Osmotic Pressure Calculator
Calculate the osmotic pressure of a solution using the van't Hoff equation: π = iMRT. Solve for osmotic pressure, concentration, temperature, or van't Hoff factor.
💧 Osmotic Pressure (van't Hoff Equation)
✅ Result
What Is Osmotic Pressure?
Osmotic pressure (π) is the minimum pressure that must be applied to a solution to prevent the inward flow of pure solvent across a semipermeable membrane. It is a colligative property, meaning it depends on the number of dissolved particles, not their identity.
When a semipermeable membrane separates a solution from pure solvent, solvent molecules naturally flow from the dilute side (pure solvent) to the concentrated side. Osmotic pressure is the force needed to stop this flow entirely.
The van't Hoff Equation
Where:
- π — Osmotic pressure (atm)
- i — van't Hoff factor (number of particles per formula unit)
- M — Molar concentration of solute (mol/L)
- R — Universal gas constant = 0.08206 L·atm/(mol·K)
- T — Absolute temperature (K)
Rearranged Forms
| Solve For | Formula |
|---|---|
| Osmotic pressure (π) | π = iMRT |
| Concentration (M) | M = π / (iRT) |
| Temperature (T) | T = π / (iMR) |
| van't Hoff factor (i) | i = π / (MRT) |
The van't Hoff Factor (i)
The van't Hoff factor represents the number of particles a solute produces when dissolved. For non-electrolytes, i = 1. For electrolytes, i depends on the degree of dissociation.
| Solute | Dissociation | Ideal i | Actual i (dilute) |
|---|---|---|---|
| Glucose (C6H12O6) | No dissociation | 1 | 1.00 |
| Sucrose | No dissociation | 1 | 1.00 |
| NaCl | Na+ + Cl− | 2 | 1.9 |
| KCl | K+ + Cl− | 2 | 1.9 |
| MgCl2 | Mg2+ + 2 Cl− | 3 | 2.5 |
| CaCl2 | Ca2+ + 2 Cl− | 3 | 2.6 |
| FeCl3 | Fe3+ + 3 Cl− | 4 | 3.4 |
| Al2(SO4)3 | 2 Al3+ + 3 SO42− | 5 | ~4 |
The actual i is often less than the ideal value because ion pairing occurs in solution (especially at higher concentrations).
How to Calculate Osmotic Pressure
- Determine the van't Hoff factor (i) based on the solute type.
- Find the molar concentration (M) of the solution.
- Convert temperature to Kelvin: T(K) = T(°C) + 273.15.
- Apply π = iMRT using R = 0.08206 L·atm/(mol·K).
0.5 M NaCl at 25°C. What is the osmotic pressure?
i = 2 (Na+ + Cl−)
T = 25 + 273.15 = 298.15 K
π = 2 × 0.5 × 0.08206 × 298.15 = 24.47 atm
This is about 360 psi — a very significant pressure!
Osmosis and Reverse Osmosis
Osmosis
Osmosis is the spontaneous movement of solvent (usually water) across a semipermeable membrane from a region of low solute concentration to a region of high solute concentration. This continues until equilibrium is reached or osmotic pressure balances the driving force.
Reverse Osmosis
By applying a pressure greater than the osmotic pressure, you can force water to flow in the opposite direction — from the concentrated solution to the dilute side. This is the principle behind:
- Water desalination: Seawater (~25 atm osmotic pressure) is pushed through membranes at 55–80 atm to produce fresh water.
- Water purification: Home RO systems operate at 3–10 atm for tap water treatment.
- Industrial separations: Concentrating fruit juices, dairy, and pharmaceutical solutions.
Biological Importance of Osmotic Pressure
- Cell survival: Cells placed in a hypertonic solution (higher external π) shrink (crenation). In a hypotonic solution (lower external π), cells swell and may burst (lysis). Isotonic solutions (equal π) maintain cell integrity.
- IV fluids: Saline solution (0.9% NaCl) is isotonic with blood plasma (~7.7 atm osmotic pressure).
- Kidney function: The kidneys use osmotic gradients to concentrate urine and regulate blood osmolality (275–295 mOsm/kg).
- Plant turgor: Osmotic pressure keeps plant cells rigid by maintaining turgor pressure against the cell wall.
Pressure Unit Conversions
| Unit | Equivalent to 1 atm |
|---|---|
| 1 atm | = 1 atm (reference) |
| kPa | = 101.325 kPa |
| mmHg (Torr) | = 760 mmHg |
| bar | = 1.01325 bar |
| psi | = 14.696 psi |
Frequently Asked Questions
Why is osmotic pressure a colligative property?
Because it depends only on the number of dissolved particles, not on what those particles are. A 1 M glucose solution and a 0.5 M NaCl solution (which gives 1 M total ions) have approximately the same osmotic pressure.
What is the osmotic pressure of blood?
Human blood plasma has an osmotic pressure of approximately 7.7 atm (5,800 mmHg) at 37°C. This is maintained by dissolved salts (mainly NaCl), proteins (oncotic pressure), and other solutes.
Can osmotic pressure be negative?
No. Osmotic pressure is always a positive value representing the pressure needed to stop osmotic flow. If you calculate a negative value, check your inputs.