SCIENCE · INVESTIGATE AND EXPLAIN

Test an enthalpy network instead of averaging incompatible paths

Use reversal, scaling and bounded cycle closure as independent consistency checks.

Learning outcome: Compare indirect sums−20 and−15 against the independent−20±1 packet. Retain both intervals, their overlap verdict and a proposed cause of nonclosure.

Starting recap

Review signed energy transfers, dimensional consistency, reaction coefficients, state functions and phase/structural evidence boundaries.

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Try

A→B−35 and B→C+15 kJ/mol imply A→C−20; the reverse is+20 and two moles require−40 kJ.

Open the experiment

Predict

If two paths disagree beyond their stated bounds, does averaging them make the state-function requirement satisfied?

Your prediction and reason

Experiment

Compare indirect sums−20 and−15 against the independent−20±1 packet. Retain both intervals, their overlap verdict and a proposed cause of nonclosure.

Challenge a closed enthalpy network

Worked teaching model · synthetic values · Fictional isomers A,B,C have identical elemental composition. Selected steps each carry±1 kJ/mol bound. Independent A→C packet is−20±1 kJ/mol at the same conditions. Test bounded consistency, not statistical significance; do not average incompatible paths without diagnosis.

A(g)→B(g) enthalpy: -35 kJ/mol B(g)→C(g) enthalpy: 15 kJ/mol

Reset keeps your prediction, captures and practice history.

Axes rescale. On the phase map, short dashes show solid–gas coexistence, long dashes liquid–gas and the solid line solid–liquid; the dot is the selected state. In the Hess diagram, the dashed line is the independent direct packet. A heating plot follows supplied energy, not elapsed time.

Numerical diagram coordinates

reaction-path step	enthalpy relative to A (kJ/mol)
0	0
1	-35
2	-20

Dashed reference
reaction-path step	enthalpy relative to A (kJ/mol)
0	0
2	-20

Calculated evidence under the stated assumptions
Quantity	Value	Unit
A→C inferred from two steps	-20	kJ/mol
C→A reverse	20	kJ/mol
Two moles A→C	-40	kJ per two mol
Two-step minimum	-22	kJ/mol
Two-step maximum	-18	kJ/mol
Independent A→C packet	-20	kJ/mol
Central cycle discrepancy	0	kJ/mol
Bounded intervals overlap	1	flag

Reversing and scaling a reaction reverses and scales its enthalpy; a closed cycle should reconcile.

The indirect path has worst-case bound±2 while the independent direct packet has±1. Overlap means compatibility within those stated bounds, not proof of identical mechanisms or statistical agreement. A nonoverlap requires inspecting conditions, states, calibration or reaction identity before averaging.

Retain the system, phase and structural assumptions with every number. Supplied or calculated evidence is not actual calorimetry, chemical handling or X-ray operation.

Reversing and scaling a reaction reverses and scales its enthalpy; a closed cycle should reconcile.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Define a state-function network

Fictional A(g), B(g) and C(g) are isomers with the same elemental composition. All packet enthalpies refer to the same conditions and one mole transformed. Since enthalpy is a state function, going A→B→C must have the same net enthalpy as A→C when the endpoints and conditions truly match.

Reverse and scale operations

If A→B is−35 kJ/mol and B→C is+15, adding the reactions cancels B and gives A→C at−20. Reversing that net reaction gives+20 kJ/mol. Transforming two moles in the original direction gives−40 kJ, while the molar value remains−20. A coefficient change scales the total reaction energy rather than changing its physical sign convention.

Test an independent packet

Each indirect step carries a stated±1 kJ/mol bound, so the sum has a worst-case±2 bound. The independent direct packet is−20±1. An indirect sum−20 gives an interval−22 to−18 that overlaps−21 to−19. Compatibility within these supplied bounds is not proof of identical mechanism or a statistical significance result.

Diagnose nonclosure

An indirect sum−15 gives−17 to−13, which does not overlap the direct packet. The discrepancy is evidence to inspect, not a reason to declare energy conservation false or automatically average the numbers. Possible causes include different phases, temperatures, composition, calibration, reaction extent or an incorrectly transcribed reaction direction.

Transfer the reasoning

A new path A→D has−12±1 and D→C has−9±1 kJ/mol. Its net−21±2 overlaps the direct−20±1 interval and is compatible at the stated level. The report should retain both independent evidence paths and the explicit bounds, preserving an earlier failed hypothesis if revised. This mathematical network does not provide a synthesis route or imply that any isomerization experiment was conducted.

Sources and evidence boundary

Conceptual sources checked 30 October 2026: Hess law. All prose, cases, code and diagrams are original. The supplied models are not measured structures, a performed laboratory investigation or certification of independent mastery. No chemical handling, heating, pressure vessel or cryogenic experiment is requested. Retain predictions, contrasting evidence and a changed-case explanation.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

How could changed physical states or reference conditions mimic a violation of Hess’s law?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Challenge a calorimetric inference with a missing heat path Next: Keep phase and reaction extent in a formation-enthalpy account

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