Chemistry · Lesson

Hess's law, formation enthalpies and energy accounting

Combine reaction enthalpy changes through an endpoint ledger. Preserve phases, reaction scaling and reference conditions, and distinguish an algebraic route from an actual reaction mechanism.

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By the end, you can

Reverse and scale enthalpy changes consistently with reaction equations.
Cancel intermediate terms in a Hess ledger.
Interpret a formation enthalpy using elemental reference states and an explicit reaction basis.

An enthalpy change belongs to endpoints

Because H is a state function, its change depends on the initial and final states. If several consistent reaction equations add to a target equation, their enthalpy changes add to the target change. This is Hess’s law. Each equation must use compatible material amounts, phases and reference conditions.

A different phase can have a different enthalpy even with the same molecular formula. Keep labels such as gas, liquid and solid. Changing temperature or other reference conditions can also require a correction; similar-looking chemical formulas alone do not establish compatible thermodynamic states.

Add equations and cancel the shared terms

An original fictional state ledger stipulates A → B with ΔH = −20.0 kJ and B → C with ΔH = +5.0 kJ for matched amounts at the same stated conditions. Adding the equations cancels B and gives A → C with ΔH = −15.0 kJ.

These are invented labelled states and enthalpies for learning the algebra. The two-step path does not establish that an actual chemical process proceeds through B. Hess’s law supplies an endpoint relation; reaction mechanisms require separate kinetic and molecular evidence.

Cancel the intermediate without changing the endpoints

Ledger row	Equation	Enthalpy change	Role in the sum
Step 1	A → B	−20.0 kJ	B appears as output
Step 2	B → C	+5.0 kJ	The same B appears as input
Sum	A → C	−15.0 kJ	Cancel B and add enthalpy changes
Reversed sum	C → A	+15.0 kJ	Exchange endpoints and reverse the sign

Original fictional ledger. Each row uses compatible matched amounts, phases and the same stipulated conditions; numbers are not measured compound data.

Change the enthalpy when changing the equation

Reversing a reaction exchanges its endpoints, so the enthalpy change reverses sign. Multiplying every stoichiometric coefficient by a factor multiplies the enthalpy change for the reaction amount by that factor. A reaction enthalpy value and its written equation must stay together.

Thus the fictional C → A change is +15.0 kJ for the matched reversed amount. Twice the A → C amount has ΔH = −30.0 kJ. Do not compare enthalpy changes on different reaction amounts without adjusting the basis.

Formation values use a chosen reference convention

A standard formation enthalpy describes forming one mole of a specified substance from its elements in their reference states under the stated conditions. An element in its reference state has zero standard formation enthalpy by convention. This zero fixes the formation ledger; it is not a claim that the element has zero absolute energy.

Standard thermodynamic quantities use specified standard states; the recommended standard pressure is 1 bar, or 100 kPa. A standard-state symbol does not itself fix temperature. Tables commonly report a named temperature such as 298.15 K, and that temperature must be retained. For the selected NIST CODATA row at 298.15 K, CO₂(g) has standard formation enthalpy approximately −393.5 kJ mol⁻¹: the associated formation equation is C(graphite) + O₂(g) → CO₂(g).

Worked examples

Use a consistent endpoint sum

The fictional ledger stipulates ΔH = −20.0 kJ for A → B and +5.0 kJ for B → C at matched amounts. Find ΔH for A → C and its reverse.

Write signed values −20.0 kJ and +5.0 kJ.
Add equations and cancel the same intermediate B.
Add enthalpy changes: −20.0 + 5.0 = −15.0 kJ.
Reverse endpoints to obtain +15.0 kJ for C → A.

A → C: −15.0 kJ; C → A: +15.0 kJ. This is an endpoint ledger, not a mechanism claim.

Try it yourself

What happens to ΔH when a reaction equation is reversed?
Show the answer and reasoning
Its sign reverses.
The endpoints exchange places.
For the fictional ledger, what enthalpy change corresponds to twice the A → C reaction amount?
Show the answer and reasoning
−30.0 kJ.
Scaling the reaction amount by two scales the associated enthalpy change by two.
May phase labels be discarded when combining enthalpy equations?
Show the answer and reasoning
No.
The same formula in different phases can have different enthalpy.
Does a standard-state symbol alone specify 298.15 K?
Show the answer and reasoning
No.
Temperature must be stated separately from the standard-state convention.

What to carry forward

Hess’s law adds compatible endpoint enthalpy changes.
Reverse signs and scale values with the written equations.
Keep phases and reference conditions.
Formation-reference zeros and actual absolute energies are different concepts.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.