Source: https://guthlabs.ai/docs/instruments/hess-s-law-enthalpy-calculator/mechanism/

instrument mechanism / verified-clean

# Hess's Law Enthalpy Calculator mechanism

The inspectable method record for Hess's Law Enthalpy Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/hess-s-law-enthalpy-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/hess-s-law-enthalpy-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/hess-s-law-enthalpy-calculator/qualification/>)

## 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`