[{"data":1,"prerenderedAt":148},["ShallowReactive",2],{"cheatsheet-colligative-properties":3},{"sheet":4},{"sheetSlug":5,"topicSlugs":6,"primaryTopic":7,"title":8,"subtitle":9,"sections":10},"colligative-properties",[5],19,"Colligative Properties","Van 't Hoff factor, freezing/boiling shifts, Raoult's law, osmotic pressure, and molar-mass back-calculation.",[11,44,53,61,69,97,105,113,122,132,140],{"heading":12,"kind":13,"columns":14,"items":17},"Van 't Hoff factor i","data",[15,16],"Solute","i (predicted)",[18,41],{"ref":19,"mode":22,"provenance":23,"rows":24,"source_hash":40},{"type":20,"topic":7,"id":21,"field":20},"rule","CP-R004","transform","owned_workbook",[25,28,31,34,37],[26,27],"nonelectrolyte (glucose, urea)","1",[29,30],"NaCl, HCl, KBr","2",[32,33],"CaCl₂, Na₂SO₄","3",[35,36],"AlCl₃, Na₃PO₄","4",[38,39],"Al₂(SO₄)₃","5","800f18bd4982c30e1a58e3ff10d25ac12e04f56e2dfcbf191566919650df8b35",{"ref":42,"mode":22,"provenance":23,"text":43,"source_hash":40},{"type":20,"topic":7,"id":21,"field":20},"i = particles per formula unit on full dissociation. Use the predicted (integer) i for forward calculations; measured i runs a bit lower at real concentrations (ion pairing).",{"heading":45,"kind":46,"items":47},"Strong-electrolyte dissociation","rules",[48],{"ref":49,"mode":22,"provenance":23,"text":51,"source_hash":52},{"type":20,"topic":7,"id":50,"field":20},"CP-R003","Each ion's concentration = compound concentration × its coefficient. Total dissolved particles = i × compound concentration. CaCl₂ → Ca²⁺ + 2Cl⁻ gives total = 3 × [CaCl₂].","e93966b8731849205890518bd74bb04a3964e4e297f0a850db97d302e4801dd7",{"heading":54,"kind":46,"items":55},"Freezing-point depression",[56],{"ref":57,"mode":22,"provenance":23,"text":59,"source_hash":60},{"type":20,"topic":7,"id":58,"field":20},"CP-R005","ΔTf = Kf·m·i (m = molality). New FP = pure FP − ΔTf. For water (FP 0 °C) the depressed FP = −ΔTf. Kf is solvent-specific (supplied).","1ac6b5f7299063bbe11a39622a290edf3b5a5c470f2aea1a42b1f42048f805b0",{"heading":62,"kind":46,"items":63},"Boiling-point elevation",[64],{"ref":65,"mode":22,"provenance":23,"text":67,"source_hash":68},{"type":20,"topic":7,"id":66,"field":20},"CP-R006","ΔTb = Kb·m·i. New BP = pure BP + ΔTb. For water (BP 100 °C) the elevated BP = 100 + ΔTb. Kb is solvent-specific (supplied).","2de5c38f7a06d45e6a3652faf47a9fea9293598a5cb6a9b8403a6df8a0cd4764",{"heading":70,"kind":13,"columns":71,"items":75},"Common constants (°C·kg/mol)",[72,73,74],"Solvent","Kf","Kb",[76],{"ref":77,"mode":22,"provenance":23,"rows":79,"source_hash":96},{"type":20,"topic":7,"id":78,"field":20},"CP-R001",[80,84,88,92],[81,82,83],"water","1.86","0.512",[85,86,87],"benzene","5.12","2.53",[89,90,91],"chloroform","4.68","3.63",[93,94,95],"camphor","37.7","n/a","72d772b1c903ceedbf7010822eebae1b2573cb1bb40cf8fb1ae144e430c0e549",{"heading":98,"kind":46,"items":99},"Raoult's law (vapor pressure)",[100],{"ref":101,"mode":22,"provenance":23,"text":103,"source_hash":104},{"type":20,"topic":7,"id":102,"field":20},"CP-R007","Nonvolatile solute: ΔP = X_solute·P°_solvent, or P_solution = X_solvent·P°_solvent. Use particle-based mole fraction (i × n_solute) for electrolytes. Two volatile components: P_total = X_A·P°_A + X_B·P°_B.","e2317bc278ecd3d57f6f99e762a79645ba269c5d7bc15c38b42798f81c83a65f",{"heading":106,"kind":46,"items":107},"Osmotic pressure",[108],{"ref":109,"mode":22,"provenance":23,"text":111,"source_hash":112},{"type":20,"topic":7,"id":110,"field":20},"CP-R009","π = i·M·R·T with MOLARITY (not molality), R = 0.0821 L·atm/(mol·K), T in K; π in atm. Given in molality/mass? You need density to convert to molarity.","a03de523676a2a3920ee56b8648de4edf718610d03f493922bf945b3b2620393",{"heading":114,"kind":115,"items":116},"Kelvin vs °C","pitfalls",[117],{"ref":118,"mode":22,"provenance":23,"text":120,"source_hash":121},{"type":20,"topic":7,"id":119,"field":20},"CP-R002","Osmotic pressure needs T in Kelvin. But ΔTf and ΔTb are the same magnitude in °C or K, so apply K constants directly. Report final FP/BP in °C.","5d9c9266f38ac72cc97b72a903db729eccc93e52028bc0558ed413571486c95c",{"heading":123,"kind":124,"items":125},"Molar mass from ΔT","steps",[126],{"ref":127,"mode":22,"provenance":129,"text":130,"source_hash":131},{"type":20,"topic":7,"id":128,"field":20},"CP-R010","original","n_solute = ΔT / (K·kg_solvent·i), K = Kf or Kb, i = 1 for a nonelectrolyte (the usual MW case). Then MW = mass_solute / n_solute.","8430455dcc58807c2b8fef48c0bc866dacf168fd462f34f2d9154c2223326ac4",{"heading":133,"kind":124,"items":134},"Molar mass from osmotic pressure",[135],{"ref":136,"mode":22,"provenance":129,"text":138,"source_hash":139},{"type":20,"topic":7,"id":137,"field":20},"CP-R011","n_solute = π·V / (R·T·i), i = 1 for biomolecules (lysozyme, hemoglobin). Then MW = mass_solute / n_solute. π is often tiny, so convert torr/mmHg to atm first.","86269f100aa2858968e88341368c9cb5e3c125e904b013c563e7bffdd67e19c7",{"heading":141,"kind":124,"items":142},"Molecular formula protocol",[143],{"ref":144,"mode":22,"provenance":129,"text":146,"source_hash":147},{"type":20,"topic":7,"id":145,"field":20},"CP-R012","Back-calc MW from ΔT or π; get the empirical formula from % composition; n = MW / empirical-formula mass (round to an integer); molecular formula = empirical × n. Single-element (Sₙ): n = MW / atomic mass.","4c443652226e1a74bb1f62dbb4607931ef13ce7934669dc0bd3743470221cf97",1787246033441]