Gibbs Free Energy / Spontaneity Calculator mechanism

Model scope

The listed formulas are standard, but the specification is ambiguous about standard versus nonstandard quantities, omits the crossover formula and the required temperature for the K-to-ΔG° path, and does not define how the spontaneity verdict handles ΔG=0 or invalid crossover temperatures.

• ΔG=ΔH−TΔS is correct when ΔH and ΔS refer to the same reaction and consistent thermodynamic state; the spec does not distinguish ΔG from ΔG° or state whether the inputs are standard quantities.
• ΔG°=−RT ln K is correct only for a dimensionless equilibrium constant K and a specified absolute temperature T; the stated 'K to back out ΔG°' input path does not explicitly require T.
• The claimed crossover temperature requires the additional formula T_eq=ΔH/ΔS and is valid only when ΔS is nonzero; a positive physical crossover temperature is not guaranteed.
• The inverse relation needed to calculate K from ΔG° is not listed explicitly: K=exp(−ΔG°/(RT)).
• A negative ΔG establishes thermodynamic favorability under the specified conditions, not that the reaction will proceed at an observable rate; kinetic limitations are not represented.

Units and conventions

• T must be in kelvin, not degrees Celsius.
• ΔH and TΔS must use compatible energy units; for example, convert ΔS from J/(mol·K) to kJ/(mol·K) before combining it with ΔH in kJ/mol.
• R must use matching energy units: 8.314462618 J/(mol·K) or 0.008314462618 kJ/(mol·K).
• K is dimensionless and must be defined from a specified standard state; it is not a quantity with units.
• The formulas assume ΔH and ΔS are applicable at the supplied temperature; temperature dependence of heat capacities is ignored unless separately modeled.
• Spontaneity means ΔG<0 is favorable, ΔG=0 is equilibrium, and ΔG>0 is unfavorable for the stated direction under the stated conditions.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "ΔH": "-100 kJ/mol",
    "ΔS": "-200 J/(mol·K)",
    "T": "298 K"
  },
  "expected_outputs": {
    "ΔG": "-40.4 kJ/mol",
    "spontaneity": "favorable (ΔG<0)",
    "crossover_temperature": "500 K"
  },
  "working": "Convert ΔS: −200 J/(mol·K) ÷ 1000 = −0.200 kJ/(mol·K). Compute TΔS: 298 K × (−0.200 kJ/(mol·K)) = −59.6 kJ/mol. Compute ΔG: −100 kJ/mol − (−59.6 kJ/mol) = −40.4 kJ/mol. Since ΔG<0, the direction is thermodynamically favorable. Set ΔG=0 for crossover: T_eq=ΔH/ΔS=(−100 kJ/mol)/(−0.200 kJ/(mol·K))=500 K."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The crossover-temperature calculation has an explicit division-by-zero failure when ΔS=0 and must return undefined or reject the request. The specification also leaves unit and direction conventions implicit, allowing a 1000-fold entropy-unit error or a reversed spontaneity verdict if conventions are not enforced.

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
• BOUNDARY_HAZARD_CATALOG.json