# Colligative Properties Calculator

> Computes freezing-point depression and boiling-point elevation of a solution from its molality (given directly or from solute mass, molar mass and solvent mass), the van 't Hoff factor and the solvent's Kf and Kb, and reports the new freezing and boiling points; it can also solve the molality and solute molar mass from a measured freezing-point depression.

- Calculator id: `colligative-properties` · Category: Chemistry (`chemistry`) · Tool name: `calculate_colligative_properties`
- Canonical page: https://tttkmbb.com/chemistry/colligative-properties · This document: https://tttkmbb.com/chemistry/colligative-properties.md · JSON definition: https://tttkmbb.com/chemistry/colligative-properties.json

## Purpose

Computes freezing-point depression and boiling-point elevation of a solution from its molality (given directly or from solute mass, molar mass and solvent mass), the van 't Hoff factor and the solvent's Kf and Kb, and reports the new freezing and boiling points; it can also solve the molality and solute molar mass from a measured freezing-point depression.

**Use when:** You need the freezing or boiling point of a solution (antifreeze, salted water, a lab solution) or want the molar mass of an unknown solute from a cryoscopic measurement.

**Do not use when:** You need osmotic pressure (use osmotic-pressure), the solute is volatile (it changes the vapour pressure itself), or the solution is concentrated (above about 1 mol/kg the linear ΔT = K·m relation loses accuracy).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `solvent` | enum: water \| benzene \| acetic_acid \| chloroform \| nitrobenzene \| ethanol \| carbon_tetrachloride |  | optional, default "water" | Solvent, which sets Kf, Kb and the pure freezing and boiling points at 1 atm. |
| `molality_mol_per_kg` | number |  | optional | Moles of solute per kilogram of solvent. Alternative to the mass inputs below. (> 0, max 100) |
| `solute_mass_g` | number | g | optional | Mass of solute dissolved; with solvent_mass_g and a molar mass it gives the molality. (> 0) |
| `solute_formula` | string |  | optional | Formula of the solute (e.g. C10H8, NaCl) to derive its molar mass. Alternative to solute_molar_mass_g_mol. |
| `solute_molar_mass_g_mol` | number | g/mol | optional | Molar mass of the solute if no formula is given. (> 0, max 10000000) |
| `solvent_mass_g` | number | g | optional | Mass of solvent in grams (not the solution mass). (> 0) |
| `van_t_hoff_factor` | number |  | optional, default 1 | Particles per formula unit: 1 for non-electrolytes, 2 for NaCl, 3 for CaCl2 (ideal values). (> 0, max 20) |
| `freezing_point_depression_c` | number | °C | optional | Observed ΔTf; when given, the molality is solved from it (and the solute molar mass when solute_mass_g and solvent_mass_g are also given). (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `molality_mol_per_kg` | number | mol/kg | Solute molality, given, derived from masses or solved from ΔTf. |
| `freezing_point_depression_c` | number | °C | i × Kf × m. |
| `boiling_point_elevation_c` | number | °C | i × Kb × m. |
| `new_freezing_point_c` | number | °C | Pure-solvent freezing point − ΔTf. |
| `new_boiling_point_c` | number | °C | Pure-solvent boiling point (1 atm) + ΔTb. |
| `solute_molar_mass_g_mol` | number | g/mol | Molar mass used, or solved from ΔTf and the masses. |
| `particle_molality_osmol_per_kg` | number | osmol/kg | i × m, the effective particle concentration. |
| `solvent_name` | string |  | Solvent name with the Kf and Kb values applied. |
| `solved_for` | string |  | temperature_changes, or molality / solute_molar_mass_g_mol when ΔTf is given. |

## Formula

`m = (solute_mass_g / solute_molar_mass_g_mol) / (solvent_mass_g / 1000); ΔTf = i × Kf × m; ΔTb = i × Kb × m; Tf = Tf,pure − ΔTf; Tb = Tb,pure + ΔTb; from a measurement: m = ΔTf / (i × Kf) and molar_mass = solute_mass_g / (m × solvent_mass_g / 1000)`

Kf and Kb in °C·kg/mol: water 1.86/0.512, benzene 5.12/2.53, acetic acid 3.90/3.07, chloroform 4.68/3.63, nitrobenzene 8.1/5.24 (OpenStax Table 11.2), ethanol 1.99/1.22 and carbon tetrachloride 29.8/5.02 (Brown et al.). The relations are ideal-dilute-solution limits for a non-volatile solute.

## Data Sources

- OpenStax Chemistry 2e – 11.4 Colligative Properties — https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties (textbook, retrieved 2026-09-24)
- LibreTexts – Colligative Properties (Brown et al., Chemistry: The Central Science, 13.5) — https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/13%3A_Properties_of_Solutions/13.05%3A_Colligative_Properties (textbook, retrieved 2026-09-24)
- Wikipedia – Freezing-point depression — https://en.wikipedia.org/wiki/Freezing-point_depression (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/colligative-properties?`
- `POST https://tttkmbb.com/api/v1/calculate/colligative-properties` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/colligative-properties · OpenAPI operationId `calculate_colligative_properties` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "colligative-properties", "inputs": {…}}`

## Example

- 1 mol/kg NaCl in water (i = 2): inputs `{"solvent":"water","molality_mol_per_kg":1,"van_t_hoff_factor":2}` → `{"freezing_point_depression_c":3.72,"new_freezing_point_c":-3.72,"boiling_point_elevation_c":1.024,"new_boiling_point_c":101.024,"particle_molality_osmol_per_kg":2,"solved_for":"temperature_changes"}`
- Molar mass: 1.00 g solute in 50.0 g water lowers Tf by 0.310 °C: inputs `{"solvent":"water","solute_mass_g":1,"solvent_mass_g":50,"freezing_point_depression_c":0.31,"van_t_hoff_factor":1}` → `{"molality_mol_per_kg":0.166667,"solute_molar_mass_g_mol":120,"new_freezing_point_c":-0.31,"boiling_point_elevation_c":0.0853,"solved_for":"solute_molar_mass_g_mol"}`

```
GET https://tttkmbb.com/api/v1/calculate/colligative-properties?solvent=water&molality_mol_per_kg=1&van_t_hoff_factor=2
```

## Limitations

You need osmotic pressure (use osmotic-pressure), the solute is volatile (it changes the vapour pressure itself), or the solution is concentrated (above about 1 mol/kg the linear ΔT = K·m relation loses accuracy). Kf and Kb in °C·kg/mol: water 1.86/0.512, benzene 5.12/2.53, acetic acid 3.90/3.07, chloroform 4.68/3.63, nitrobenzene 8.1/5.24 (OpenStax Table 11.2), ethanol 1.99/1.22 and carbon tetrachloride 29.8/5.02 (Brown et al.). The relations are ideal-dilute-solution limits for a non-volatile solute. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Molality or molarity?**

Colligative constants are defined per kilogram of solvent (molality), not per litre of solution; for dilute aqueous solutions the two are numerically close, but use solvent mass here.

**Why does salt water freeze less than predicted?**

The ideal i = 2 for NaCl overstates the effect: ion pairing gives a measured i of about 1.9 at 0.1 mol/kg and lower at higher concentration. Enter a measured van 't Hoff factor for better accuracy.

## Related

- [Osmotic Pressure Calculator](https://tttkmbb.com/chemistry/osmotic-pressure.md) — The third colligative property, from molarity.
- [Molar Mass Calculator](https://tttkmbb.com/chemistry/molar-mass.md) — Molar mass of the solute from its formula.
- [Moles to Grams Calculator](https://tttkmbb.com/chemistry/moles-mass.md) — Convert solute mass to moles for the molality.