Chemical thermodynamics: enthalpy, entropy and Gibbs free energy
The first law and enthalpy, Hess's law with enthalpies of formation, entropy and the second law, spontaneity with ΔG and the link with a cell's voltage.
Why does methane keep burning on its own once lit, while water does not spontaneously split into hydrogen and oxygen? Chemical thermodynamics answers with three quantities: enthalpy, entropy and free energy. It tells you whether a reaction can happen and how much energy it exchanges; it does not tell you how fast, which is the job of kinetics.
System, surroundings and the first law
The system is the reaction under study, the surroundings everything else. The first law says energy is conserved: the change in internal energy is ΔU = q + w, heat absorbed plus work received. At constant pressure, the usual situation in the lab, the heat exchanged is the change in enthalpy ΔH.
- ΔH < 0: exothermic reaction, gives off heat (combustions, neutralisations);
- ΔH > 0: endothermic reaction, absorbs heat (ammonium nitrate dissolving in instant cold packs).
Enthalpies of formation and Hess’s law
Enthalpy is a state function: only the start and end points matter, not the path. Hence Hess’s law: the ΔH of a reaction is the sum of those of intermediate reactions, and in practice it comes from the standard enthalpies of formation ΔH°f (zero for elements in their stable form):
ΔH°reaction = Σ ΔH°f(products) − Σ ΔH°f(reactants)
Example, the combustion of methane CH4 + 2 O2 → CO2 + 2 H2O(l), with ΔH°f in kJ/mol: CH4 −74.8; CO2 −393.5; H2O(l) −285.8. ΔH° = [−393.5 + 2(−285.8)] − [−74.8] = −890.3 kJ/mol: every mole of methane burned releases about 890 kJ.
Entropy and the second law
Entropy S measures in how many different ways the same macroscopic state can be realised, intuitively its “disorder”. It grows going from solid to liquid to gas, when a solid dissolves, and when the moles of gas increase. The second law says that in a spontaneous process the total entropy, system plus surroundings, increases.
Gibbs free energy
To avoid computing the entropy of the surroundings every time, we use the free energy:
ΔG = ΔH − T·ΔS
At constant temperature and pressure a reaction is spontaneous if ΔG < 0, at equilibrium if ΔG = 0, non-spontaneous if ΔG > 0.
| ΔH | ΔS | Spontaneous? | Example |
|---|---|---|---|
| < 0 | > 0 | always | combustions |
| > 0 | < 0 | never | making ozone from oxygen |
| < 0 | < 0 | at low temperature | water freezing |
| > 0 | > 0 | at high temperature | ice melting, CaCO3 → CaO + CO2 |
The crossover temperature is T = ΔH/ΔS. For the decomposition of calcium carbonate (ΔH° ≈ +178 kJ/mol, ΔS° ≈ +161 J/(mol·K)) it is about 1100 K, around 830 °C: the minimum temperature of a lime kiln.
Free energy and electrical work
ΔG is also the maximum non-expansion work a reaction can deliver. In a battery it becomes electrical work: ΔG = −n·F·E, where n is the number of electrons exchanged, F = 96,485 C/mol the Faraday constant and E the cell voltage. It is the bridge between thermodynamics and electrochemistry, which you will meet again in the lesson on batteries.
