Hess's Law Enthalpy Calculator mechanism

Model scope

The core Hess-law algorithm is standard and correct, but the specification is ambiguous about energy units, reaction extent, thermodynamic conditions, phase states, balance validation, and solver behavior for rank-deficient systems. The verdict is NEEDS_REVIEW until those requirements are made explicit.

• The stated formula ΔH_overall = Σ(coefficient × ΔH_step) is correct only when the signed step multipliers produce the target reaction exactly after cancellation of all species.
• The linear-algebra engine must detect no-solution and underdetermined/multiple-solution cases rather than returning an arbitrary result.
• Reaction species must include physical states, because Hess-law enthalpies can differ between phases such as H2O(l) and H2O(g).
• All reactions must refer to the same thermodynamic convention, temperature, pressure, and standard states when standard enthalpies are being combined.
• The specification does not explicitly require atom/charge balance validation for the target and every supplied reaction.

Units and conventions

• Each ΔH value is an enthalpy change for one stoichiometric reaction extent as written, not necessarily per mole of a named substance.
• All ΔH values within one calculation must use the same energy unit unless an explicit conversion is supplied; vector 3 deliberately supplies J/mol inputs and requests kJ per target reaction.
• Stoichiometric coefficients are dimensionless, and reversing a reaction changes the sign of ΔH; multiplying a reaction by k multiplies ΔH by k.
• Reaction states, temperature, pressure, and standard-state conventions are assumed consistent across all steps.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "target_equation": "CH4(g) + 2 O2(g) -> CO2(g) + 2 H2O(l)",
    "known_reactions": [
      {
        "id": "R1",
        "equation": "C(graphite) + O2(g) -> CO2(g)",
        "delta_H": "-393.51 kJ"
      },
      {
        "id": "R2",
        "equation": "H2(g) + 1/2 O2(g) -> H2O(l)",
        "delta_H": "-285.83 kJ"
      },
      {
        "id": "R3",
        "equation": "CH4(g) -> C(graphite) + 2 H2(g)",
        "delta_H": "+74.85 kJ"
      }
    ]
  },
  "expected_outputs": {
    "overall_delta_H": "-890.32 kJ",
    "step_multipliers": {
      "R1": "1",
      "R2": "2",
      "R3": "1"
    },
    "oriented_steps": [
      "R1 as written",
      "2 × R2 as written",
      "R3 as written"
    ]
  },
  "reference_data": {
    "combined_equation": "R1 + 2R2 + R3 = CH4(g) + 2 O2(g) -> CO2(g) + 2 H2O(l)",
    "method": "Signed stoichiometric linear combination"
  },
  "working": "R1 + 2R2 + R3: C + O2 -> CO2; 2H2 + O2 -> 2H2O; CH4 -> C + 2H2. Cancel C and 2H2 from opposite sides. Remaining equation: CH4 + 2O2 -> CO2 + 2H2O. Arithmetic: ΔH = 1(-393.51) + 2(-285.83) + 1(+74.85) = -393.51 - 571.66 + 74.85 = -965.17 + 74.85 = -890.32 kJ."
}

Failure boundary

• Division by zero or singular-system hazards can occur if the reaction matrix is rank-deficient; the solver must report underdetermined or inconsistent inputs.
• A supplied reaction may be unbalanced in atoms or charge; this must be rejected before solving.
• Missing or inconsistent phase labels can silently produce an incorrect enthalpy.
• Mixing J, kJ, cal, kcal, or values reported per mole of different reference species can produce errors unless units and reaction extent are explicit.
• A zero or near-zero pivot requires numerical tolerance handling; exact rational stoichiometry is preferable where possible.
• The instrument should not claim a unique answer when multiple valid step combinations exist.
• Negative multipliers must be displayed clearly as reaction reversals, and fractional multipliers must be displayed without rounding that changes the target equation.

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-tranche8/tranche8-results.json