Colligative Properties Calculator
Boiling point elevation and freezing point depression from molality, the van ’t Hoff factor and the solvent’s Kb or Kf, with the new boiling or freezing point, or osmotic pressure from molarity and temperature.
Result…
How it's calculated
Boiling point elevation: ΔTb = i × Kb × m Freezing point depression: ΔTf = i × Kf × m m = (mass of solute ÷ molar mass) ÷ kg of solvent Osmotic pressure: π = i × M × R × T (R = 8.31446261815324 J/(mol·K), T in K)
Colligative properties depend on how many solute particles are dissolved, not on what they are. A non-volatile solute lowers the solvent’s vapour pressure, so the solution boils at a higher temperature and freezes at a lower one; the change is the solvent’s constant (Kb or Kf) times the molality, times the van ’t Hoff factor i, the number of particles each formula unit gives. Osmotic pressure follows the same idea with molarity and absolute temperature. The solvent list uses the constants and normal boiling and freezing points from the LibreTexts general chemistry table; choose Other to enter your own. Results are ideal-solution estimates.
Your numbers, step by step
About the Colligative Properties calculator
This colligative properties calculator finds how much a dissolved substance lowers a solvent’s freezing point or raises its boiling point, and the osmotic pressure of a solution. Pick the solvent from the list, which fills in Kb or Kf and the normal boiling or freezing point, or choose Other and enter your own values. Give the molality directly, or the masses of solute and solvent with the molar mass, and set the van ’t Hoff factor for the number of particles each formula unit releases. You get the change in temperature and the new freezing or boiling point in both °C and °F. In osmotic pressure mode, it uses molarity and temperature and reports kPa, atm, bar, mmHg and psi. The steps show each substitution, which helps with homework and lab reports.
How to use it
- Under “Find”, choose “Freezing point”, “Boiling point” or “Osmotic pressure”.
- Pick the “Solvent”, or choose “Other (enter the values)” and fill in the “Solvent constant (Kb or Kf)” and the normal point.
- Set the “Van ’t Hoff factor (i)”: 1 for sugar or urea, 2 for NaCl, 3 for CaCl2 if fully dissociated.
- Under “Molality from”, enter the “Molality”, or choose “Masses” and enter the solute mass, its molar mass and the solvent mass.
- For osmotic pressure, enter the “Molarity” and the “Temperature” with its unit instead.
Worked example
29.22 g of sodium chloride (58.44 g/mol) is dissolved in 1 kg of water. Molality = 29.22 ÷ 58.44 ÷ 1 = 0.5 mol/kg. With i = 2 and Kf = 1.86 °C·kg/mol, ΔTf = 2 × 1.86 × 0.5 = 1.86 °C, so the solution freezes at about −1.86 °C (28.65 °F). For osmotic pressure, a 0.1 mol/L sugar solution (i = 1) at 25 °C (298.15 K) gives π = 0.1 × 8.31446 × 298.15 = 247.9 kPa, or 2.447 atm.
Updated
Questions people ask
How do I calculate freezing point depression?
Multiply the van ’t Hoff factor by the solvent’s Kf and the molality: ΔTf = i × Kf × m. Subtract the result from the pure solvent’s freezing point.
What are Kb and Kf for water?
The LibreTexts general chemistry table gives Kb = 0.5121 °C·kg/mol and Kf = 1.86 °C·kg/mol, the values this calculator uses. Other books round them slightly differently.
What is the van ’t Hoff factor?
The number of particles one formula unit gives in solution. Real values for salts are a little below the ideal count because some ions pair up, more so as the solution gets more concentrated.
Why do colligative formulas use molality and not molarity?
Boiling and freezing point changes depend on particles per amount of solvent, and molality stays fixed as temperature changes. The molality calculator converts from molarity if you have the density.
Does this work for concentrated solutions or antifreeze mixtures?
Only roughly. The formulas are for dilute, ideal solutions of a non-volatile solute; strong solutions and mixtures like glycol and water depart from them, so use measured data for those.