L. For exam purposes, 0.30 Osm is the reference point for judging tonicity.
Why does real osmotic pressure run a bit lower than the ideal calculation?
The van't Hoff factor i assumes complete, ideal dissociation. Real solutions have some ion pairing, especially at higher concentration, so the effective osmotic coefficient is a bit below the ideal integer i, measured pressure comes in slightly under the simple π = iMRT prediction.
Can a solution be iso-osmotic but not isotonic?
Yes. This is exactly the urea case. Total osmolarity only counts particles; tonicity depends on whether the membrane actually stops those particles from crossing. A freely permeant solute like urea can match blood's osmolarity on paper while still letting water move freely, since it can't stay concentrated on one side of the membrane.
Practice problems
1. Find the osmolarity and osmotic pressure of 0.1 M MgCl₂ at 37°C (i = 3).
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2. Is 0.30 M glucose (i = 1) at 25°C isotonic, hypotonic, or hypertonic to blood?
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Sources and how to cite this page
Osmotic pressure is calculated from the van’t Hoff equation, π = iMRT, where i is the van’t Hoff factor (the number of particles a formula unit dissociates into), M is molarity, R is the gas constant 0.08206 L·atm mol−¹K−¹, and T is absolute temperature. The equation is exact only in the dilute limit; real electrolyte solutions deviate because ions are not fully independent, which is described by the osmotic coefficient.
Osmolarity is not tonicity. Osmolarity counts every dissolved particle. Tonicity counts only the particles that cannot cross the membrane, so it is what actually determines whether a cell swells or shrinks. Urea is the standard example: it raises osmolarity but crosses membranes freely, so a urea solution can be iso-osmotic and still hypotonic.