How to use the colligative properties calculator
- Enter the solute mass and molar mass, the van't Hoff factor and the solvent mass.
- Add the solution volume if you want the osmotic pressure.
- In More options, replace the example constants with those of your own solvent: Kf, Kb, the normal freezing and boiling points, molar mass and vapor pressure.
- Read the new freezing point, boiling point, vapor pressure and osmotic pressure.
Formula
Molality m = moles of solute / kg of solvent
Freezing point depression = i x Kf x m; boiling point elevation = i x Kb x m
Vapor pressure = (moles solvent / (moles solvent + i x moles solute)) x pure vapor pressure
Osmotic pressure = i x M x R x T, with R = 0.082057 L atm / (mol K)
The van't Hoff factor i is the number of particles each formula unit gives in solution. M is molarity in mol per liter and T is in kelvin.
Salt in water and sugar in water
5.844 g of table salt (58.44 g/mol) is 0.1 mol. Dissolved in 100 g of water that is a molality of 1 mol/kg. With i = 2 and the water constants Kf = 1.86 and Kb = 0.512, the freezing point drops by 3.72 degrees to -3.72 C and the boiling point rises by 1.024 degrees. The solvent mole fraction is 0.965223, giving a vapor pressure of 22.9337 torr against 23.76, a lowering of 0.8263 torr. In 104 mL of solution the osmotic pressure is 47.049 atm.
34.23 g of sugar (342.3 g/mol) in 200 g of water is 0.5 mol/kg, with i = 1: the freezing point falls by 0.93 degrees and the boiling point rises by 0.256. A solution of 400 g of antifreeze (62.07 g/mol) in 600 g of water is 10.74 mol/kg and freezes about 19.98 degrees lower.
What colligative means
A colligative property depends on how many dissolved particles there are, not what they are. Any solute lowers the freezing point and vapor pressure of the solvent and raises its boiling point, in proportion to the particle concentration. That is why salt melts ice on roads and why antifreeze keeps an engine from freezing.
Related chemistry tools include the solution dilution calculator, the moles to grams calculator, the pH and weak acid calculator and the ideal gas law calculator.
Why real results differ
These formulas assume an ideal dilute solution. In strong solutions, ions attract each other, so a salt acts as if it has fewer than the full number of particles, and the real i is lower than 2 for salt. The constants Kf and Kb belong to the solvent and are the values for water here as an example. Check a reference for your own solvent.
Assumptions and limits
- The solute is non-volatile and the solution is ideal and dilute. Mixed solvents and strong solutions are not modeled.
- The van't Hoff factor is your estimate; the page does not look up salts or apply ion-pairing corrections.
- The constants shown are example values for water. They are not looked up for you, so enter those for your solvent.
- Osmotic pressure needs the solution volume and a temperature, 25 C by default.
Frequently asked questions
How do I calculate freezing point depression?
Multiply the van't Hoff factor, the freezing constant Kf and the molality. For 1 mol/kg of salt in water with i = 2: 2 x 1.86 x 1 = 3.72 degrees below the normal freezing point.
What is the van't Hoff factor?
It counts the particles one formula unit produces in solution. Sugar is 1, table salt close to 2 and calcium chloride close to 3. In real solutions the measured value is a little lower than the ideal whole number.
Why does salt lower the freezing point of water?
Dissolved particles interfere with water molecules forming ice, so a lower temperature is needed before the water can freeze. The effect grows with the number of particles per kilogram of water.
What is osmotic pressure?
It is the pressure that must be applied to a solution to stop pure solvent flowing into it through a semipermeable membrane. It equals i M R T, and it is large even for modest concentrations.