Hess’s Law
Construct a Hess accounting path by reversal, scaling and cancellation with energy conservation.
AP Chemistry Topic 6.9 · CED printed p. 121 / PDF p. 128. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- System and surroundings as a chosen boundary
- Moles, balanced equations and limiting reactants
- Intermolecular versus intramolecular interactions
- Activation energy versus overall energy change
A complicated transformation can be represented as several steps whose intermediate species cancel. For a heating-and-melting path, the steps might be warm solid, melt, then warm liquid. For a reaction path, supplied thermochemical equations can be reversed or scaled to create the target net equation. Plan the species ledger before arithmetic: which substance must appear on the target’s left, which on the right, and which should cancel entirely? A Hess path is an accounting path; it need not be the actual kinetic mechanism.
Each step transfers energy. Conservation requires the net transfer for the same starting and ending species, phases and conditions to equal the sum of the step transfers. At constant pressure this gives ΔHnet =ΣΔHsteps. If two paths between identical endpoints gave different net heat in this model, combining one forward with the other reversed would produce energy from a closed cycle, contradicting conservation. Use this reasoning without requiring the excluded formal vocabulary of state functions.
Three operations keep the energy ledger aligned with the species ledger. Reverse a reaction and reverse ΔH’s sign. Multiply every coefficient by a factor and multiply ΔH by that factor. Add equations and add their enthalpy changes after canceling identical species. Check phases as well as formulas: H2O(l) does not cancel H2O(g) unless a phase step is included. Do not average enthalpies or discard a coefficient because it looks awkward. The final answer belongs to the target equation exactly as written.
Let's work through it
Find C(graphite,s) +½O2(g) → CO(g), using C +O2 → CO2, ΔH =−393.5 kJ, and CO +½O2 → CO2, ΔH =−283.0 kJ.
- The target requires CO as a product, so reverse the second equation: CO2 → CO +½O2, ΔH =+283.0 kJ.
- Add to the first equation. CO2 cancels; half the O2 cancels, leaving the target.
- Sum ΔH =−393.5+283.0 =−110.5 kJ. The negative sign is consistent with net energy release for the target; the pathway’s canceled CO2 is an accounting intermediate, not proof of a kinetic intermediate.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
What two things change when you reverse a thermochemical equation?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
What two things change when you reverse a thermochemical equation?
Worked answer and reason
Reactants/products exchange sides, and ΔH changes sign while retaining magnitude.
Reversing the same transformation reverses its heat transfer.
Retrieval 2
Can liquid water and vapor water cancel in a Hess sum?
Worked answer and reason
No. Include the appropriate phase-change equation if needed.
Identical chemical formula does not make different phases identical enthalpy endpoints.
Retrieval 3
Why do step enthalpies add?
Worked answer and reason
At constant pressure, conservation of energy makes the net heat for the same complete endpoints equal the sum of the step transfers.
The intermediate bookkeeping cannot create or destroy energy.
Catch the tempting mistake
- Hess’s law identifies the actual reaction mechanism.
- It constructs an energy-accounting path; the actual elementary sequence needs kinetic evidence.
- Multiply coefficients but leave ΔH unchanged.
- Changing represented amount changes heat by the same factor.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 6 problem 15 · ap synthesis · symbolic
- Unit 6 problem 16 · ap synthesis · multiple
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For the teacher
- Ask students to show cancellation before adding numbers.
- Accept different valid paths that give the same target phases and conditions.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 6.9.A
- Represent a chemical or physical process as a sequence of steps.
- 6.9.B
- Explain the relationship between the enthalpy of a chemical or physical process and the sum of the enthalpies of the individual steps.
- 6.9.A.1
- Many processes can be broken down into a series of steps. Each step in the series has its own energy change.
- 6.9.B.1
- Because total energy is conserved (first law of thermodynamics), and each individual reaction in a sequence transfers thermal energy to or from the surroundings, the net thermal energy transferred in the sequence will be equal to the sum of the thermal energy transfers in each of the steps. These thermal energy transfers are the result of potential energy changes among the species in the reaction sequence; thus, at constant pressure, the enthalpy change of the overall process is equal to the sum of the enthalpy changes of the individual steps.
- 6.9.B.2
- The following are essential principles of Hess’s law: i. When a reaction is reversed, the enthalpy change stays constant in magnitude but becomes reversed in mathematical sign. ii. When a reaction is multiplied by a factor c, the enthalpy change is multiplied by the same factor c. iii. When two (or more) reactions are added to obtain an overall reaction, the individual enthalpy changes of each reaction are added to obtain the net enthalpy change of the overall reaction.
- The concept of state functions will not be assessed on the AP Exam.
Science references for this teaching
- College Board AP Chemistry Course and Exam Description, Fall 2024 — Exact unit learning requirements and exclusions; supplied PDF is pinned by the integration catalog.
- OpenStax Chemistry 2e: Energy Basics — Scientific check: system boundaries, energy conservation, thermal transfer and heat capacities.
- OpenStax Chemistry 2e: Enthalpy — Scientific check: stoichiometric enthalpy, formation values, sign reversal/scaling and Hess cycles.
Glossary and deeper reading · 4 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Mole
A mole is an amount of substance containing exactly 6.02214076 × 10²³ specified entities. The entities can be atoms, molecules, ions, or formula units, so the counted entity must be named. For example, one mole of oxygen molecules contains two moles of oxygen atoms.
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Limiting reactant
The limiting reactant is consumed first under the specified complete-reaction model and limits the product amount. Identifying it requires comparing available amounts with the balanced equation's ratios. For example, abundant hydrogen cannot produce more water after the available oxygen has been consumed.
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Activation energy
Activation energy is the energy barrier associated with a reaction pathway in an introductory energy-profile model. It concerns the pathway and is distinct from the reactant-to-product energy change. For example, a thermodynamically favored reaction can remain slow when its activation barrier is large.
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Enthalpy
Enthalpy is a state function defined from internal energy, pressure, and volume. At constant pressure with only pressure–volume work, an enthalpy change equals the heat transferred to the system. For example, a negative reaction enthalpy indicates heat release for the written reaction under those conditions.