Hess's Law

Hess's Law, formally known as Hess's Law of Constant Heat Summation, states that the total enthalpy change of a chemical reaction is the same regardless of whether the reaction takes place in one step or in a series of intermediate steps. In other words, enthalpy is a state function — it depends only on the initial and final states of the system, not on the pathway taken. This powerful principle was formulated by the Swiss-Russian chemist Germain Hess in 1840 and remains one of the cornerstones of thermochemistry. The practical importance of Hess's Law cannot be overstated. Many reactions are difficult or impossible to measure directly in a calorimeter — for example, the formation of carbon monoxide from its elements is complicated by the simultaneous formation of carbon dioxide. By combining enthalpies of reactions that can be measured, chemists can calculate the enthalpy of reactions that cannot. This makes Hess's Law an indispensable tool in both laboratory chemistry and industrial process design. Hess's Law is a direct consequence of the first law of thermodynamics, which states that energy is conserved. Because enthalpy (H) is a state function, any path connecting the same reactants to the same products must involve the same net energy change. Students can apply Hess's Law by manipulating thermochemical equations — reversing them (which changes the sign of ΔH), or multiplying them by coefficients (which scales ΔH proportionally) — and then adding the equations together to obtain the target reaction.

Key takeaways
  • Identify the Target Reaction
  • Gather Known Thermochemical Equations
  • Reverse and/or Scale Equations as Needed
  • Add the Equations and Sum the Enthalpies
  • Verify Using an Energy Cycle (Diagram)

Identify the Target Reaction

Write down the chemical equation whose enthalpy change (ΔH) you wish to find. This is called the target equation. For example, you may want to find ΔH for the reaction: C(graphite) + ½O₂(g) → CO(g).

Gather Known Thermochemical Equations

Collect a set of reactions with known ΔH values whose species include all the reactants and products in the target reaction. Standard enthalpies of combustion or formation are commonly used. Example known equations: (A) C(graphite) + O₂(g) → CO₂(g), ΔH_A = −393.5 kJ/mol; (B) CO(g) + ½O₂(g) → CO₂(g), ΔH_B = −283.0 kJ/mol.

Reverse and/or Scale Equations as Needed

Manipulate each known equation so that when they are added, intermediates cancel and the result equals the target equation. If you reverse an equation, flip the sign of its ΔH. If you multiply an equation by a factor n, multiply its ΔH by n. In the example: keep equation (A) as written; reverse equation (B) to get CO₂(g) → CO(g) + ½O₂(g), giving ΔH = +283.0 kJ/mol.

Add the Equations and Sum the Enthalpies

Add all the manipulated equations together. Cancel species that appear on both sides (intermediates). Sum all the individual ΔH values to get the ΔH of the target reaction. In the example: adding (A) and reversed (B): C(graphite) + O₂(g) + CO₂(g) → CO₂(g) + CO(g) + ½O₂(g). Cancelling CO₂ and ½O₂ gives C(graphite) + ½O₂(g) → CO(g), with ΔH = −393.5 + 283.0 = −110.5 kJ/mol.

Verify Using an Energy Cycle (Diagram)

A Born–Haber or Hess energy cycle diagram can visually confirm your result. Draw two paths from reactants to products: the direct path (target reaction) and the indirect path (via intermediates). Both paths must give the same total ΔH, confirming the law. This also provides a useful self-check: if the paths do not balance, recheck signs and stoichiometry.

The Key Equation

ΔHreaction∘=∑ΔHf, products∘−∑ΔHf, reactants∘\Delta H^\circ_{\text{reaction}} = \sum \Delta H^\circ_{\text{f, products}} - \sum \Delta H^\circ_{\text{f, reactants}}
  • \Delta H^\circ_{\text{reaction}} — Standard Enthalpy of Reaction (kJ mol⁻¹): The total heat absorbed or released during a reaction at standard conditions (298 K, 1 atm). Negative values indicate exothermic reactions; positive values indicate endothermic reactions.
  • \Delta H^\circ_{\text{f, products}} — Standard Enthalpy of Formation of Products (kJ mol⁻¹): The enthalpy change when one mole of each product is formed from its elements in their standard states. Each value is multiplied by the stoichiometric coefficient of the corresponding product.
  • \Delta H^\circ_{\text{f, reactants}} — Standard Enthalpy of Formation of Reactants (kJ mol⁻¹): The enthalpy change when one mole of each reactant is formed from its elements in their standard states. Each value is multiplied by the stoichiometric coefficient of the corresponding reactant.

Worked Example

Problem. Calculate the standard enthalpy change for the reaction \ce{C(graphite) + 2H_2(g) -> CH_4(g)} using the following data: (1) \ce{C(graphite) + O_2(g) -> CO_2(g)}, ΔH₁ = −393.5 kJ/mol; (2) \ce{H_2(g) + 1/2 O_2(g) -> H_2O(l)}, ΔH₂ = −285.8 kJ/mol; (3) \ce{CH_4(g) + 2O_2(g) -> CO_2(g) + 2H_2O(l)}, ΔH₃ = −890.3 kJ/mol.

ΔH∘=−393.5+(−571.6)+890.3=−74.8 kJ mol−1\Delta H^\circ = -393.5 + (-571.6) + 890.3 = -74.8 \text{ kJ mol}^{-1}

Answer. The standard enthalpy of formation of methane is −74.8 kJ/mol. This is an exothermic process.

Figure
Diagram
Hess's Law Energy Cycle: Formation of CO(g)Elements(C + O₂)C(s) + O₂(g)ReactantsProductsCO(g) + ½O₂(g)IntermediateCO₂(g)Common ProductPath AΔH_A = −393.5kJ/molΔH_target = −110.5 kJ/mol(Target: Path C)ΔH_B = −283.0kJ/mol↑ Higher Enthalpy↓ Lower Enthalpy
Origins · 1 minGermain Henri Hess and how this was discovered
GH
Germain Henri Hess
1802–1850 · Swiss-Russian

Germain Hess was a Swiss-born chemist who spent most of his career in Russia, where he conducted meticulous calorimetric experiments. In 1840 he published his law of constant heat summation, demonstrating that the total heat evolved or absorbed in a chemical transformation is independent of the path by which the change is brought about. This work predated the formal establishment of thermodynamics and provided crucial empirical support for the first law of thermodynamics. Hess also made important contributions to the mineralogy of Russia and the chemistry of sugars. Hess conducted his landmark experiments using a simple ice calorimeter — essentially measuring how much ice melted when a reaction occurred. Despite the simplicity of his equipment, his results were accurate enough to remain valid more than 180 years later.

  • Enthalpy and Thermochemical Equations — Hess's Law relies on correctly writing and manipulating thermochemical equations with their associated ΔH values; understanding enthalpy is a prerequisite.
  • Standard Enthalpies of Formation — One of the most common applications of Hess's Law is calculating reaction enthalpies from tabulated standard enthalpies of formation using ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants).
  • Calorimetry and Heat Measurement — The experimental data used in Hess's Law calculations (ΔH values) are obtained through calorimetry; understanding how heat is measured gives context to thermochemical data.
  • State Functions and Path Independence — Hess's Law is a direct consequence of enthalpy being a state function; understanding why path does not matter deepens conceptual understanding of the law.
  • Bond Enthalpy and Bond Energy — Bond enthalpies provide an alternative, atomic-level method of estimating reaction enthalpies and can be combined with Hess's Law thinking to construct energy cycles.