Hess's Law and Enthalpy Diagrams
Hess's law says the enthalpy change of a reaction is the same whether it happens in one step or several. Enthalpy is a state function — it depends only on the start and end points, not the path — so you can add known reactions together to reach one you cannot measure directly.
Why enthalpy is path-independent
A state function depends only on the current state of a system, not on how it got there. Altitude is a good analogy: the height difference between two towns is fixed no matter which road you drive between them. Enthalpy behaves the same way, which is what makes Hess's law possible — any route from reactants to products gives the same total ΔH.
The two rules for manipulating steps
- Reverse a reaction → change the sign of ΔH. If forming a compound releases 286 kJ, breaking it apart absorbs 286 kJ.
- Multiply a reaction by a number → multiply ΔH by the same number. Doubling the amounts doubles the heat.
Arrange the given equations so that, when added, the unwanted species cancel and only your target reaction remains. The sum of the adjusted ΔH values is the answer.
The shortcut: enthalpies of formation
When you have a table of standard enthalpies of formation (ΔH°f), you can skip the step-by-step bookkeeping:
Every element in its standard state has ΔH°f = 0. Multiply each substance's ΔH°f by its coefficient, sum the products, sum the reactants, and subtract. This formula is itself just Hess's law applied to formation reactions.
Worked example: thermite
Fe₂O₃(s) + 2 Al(s) → Al₂O₃(s) + 2 Fe(s). Using ΔH°f values (Al₂O₃ −1676, Fe₂O₃ −824.2 kJ/mol, elements 0):
The large negative value shows why the thermite reaction is intensely exothermic — hot enough to weld railway tracks.
Reading an enthalpy diagram
On an energy profile, products below the reactants mean an exothermic reaction (ΔH negative). Products above mean endothermic (ΔH positive). The activation energy is the height of the hump from the reactants up to the transition state, and a catalyst lowers that hump without changing ΔH, because the start and end points are unmoved.
Common mistakes
- Forgetting to flip the sign of ΔH when a step is reversed.
- Scaling the equation but not ΔH (or the reverse).
- Mixing up the formation formula order — it is always products minus reactants, never the other way round.
- Assigning a non-zero ΔH°f to an element in its standard state, which is defined as zero.
Measure heat in the lab with the Calorimetry Calculator (q = mcΔT), which is how the ΔH values in these tables are determined experimentally.
The General Chemistry Workbook covers calorimetry, Hess's law and formation enthalpies with worked examples and a full data table.
Frequently Asked Questions
Hess's law states that the total enthalpy change of a reaction is the same regardless of the number of steps taken, because enthalpy is a state function. This lets you add known reactions together to find a heat of reaction you cannot measure directly.
Reversing a reaction changes the sign of its enthalpy change. If the forward reaction releases energy, the reverse absorbs the same amount, so a negative ΔH becomes positive and vice versa.
Subtract the summed standard formation enthalpies of the reactants from those of the products, each multiplied by its coefficient: ΔH°rxn = Σ ΔH°f(products) − Σ ΔH°f(reactants). Elements in their standard state have a formation enthalpy of zero.
Standard enthalpy of formation is defined relative to elements in their standard states, so forming an element from itself involves no change. That is why every pure element in its standard state has ΔH°f = 0 by definition.
No. A catalyst lowers the activation energy by providing a different pathway, but the reactants and products are unchanged, so ΔH stays the same. Only the height of the energy hump changes, not the start and end points.