{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"colligative-properties"},"result":{"entity_type":"calculator","id":"colligative-properties","calculator_id":"colligative-properties","canonical_url":"https://tttkmbb.com/chemistry/colligative-properties","name":"Colligative Properties Calculator","title":"Colligative Properties Calculator – Freezing-Point Depression and Boiling-Point Elevation (ΔT = i·K·m)","category":"chemistry","category_name":"Chemistry","tool_name":"calculate_colligative_properties","featured_mcp_tool":false,"description":"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).","inputs":[{"name":"solvent","label":"Solvent","type":"enum","required":false,"default":"water","values":[{"value":"water","label":"Water (Kf 1.86, Kb 0.512)"},{"value":"benzene","label":"Benzene (Kf 5.12, Kb 2.53)"},{"value":"acetic_acid","label":"Acetic acid (Kf 3.90, Kb 3.07)","aliases":["acetic","ethanoic acid"]},{"value":"chloroform","label":"Chloroform (Kf 4.68, Kb 3.63)"},{"value":"nitrobenzene","label":"Nitrobenzene (Kf 8.1, Kb 5.24)"},{"value":"ethanol","label":"Ethanol (Kf 1.99, Kb 1.22)"},{"value":"carbon_tetrachloride","label":"Carbon tetrachloride (Kf 29.8, Kb 5.02)","aliases":["ccl4","tetrachloromethane"]}],"description":"Solvent, which sets Kf, Kb and the pure freezing and boiling points at 1 atm.","example":"water"},{"name":"molality_mol_per_kg","label":"Molality","type":"number","required":false,"max":100,"exclusive_min":0,"description":"Moles of solute per kilogram of solvent. Alternative to the mass inputs below.","example":1},{"name":"solute_mass_g","label":"Solute mass","type":"number","unit":"g","required":false,"exclusive_min":0,"description":"Mass of solute dissolved; with solvent_mass_g and a molar mass it gives the molality."},{"name":"solute_formula","label":"Solute formula","type":"string","required":false,"description":"Formula of the solute (e.g. C10H8, NaCl) to derive its molar mass. Alternative to solute_molar_mass_g_mol."},{"name":"solute_molar_mass_g_mol","label":"Solute molar mass","type":"number","unit":"g/mol","required":false,"max":10000000,"exclusive_min":0,"description":"Molar mass of the solute if no formula is given."},{"name":"solvent_mass_g","label":"Solvent mass","type":"number","unit":"g","required":false,"exclusive_min":0,"description":"Mass of solvent in grams (not the solution mass)."},{"name":"van_t_hoff_factor","label":"van 't Hoff factor i","type":"number","required":false,"default":1,"max":20,"exclusive_min":0,"description":"Particles per formula unit: 1 for non-electrolytes, 2 for NaCl, 3 for CaCl2 (ideal values).","example":2},{"name":"freezing_point_depression_c","label":"Measured freezing-point depression","type":"number","unit":"°C","required":false,"exclusive_min":0,"description":"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)."}],"outputs":[{"name":"molality_mol_per_kg","label":"Molality","type":"number","unit":"mol/kg","decimals":6,"description":"Solute molality, given, derived from masses or solved from ΔTf."},{"name":"freezing_point_depression_c","label":"Freezing-point depression ΔTf","type":"number","unit":"°C","decimals":4,"description":"i × Kf × m."},{"name":"boiling_point_elevation_c","label":"Boiling-point elevation ΔTb","type":"number","unit":"°C","decimals":4,"description":"i × Kb × m."},{"name":"new_freezing_point_c","label":"Freezing point of solution","type":"number","unit":"°C","decimals":3,"description":"Pure-solvent freezing point − ΔTf."},{"name":"new_boiling_point_c","label":"Boiling point of solution","type":"number","unit":"°C","decimals":3,"description":"Pure-solvent boiling point (1 atm) + ΔTb."},{"name":"solute_molar_mass_g_mol","label":"Solute molar mass","type":"number","unit":"g/mol","decimals":3,"description":"Molar mass used, or solved from ΔTf and the masses."},{"name":"particle_molality_osmol_per_kg","label":"Particle molality","type":"number","unit":"osmol/kg","decimals":6,"description":"i × m, the effective particle concentration."},{"name":"solvent_name","label":"Solvent","type":"string","decimals":4,"description":"Solvent name with the Kf and Kb values applied."},{"name":"solved_for","label":"Solved for","type":"string","decimals":4,"description":"temperature_changes, or molality / solute_molar_mass_g_mol when ΔTf is given."}],"input_schema":{"type":"object","properties":{"solvent":{"description":"Solvent, which sets Kf, Kb and the pure freezing and boiling points at 1 atm.","type":"string","enum":["water","benzene","acetic_acid","chloroform","nitrobenzene","ethanol","carbon_tetrachloride"],"default":"water","examples":["water"]},"molality_mol_per_kg":{"description":"Moles of solute per kilogram of solvent. Alternative to the mass inputs below.","type":"number","maximum":100,"exclusiveMinimum":0,"examples":[1]},"solute_mass_g":{"description":"Mass of solute dissolved; with solvent_mass_g and a molar mass it gives the molality. Unit: g.","type":"number","exclusiveMinimum":0,"x-unit":"g"},"solute_formula":{"description":"Formula of the solute (e.g. C10H8, NaCl) to derive its molar mass. Alternative to solute_molar_mass_g_mol.","type":"string"},"solute_molar_mass_g_mol":{"description":"Molar mass of the solute if no formula is given. Unit: g/mol.","type":"number","maximum":10000000,"exclusiveMinimum":0,"x-unit":"g/mol"},"solvent_mass_g":{"description":"Mass of solvent in grams (not the solution mass). Unit: g.","type":"number","exclusiveMinimum":0,"x-unit":"g"},"van_t_hoff_factor":{"description":"Particles per formula unit: 1 for non-electrolytes, 2 for NaCl, 3 for CaCl2 (ideal values).","type":"number","maximum":20,"exclusiveMinimum":0,"default":1,"examples":[2]},"freezing_point_depression_c":{"description":"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). Unit: °C.","type":"number","exclusiveMinimum":0,"x-unit":"°C"}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"molality_mol_per_kg":{"description":"Solute molality, given, derived from masses or solved from ΔTf. Unit: mol/kg.","type":"number","x-unit":"mol/kg"},"freezing_point_depression_c":{"description":"i × Kf × m. Unit: °C.","type":"number","x-unit":"°C"},"boiling_point_elevation_c":{"description":"i × Kb × m. Unit: °C.","type":"number","x-unit":"°C"},"new_freezing_point_c":{"description":"Pure-solvent freezing point − ΔTf. Unit: °C.","type":"number","x-unit":"°C"},"new_boiling_point_c":{"description":"Pure-solvent boiling point (1 atm) + ΔTb. Unit: °C.","type":"number","x-unit":"°C"},"solute_molar_mass_g_mol":{"description":"Molar mass used, or solved from ΔTf and the masses. Unit: g/mol.","type":"number","x-unit":"g/mol"},"particle_molality_osmol_per_kg":{"description":"i × m, the effective particle concentration. Unit: osmol/kg.","type":"number","x-unit":"osmol/kg"},"solvent_name":{"description":"Solvent name with the Kf and Kb values applied.","type":"string"},"solved_for":{"description":"temperature_changes, or molality / solute_molar_mass_g_mol when ΔTf is given.","type":"string"}}},"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)","method":"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.","sources":[{"name":"OpenStax Chemistry 2e – 11.4 Colligative Properties","url":"https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties","type":"textbook","retrieved_at":"2026-09-24"},{"name":"LibreTexts – Colligative Properties (Brown et al., Chemistry: The Central Science, 13.5)","url":"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","type":"textbook","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Freezing-point depression","url":"https://en.wikipedia.org/wiki/Freezing-point_depression","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"1 mol/kg NaCl in water (i = 2)","inputs":{"solvent":"water","molality_mol_per_kg":1,"van_t_hoff_factor":2},"expected":{"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"},"url":"https://tttkmbb.com/api/v1/calculate/colligative-properties?solvent=water&molality_mol_per_kg=1&van_t_hoff_factor=2"},{"name":"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},"expected":{"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"},"url":"https://tttkmbb.com/api/v1/calculate/colligative-properties?solvent=water&solute_mass_g=1&solvent_mass_g=50&freezing_point_depression_c=0.31&van_t_hoff_factor=1"}],"faq":[{"q":"Molality or molarity?","a":"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."},{"q":"Why does salt water freeze less than predicted?","a":"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."}],"tags":["freezing point depression","boiling point elevation","colligative properties","cryoscopic constant","molality","molar mass from freezing point"],"related":[{"calculator_id":"osmotic-pressure","reason":"The third colligative property, from molarity."},{"calculator_id":"molar-mass","reason":"Molar mass of the solute from its formula."},{"calculator_id":"moles-mass","reason":"Convert solute mass to moles for the molality."}],"links":{"html":"https://tttkmbb.com/chemistry/colligative-properties","markdown":"https://tttkmbb.com/chemistry/colligative-properties.md","json":"https://tttkmbb.com/chemistry/colligative-properties.json","api":"https://tttkmbb.com/api/v1/calculate/colligative-properties","schema":"https://tttkmbb.com/api/v1/calculators/colligative-properties","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:47:54Z","next_actions":[{"tool":"run_calculator","calculator_id":"colligative-properties","reason":"Run Colligative Properties Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/chemistry/colligative-properties.md"}}