Enthalpy Formula
The enthalpy formula ΔH = ΔU + PΔV relates heat change to internal energy and work.
Learn thermochemistry with worked examples.
The Formula
Enthalpy (H) is a measure of the total heat content of a system at constant pressure. The change in enthalpy (ΔH) tells us how much heat is absorbed or released during a chemical reaction or physical process.
For reactions at constant pressure (which is most reactions in open containers), ΔH equals the heat exchanged with the surroundings. This makes enthalpy extremely practical — it directly tells you the heat of a reaction.
If ΔH is negative, the reaction is exothermic (releases heat). If ΔH is positive, the reaction is endothermic (absorbs heat).
Variables
| Symbol | Meaning |
|---|---|
| ΔH | Change in enthalpy (measured in joules, J, or kilojoules, kJ) |
| ΔU | Change in internal energy (measured in joules, J) |
| P | Pressure (measured in pascals, Pa) |
| ΔV | Change in volume (measured in cubic meters, m³) |
Related Formulas
- Hess's Law: ΔHrxn = Σ ΔHf(products) − Σ ΔHf(reactants)
- At constant pressure: ΔH = qp (heat at constant pressure)
- Using bond energies: ΔH = Σ(bonds broken) − Σ(bonds formed)
Example 1
Calculate the enthalpy of combustion of methane using standard enthalpies of formation. CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l). Given: ΔH°f[CH₄] = −74.8 kJ/mol, ΔH°f[CO₂] = −393.5 kJ/mol, ΔH°f[H₂O(l)] = −285.8 kJ/mol, ΔH°f[O₂] = 0 kJ/mol.
Apply Hess's Law: ΔH = Σ ΔH°f(products) − Σ ΔH°f(reactants)
Products: (−393.5) + 2(−285.8) = −393.5 + (−571.6) = −965.1 kJ
Reactants: (−74.8) + 2(0) = −74.8 kJ
ΔH = −965.1 − (−74.8) = −965.1 + 74.8
ΔH = −890.3 kJ/mol (exothermic — methane combustion releases heat)
Example 2
A gas expands from 2.0 L to 5.0 L at a constant pressure of 1.5 atm. The internal energy decreases by 200 J. What is ΔH?
Convert pressure to Pa: 1.5 atm × 101,325 Pa/atm = 151,988 Pa
Calculate ΔV: 5.0 − 2.0 = 3.0 L = 0.003 m³
Calculate PΔV: 151,988 × 0.003 = 455.96 J
ΔH = ΔU + PΔV = −200 + 455.96
ΔH ≈ +256 J (the system absorbs heat from the surroundings despite losing internal energy, because of the expansion work)
When to Use It
Use the enthalpy formula for heat calculations in chemical and physical processes.
- Calculating heat released or absorbed in chemical reactions
- Predicting whether reactions are exothermic or endothermic
- Using Hess's Law to find enthalpy changes for complex reactions
- Designing calorimetry experiments
- Calculating the energy content of fuels