Theory — Free Energy and Spontaneity
Thermodynamics: free energy and spontaneity
Whether a reaction proceeds on its own is decided by the Gibbs free energy. It combines the heat exchanged, the enthalpy change ΔH, with the change in disorder, the entropy change ΔS, at temperature T in kelvin.
Because ΔS is usually given in joules and ΔH in kilojoules, divide the TΔS term by 1000 before subtracting. Redox and thermodynamics meet in one equation: the free energy of a cell reaction is set by its potential, where n is the moles of electrons transferred and F is the Faraday constant, 96485 coulombs per mole.
| Reduction half-reaction | E° (V) |
|---|---|
| Ag⁺ + e⁻ → Ag | +0.80 |
| Cu²⁺ + 2e⁻ → Cu | +0.34 |
| 2H⁺ + 2e⁻ → H₂ | 0.00 |
| Pb²⁺ + 2e⁻ → Pb | −0.13 |
| Ni²⁺ + 2e⁻ → Ni | −0.25 |
| Fe²⁺ + 2e⁻ → Fe | −0.44 |
| Zn²⁺ + 2e⁻ → Zn | −0.76 |
Gibbs free energy
ΔG = ΔH − TΔS predicts whether a reaction is spontaneous.
Sign of ΔG
Negative ΔG is spontaneous; positive is nonspontaneous; zero is at equilibrium.
ΔG from E°
ΔG° = −nFE°; a positive cell potential gives a negative ΔG°.
Apparatus
The equipment a real thermochemistry experiment uses to measure heat and relate cell potential to free energy. In the simulation these are modelled for you, but the readings correspond to what each instrument would measure.
Instructions — Running the Virtual Experiment
This is a predict, reveal, and compare lab. In every part you work out the answer yourself first, enter it, and only then does the simulation reveal the experimental value so you can check your work against it.
Simulation — The Electrochemistry Bench
Free energy
Free energy from potential
Team Questions
Example Lab Report
A worked example showing the expected format and the calculate, reveal, and compare workflow.
Thermodynamics: Free Energy and Spontaneity
Chemistry | Section: [Your Section] | Date: [Date]
Lab Members: [Names of all members present]
Objective
To calculate Gibbs free energy and judge spontaneity, and to relate cell potential to free energy through ΔG° = −nFE°.
Theory
The Gibbs free energy combines enthalpy and entropy: ΔG = ΔH − TΔS. A negative ΔG means the reaction is spontaneous. Free energy is linked to a cell potential by ΔG° = −nFE°.
Results (worked example)
| Quantity | Value |
|---|---|
| ΔG for ΔH = −92 kJ, ΔS = −199 J/K at 298 K | −32.7 kJ (spontaneous) |
| ΔG° from −nFE° (n = 2, E° = 1.10 V) | −212.3 kJ |
The free energy of the ammonia synthesis is negative at 298 K, so it is spontaneous, and the negative ΔG° from the cell potential confirms the Zn–Cu reaction is spontaneous.
Conclusion
Free energy predicted spontaneity from ΔH and ΔS, and ΔG° = −nFE° tied the cell potential to the same conclusion.
Practice Questions
Show all work. Use ΔG = ΔH − TΔS (watch J vs kJ) and ΔG° = −nFE° with F = 96485 C/mol.