π = iCRT in real time. Compare cell tonicity (hyper / iso / hypo), and instantly read the operating pressure required for reverse-osmosis seawater desalination.
Solution presets
Concentration C
mol/L
van't Hoff factor i
Temperature T
°C
Cell interior C_cell
mol/L
Applied pressure Papp (for RO)
atm
Push Papp > π on the concentrated side to drive reverse osmosis (water flows back).
Isotonic (in equilibrium)
Results
Osmotic pressure π
—
atm
π
—
kPa
Column rise Δh (equil.)
—
cm
Net water flow
→
(dilute → conc.)
Osmosis / reverse osmosis across a semipermeable membrane (live)
Concentration vs π
Solution comparison
Theory & Key Formulas
$\pi = iCRT$ (van't Hoff equation)
$i$ — van't Hoff factor (non-electrolyte = 1, NaCl ≈ 1.86) $R = 0.08206\,\text{L·atm/(mol·K)}$, $T$ in kelvin Osmosis: water crosses the membrane to the concentrated side until the column $\Delta h$ satisfies $\rho g\,\Delta h = \pi$ (equilibrium). Reverse osmosis: when applied pressure $P_{app} \gt \pi$, water is pushed back (conc. → dilute). Check: $i=1,\ C=1\,\text{mol/L},\ T=298\,\text{K}\ \Rightarrow\ \pi\approx 24.5$ atm ($\approx 24.8$ bar).
💬 Discussion
🙋
When salt is sprinkled on a cucumber and water beads out, is that osmosis?
🎓
Exactly. Water leaves the cucumber cells through their semipermeable membranes toward the higher-concentration salt outside. The reverse case is isotonic saline (0.9% NaCl) — its osmotic pressure matches body cells, so there is no net water flow.
🙋
Why does NaCl have a van't Hoff factor near 2?
🎓
Because NaCl dissociates into Na⁺ and Cl⁻, so 1 mole of solid acts like 2 moles of particles in solution. In concentrated solutions ion-ion interactions reduce dissociation slightly, so i lands near 1.86 instead of exactly 2.
🙋
How much pressure does seawater desalination really need?
🎓
Seawater has osmotic pressure around 27 atm (2.7 MPa). Real RO plants run at 5–8 MPa to drive enough flux through the membranes. Pick the seawater preset and the calculator confirms why these plants are energy-hungry.
Frequently asked questions
Q. How does antifreeze relate to osmotic pressure?
A. Adding ethylene glycol raises osmotic pressure and lowers freezing point (ΔTf = Kf × i × C). Both are colligative properties — they depend on the number of dissolved particles, which is exactly what π = iCRT counts.
Q. Why is IV saline 0.9% NaCl?
A. The osmotic pressure of plasma is about 7.7 atm. 0.9% NaCl gives ≈ 0.154 mol/L × 1.9 ≈ 0.29 osmol/L, matching plasma. More concentrated solutions shrink red blood cells; weaker ones cause haemolysis.
Q. Is plant water uptake really osmosis?
A. Mostly water-potential gradients. Root cell sap is more concentrated than soil water, so water is drawn in by the osmotic gradient. The "root pressure" generated this way contributes to lifting water, although leaf transpiration is the dominant pull in tall plants.
Q. Difference between dialysis and reverse osmosis?
A. Dialysis exploits diffusion across a membrane to remove small solutes (e.g. urea). RO uses pressure to force water through a tighter membrane that rejects almost all solutes including ions. RO membranes have pores ~0.1 nm, far smaller than dialysis membranes.
About this calculator
The van't Hoff equation $\pi = iCRT$ is the simplest reliable model of osmotic pressure: it pretends solute particles behave like an ideal gas inside a solvent. Pick a solution preset or move the sliders, and the page recomputes π in atmospheres and kPa, the cell-vs-solution tonicity, and the water-flux direction.
The "Cell & osmosis" tab paints a single cell against the chosen external solution; the cell radius shrinks or swells with the calculated tonicity ratio. The other tabs sweep concentration and benchmark common laboratory solutions for quick reference.
Real-world applications
Pharmaceutical IV solutions. Saline drips, glucose drips, and Ringer's solution must be isotonic with plasma to avoid haemolysis or cell shrinking. Manufacturers use π = iCRT during in-process control to verify each batch.
Reverse-osmosis desalination. Seawater needs roughly 27 atm of osmotic pressure overcome before water can pass through an RO membrane. Plants typically run at 50–80 atm to maintain a useful permeate flux.
Food & biology labs. Cell biology, plant physiology, and food preservation all rely on tonicity. The simulator is handy for teaching freezing-point depression, plasmolysis, and even drug-delivery liposome design.
Common misconceptions
"π = iCRT works for any solution." The equation is reliable only for dilute, ideal solutions. Strong electrolytes at high concentration deviate due to ion-ion interactions; tune i carefully (NaCl ≈ 1.86, not exactly 2).
"Pressure depends on concentration only." Temperature multiplies π linearly through T. A 25 °C → 40 °C swing changes π by ~5%. Always set the temperature slider to match your scenario.
"Hypertonic always means immediate shrinkage." Cell-membrane water permeability and intracellular non-permeating solutes change the rate and final volume. Plant cells with rigid walls show turgor and respond differently from animal cells.
Enter solute concentration in mol/L (range 0.01–2.0 M) using the concOSNum input or slider
Set temperature in °C over the 0–50 °C input range; the calculation converts it to absolute temperature K for π = iCRT
Input van 't Hoff factor (i = 1 for glucose, i = 2 for NaCl, i = 3 for CaCl₂) in vantNum field
Click Calculate to compute osmotic pressure using π = iCRT
Review cell potential or turgor pressure response in cellNum output
Worked Example
A 0.15 M NaCl solution at 298 K (body temperature) with van 't Hoff factor i = 1.86 generates osmotic pressure: π = 1.86 × 0.15 × 8.314 × 298 = 69.2 kPa. This equals approximately 0.68 atm, matching physiological conditions in red blood cells. Plant cells at 293 K in 0.3 M sucrose (i = 1.0) develop π = 7.4 atm (750 kPa), creating cellular turgor needed for structural rigidity.
Practical Notes
Electrolytes (NaCl, KCl) show i ≈ 1.8–1.9 due to ion pairing; non-electrolytes (glucose, sucrose) maintain i = 1.0
Hypertonic solutions (π > 300 kPa) cause crenation in mammalian cells; hypotonic solutions trigger hemolysis
Temperature increases linearly with osmotic pressure; 10 K rise raises π by ~3–4% for constant concentration
Industrial dialysis and reverse-osmosis systems operate at pressures exceeding 5 MPa to overcome natural osmotic gradients