Hess's Law Formula
Hess's law states that total enthalpy change equals the sum of individual step enthalpies.
Learn with worked examples.
The Formula
Hess's law states that the total enthalpy change for a reaction is independent of the pathway taken. Whether a reaction happens in one step or multiple steps, the overall enthalpy change is the same.
Swiss-Russian chemist Germain Henri Hess published this law in 1840. It is a direct consequence of the conservation of energy (first law of thermodynamics). This law is extremely useful because it allows us to calculate enthalpy changes for reactions that are difficult to measure directly.
Using standard enthalpies of formation (ΔH_f), we can calculate the enthalpy of any reaction. The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states. By convention, the standard enthalpy of formation of any element in its standard state is zero.
Variables
| Symbol | Meaning |
|---|---|
| ΔHrxn | Enthalpy change of the reaction (kJ/mol) |
| ΔHf | Standard enthalpy of formation (kJ/mol) |
| Σ | Sum over all products or reactants (with stoichiometric coefficients) |
Example 1
Calculate the enthalpy of combustion of methane: CH₄ + 2O₂ → CO₂ + 2H₂O. Given: ΔHf(CH₄) = −74.8, ΔHf(CO₂) = −393.5, ΔHf(H₂O) = −285.8 kJ/mol
Products: ΔHf(CO₂) + 2 × ΔHf(H₂O) = −393.5 + 2(−285.8) = −965.1 kJ
Reactants: ΔHf(CH₄) + 2 × ΔHf(O₂) = −74.8 + 0 = −74.8 kJ
ΔHrxn = −965.1 − (−74.8)
ΔHrxn = −890.3 kJ/mol (strongly exothermic)
Example 2
Find ΔH for: 2NO + O₂ → 2NO₂, given: N₂ + O₂ → 2NO (ΔH = +180 kJ) and N₂ + 2O₂ → 2NO₂ (ΔH = +66 kJ)
Reverse reaction 1: 2NO → N₂ + O₂ (ΔH = −180 kJ)
Add reaction 2: N₂ + 2O₂ → 2NO₂ (ΔH = +66 kJ)
Sum: 2NO + O₂ → 2NO₂
ΔH = −180 + 66 = −114 kJ
When to Use It
Use Hess's law to calculate enthalpy changes for reactions that cannot be easily measured directly.
- Computing reaction enthalpies from formation data tables
- Predicting the heat released or absorbed in industrial processes
- Designing calorimetry experiments
- Verifying experimental enthalpy measurements