How it Works
Enthalpy (H) is a state function: its value depends only on the current condition of a system, not on the route by which that condition was reached. The diagram plots enthalpy on the vertical axis. A solid green line marks the reactants' starting level and the fixed, real-world enthalpy of the direct reaction (ΔH₁); an amber path shows an alternative two-step route through an intermediate species, with its own step enthalpies ΔH₂ and ΔH₃. Because enthalpy cannot depend on path, Hess's Law guarantees that ΔH₁ = ΔH₂ + ΔH₃ whenever the steps are the true, correctly measured values for that cycle.
Use the sliders to change ΔH₂ and ΔH₃ away from their literature values and watch the amber "sum" level visibly separate from the fixed green "direct" level — a live picture of what an unbalanced (physically wrong) thermochemical cycle looks like. Press Reset and the two paths snap back together, because real step enthalpies for a genuine multi-step route always add up to the true overall enthalpy change. Switch between the four preset cycles to see this hold for combustion, allotrope conversion, and phase-change pathways alike.
Two-step cycle: ΔH₁ = ΔH₂ + ΔH₃
General form: ΔH°_rxn = Σ ΔH°_f(products) − Σ ΔH°_f(reactants)
Balance check: |ΔH₂ + ΔH₃ − ΔH₁| ≈ 0 ⇒ cycle balanced
Frequently Asked Questions
What is Hess's Law?
Hess's Law states that the total enthalpy change for a chemical reaction is the same regardless of the route taken from reactants to products, as long as the initial and final conditions are identical. If a reaction can be written as the sum of several steps, the overall ΔH equals the sum of the ΔH values of those steps.
Why does Hess's Law work — what is a state function?
Enthalpy is a state function, meaning its value depends only on the current state of a system (temperature, pressure, composition) and not on how that state was reached. Because enthalpy does not remember the path, any two routes between the same starting reactants and ending products must release or absorb exactly the same net energy.
How do you use Hess's Law to calculate an unknown ΔH?
You combine known reactions — reversing them (which flips the sign of ΔH) or scaling them by a multiplier (which scales ΔH by the same factor) — so that when added together, the reactants and intermediates cancel and only the target reaction remains. Adding the adjusted ΔH values of those known reactions gives the unknown ΔH.
What is standard enthalpy of formation and how does it relate to Hess's Law?
The standard enthalpy of formation, ΔH°f, is the enthalpy change when one mole of a compound forms from its elements in their standard states. Hess's Law lets you calculate the enthalpy of any reaction as the sum of the formation enthalpies of the products minus the sum of the formation enthalpies of the reactants, because forming and then reassembling atoms is just another valid path.
Does the number of steps in a reaction pathway change the total enthalpy released?
No. Whether a reaction proceeds directly in one step or through five intermediates, the net enthalpy change between the same initial reactants and final products is identical, because enthalpy is a state function. Extra intermediate steps only rearrange how the energy is released or absorbed along the way, not the total amount.
What is a Born-Haber cycle and how does it use Hess's Law?
A Born-Haber cycle is a specific application of Hess's Law used to find the lattice energy of an ionic compound by summing a series of steps — sublimation, ionization, dissociation, electron affinity, and lattice formation — that connect elements in their standard states to the final ionic solid. Because enthalpy is path-independent, the known steps can be added and rearranged to solve for the one unmeasured quantity.
Why must equations be reversed or scaled consistently when combining them by Hess's Law?
Reversing a chemical equation reverses the direction of energy flow, so its ΔH must change sign; multiplying an equation by a coefficient scales the amount of substance reacting, so its ΔH must be multiplied by that same coefficient. Skipping these adjustments would break the energy balance and give an answer for a different, unintended reaction.
What sign convention is used for ΔH in these energy cycles?
By convention, a negative ΔH means the reaction releases energy to the surroundings (exothermic) and the product level sits below the reactant level on the diagram; a positive ΔH means the reaction absorbs energy (endothermic) and the product level sits above. All values in this simulator are given in kilojoules per mole (kJ/mol) at standard conditions.
Is Hess's Law only valid for enthalpy, or does it apply to other quantities too?
Hess's Law works for enthalpy because enthalpy is a state function, but the same path-independence logic applies to any other state function, including internal energy, entropy, and Gibbs free energy. It does not apply to path-dependent quantities like heat or work measured individually, since those can differ between routes even when the net enthalpy change is the same.