Colligative properties (ΔTb, ΔTf, π) calculator

Chemistry · Solutions

Boiling-point elevation, freezing-point depression and osmotic pressure

Enter a solute mass, molar mass, van’t Hoff factor and solvent data to compute molality, ΔTb, ΔTf and π, or switch to molar-mass mode to infer an unknown M from an experiment. A classic classroom exercise is to compare a 1.0 m non-electrolyte with an ideal NaCl solution (i ≈ 2) and see how doubling the number of dissolved particles roughly doubles the colligative effects.

How to use (3 steps)

Choose the mode: property calculation (ΔTb, ΔTf, π) or molar mass from colligative data.
Start from the water example or select another solvent, then adjust solute mass, molar mass, i, volumes and temperature.
Read off the summary and step-by-step log, then copy the URL to share the exact scenario with students or colleagues.

All calculations run in your browser only; no solute, solvent or result data are sent to any server.

Inputs

Use grams for masses, litres for volumes and kelvins for temperature. The default water example corresponds to a 1.0 m non-electrolyte solution.

Quick examples:

Property mode (ΔTb, ΔTf, π) Molar mass from colligative data

Solvent

Choosing a preset fills Kb, Kf, Tb⁰ and Tf⁰ for you; you can still edit the constants manually.

Solvent name

Boiling-point elevation constant Kb (K·kg/mol)

Freezing-point depression constant Kf (K·kg/mol)

Pure solvent boiling point Tb⁰ (°C)

Pure solvent freezing point Tf⁰ (°C)

Solute name

Molar mass M (g/mol)

van’t Hoff factor i

For a non-electrolyte, take i = 1. For NaCl that dissociates ideally into two ions, i ≈ 2.

Solute mass (g)

Solvent mass (g)

Solution volume (L, optional for π)

Temperature T (K) for π

Results

Mode: Property mode (ΔTb, ΔTf, π)

Colligative data: From boiling-point elevation ΔTb

This section summarizes molality, colligative changes (ΔTb, ΔTf, π) and, in molar-mass mode, the estimated molar mass M consistent with your measurements.

How it is calculated

Steps will appear here after calculation.

Formulas (LaTeX)

Use these LaTeX forms for handouts, slides, or worked examples. They follow the same sign and unit conventions as this calculator.

FAQ

What are colligative properties?

Colligative properties are solution properties that depend mainly on the number of dissolved particles, not on their chemical identity. Classic examples are boiling-point elevation, freezing-point depression, vapour-pressure lowering and osmotic pressure. This tool focuses on ΔTb, ΔTf and π for simple, dilute solutions using the textbook relations ΔTb = i Kb m, ΔTf = i Kf m and π = i c R T.

Can I use electrolytes with this tool?

Yes. Set the van’t Hoff factor i to the effective number of dissolved particles per formula unit (for example i ≈ 2 for ideal NaCl, i ≈ 3 for ideal CaCl₂). For concentrated or strongly non-ideal solutions, this simple i-factor model only gives an approximate result.

What is the difference between molality m and molarity c?

Molality m uses the number of moles of solute per kilogram of solvent (mol/kg), while molarity c uses moles of solute per litre of solution (mol/L). This calculator uses molality together with Kb and Kf to compute ΔTb and ΔTf, and uses molarity and temperature when computing the osmotic pressure π. In practice that means you enter masses (in g) for solute and solvent, and only need solution volume and temperature when you are interested in π.

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