Library / Solution chemistry, equilibria and kinetics / SCH-48
Solution chemistry, equilibria and kinetics
Osmotic pressure of a dilute solution
Osmotic pressure of a dilute solution across a membrane that passes only the solvent, from the formula-unit concentration c in mol/L, the effective van’t Hoff factor i and the temperature.
- Ref
- SCH-48
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- Π [Pa]
The van’t Hoff equation for osmotic pressure is Π = i c R T, which has the form of the ideal gas law. With c in mol/L it needs a factor of 1000 to convert to mol/m³ to give pascals. i is the effective number of particles per formula unit, so near 2 for a fully dissociated 1:1 salt, and less in practice. It applies to dilute solutions and a membrane permeable only to the solvent.
Osmotic pressure of a dilute solution across a membrane that passes only the solvent, from the formula-unit concentration c in mol/L, the effective van’t Hoff factor i and the temperature. The factor 1000 converts mol/L to mol/m³, giving pascals.
Calculator
- Osmotic pressure in bar0.2494 bar
- Equivalent height of water, Π/(ρ g) with ρ = 1000 kg/m³2.543 m
- Particle concentration, i c0.01 mol/L
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A 0.01 mol/L solution at 300 K has an osmotic pressure of 24,940 Pa (0.2494 bar), which would support 2.543 m of water.
- Osmotic pressures are large even for dilute solutions, which is why seawater at about 0.6 mol/L of salt needs over 25 bar to desalinate by reverse osmosis.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Pa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| c Formula-unit concentration | 1e-5 to 2 mol/L | 24.94 | 4,989,000 | 4,989,000 | +10% | +10 % |
| i Effective van’t Hoff factor | 1 to 5 | 24,940 | 124,700 | 99,770 | +10% | +10 % |
| T Temperature | 250 to 400 K | 20,790 | 33,260 | 12,470 | +10% | +10 % |
Sweep of Formula-unit concentration
| Formula-unit concentration (mol/L) | Osmotic pressure (Pa) |
|---|---|
| 1e-5 | 24.94 |
| 4.599e-5 | 114.7 |
| 2.115e-4 | 527.5 |
| 9.725e-4 | 2,426 |
| 0.004472 | 11,160 |
| 0.02057 | 51,300 |
| 0.09457 | 235,900 |
| 0.4349 | 1,085,000 |
| 2 | 4,989,000 |
Sweep one variable
Variables and how each one contributes
Osmotic pressure
What the equation gives you. Everything else feeds it.
Effective van’t Hoff factor
The effective van’t Hoff factor (particles per formula unit). Raises the osmotic pressure in direct proportion. Raising it by 10 % (to 1.1) moves the result by +10 %, from 24,940 to 27,440 Pa.
Formula-unit concentration
The formula-unit concentration, in mol/L. Raises the osmotic pressure in direct proportion. Raising it by 10 % (to 0.011) moves the result by +10 %, from 24,940 to 27,440 Pa.
Temperature
The absolute temperature, in K. Raises the osmotic pressure in direct proportion. Raising it by 10 % (to 330) moves the result by +10 %, from 24,940 to 27,440 Pa.
Worked example with the values above
- Particle concentration in mol/m³: i × 1000 × c = 1 × 1000 × 0.01 = 10.
- R T = 8.3144626 × 300 = 2,494.3 J/mol.
- Π = 10 × 2,494.3 = 24,943 Pa.
Assumptions and limits
- Dilute or ideal solutions with a non-volatile solute, unless a second volatile component is stated.
- Constant temperature (or constant pressure for boiling-point elevation) and a membrane that passes only the solvent for osmosis.
Common mistakes
- Using molarity where molality is needed for freezing and boiling points.
- Forgetting the van’t Hoff factor for salts.
- Adding the elevation or depression to the temperature in the wrong direction.
Statistics and uncertainty
Colligative formulas assume ideal behaviour, which holds only for dilute solutions. The effective particle factor i of an electrolyte is below its ideal value, by 5 % to 30 % even at 0.1 mol/kg.
Where it is used
- Estimating antifreeze, de-icing and desalination behaviour.
- Finding molar masses and reading simple phase diagrams.
Maths you need
- Raoult’s law: partial pressure = mole fraction × pure vapour pressure
- Colligative properties: properties that depend on particle number
- Molality: moles of solute per kilogram of solvent