Colligative Properties Suite mechanism

Model scope

Core colligative-property equations are recognizable and standard under ideal dilute-solution assumptions, but the specification is not complete enough for an unambiguous implementation. Exact ambiguities requiring review are: whether the vapor-pressure output means P_solution or ΔP; which pure-solvent boiling/freezing reference points are used for new temperatures; whether osmotic-pressure R uses L·atm or SI units; and how solvent selection maps to Kb, Kf, pure phase-transition points, and temperature-specific vapor-pressure data.

• ΔTb=i·Kb·m and ΔTf=i·Kf·m are standard dilute-solution formulas when m is solute molality in mol/kg solvent and Kb/Kf use matching K·kg·mol^-1 units.
• π=iMRT is the standard ideal dilute-solution formula, but it requires absolute temperature and a consistent molarity/R unit system; concentrated solutions require activities or an osmotic-coefficient correction.
• P_solution=x_solvent·P°_solvent is Raoult's-law solution vapor pressure, not vapor-pressure lowering. The lowering formula is ΔP=P°_solvent−P_solution=x_solute·P°_solvent for a binary ideal solution.
• The claimed new boiling and freezing points require additional formulas and pure-solvent reference values: Tb,new=Tb°+ΔTb and Tf,new=Tf°−ΔTf. These formulas and required baseline inputs are absent.
• The phrase 'Kb/Kf (or solvent selection)' is incomplete unless the solvent table supplies Kb, Kf, normal boiling/freezing points, and the temperature-dependent pure-solvent vapor pressure.

Units and conventions

• m is molality in mol solute per kg solvent; Kb and Kf are in K·kg·mol^-1, numerically equivalent to °C·kg·mol^-1 for temperature differences.
• M is molarity in mol/L when R=0.082057 L·atm·mol^-1·K^-1, or M must be converted to mol/m^3 when using an SI R value.
• T in π=iMRT must be in kelvin, not °C.
• i is dimensionless and represents the effective van't Hoff factor under the stated solution conditions.
• x_solvent is the mole fraction of solvent, constrained to 0≤x_solvent≤1; P° and P_solution must use the same pressure units and the same temperature.
• Raoult's law assumes an ideal solution and uses the pure-solvent vapor pressure at the specified temperature.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "property": "boiling_point_elevation",
    "solvent": "water",
    "i": 2,
    "Kb": 0.512,
    "Kb_units": "K·kg·mol^-1",
    "m": 0.5,
    "m_units": "mol·kg^-1",
    "Tb_pure_C": 100
  },
  "expected_outputs": {
    "delta_Tb_K": 0.512,
    "new_boiling_point_C": 100.512
  },
  "working": "ΔTb=i·Kb·m=2.0×0.512×0.500=1.024×0.500=0.512 K. Tb,new=Tb°+ΔTb=100.000+0.512=100.512 °C."
}

Failure boundary

• Division-by-zero and invalid-input hazards can arise in upstream calculations of molarity, molality, or mole fractions if solvent mass, solution volume, or total mole amount is zero.
• Reject negative molality, molarity, temperature, Kb, Kf, or pressure values; enforce 0≤x_solvent≤1.
• Using Celsius directly in π=iMRT produces an incorrect result; temperature must be converted to kelvin.
• Mixing molality and molarity, or using Kb/Kf with incompatible units, produces dimensionally incorrect temperature changes.
• The van't Hoff factor is not always an integer and may vary with concentration, dissociation, association, or ion pairing; treating it as exact requires an explicit approximation.
• The dilute ideal-solution formulas may be inaccurate for concentrated electrolytes or nonideal solutions.
• P°_solvent is strongly temperature-dependent; the solvent vapor-pressure table must identify the temperature and pressure units.
• The current vapor-pressure formula does not directly return the claimed vapor-pressure lowering.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json