Spontaneous Reactions & Gibbs Free Energy
Thermodynamics, spontaneity, and the driving forces of chemical change
📺 Video Lectures
Detailed explanations of spontaneous reactions, Gibbs free energy, and thermodynamics.
1. What is a Spontaneous Reaction?
A spontaneous reaction is a chemical or physical process that occurs without any external energy input once it has been initiated. Spontaneity is a thermodynamic concept – it indicates whether a process is capable of proceeding in a given direction, but it says nothing about how fast it happens. For example, the rusting of iron is spontaneous (ΔG < 0) but occurs very slowly. An explosion, on the other hand, is both spontaneous and fast.
2. Gibbs Free Energy (ΔG)
The Gibbs free energy change (ΔG) determines whether a reaction is spontaneous at constant temperature and pressure. It combines enthalpy (ΔH, heat change) and entropy (ΔS, disorder change):
where ΔG = Gibbs free energy change (kJ/mol), ΔH = enthalpy change (kJ/mol), T = absolute temperature (K), ΔS = entropy change (kJ/mol·K).
At equilibrium, ΔG = 0. The standard free energy change (ΔG°) relates to the equilibrium constant K:
where R = 8.314 J·mol⁻¹·K⁻¹. A large negative ΔG° corresponds to a large K (products favoured), and a large positive ΔG° gives a small K (reactants favoured).
3. How ΔH, ΔS, and T Affect Spontaneity
| ΔH | ΔS | Effect on ΔG = ΔH – TΔS | Spontaneity |
|---|---|---|---|
| Negative (exothermic) | Positive (increase disorder) | ΔG always negative | Spontaneous at all T |
| Positive (endothermic) | Negative (decrease disorder) | ΔG always positive | Non‑spontaneous at all T |
| Negative | Negative | ΔG negative at low T, positive at high T | Spontaneous below T = ΔH/ΔS |
| Positive | Positive | ΔG negative at high T, positive at low T | Spontaneous above T = ΔH/ΔS |
4. Non‑Spontaneous (Endergonic) Processes & Coupling
A non‑spontaneous reaction (endergonic, ΔG > 0) can occur if it is coupled with a highly exergonic reaction (ΔG << 0) such that the overall ΔG is negative. This is how living cells drive unfavourable reactions (e.g., ATP hydrolysis drives many biosynthetic pathways).
5. Real‑World Examples
- Rusting of iron: 4Fe + 3O₂ → 2Fe₂O₃
- Combustion of methane: CH₄ + 2O₂ → CO₂ + 2H₂O
- Melting of ice above 0°C
- Dissolution of NaCl in water (slightly spontaneous)
- Formation of glucose from CO₂ and H₂O (photosynthesis requires light energy)
- Decomposition of water into H₂ and O₂ (requires electrolysis)
- Freezing of water below 0°C (spontaneous in reverse direction)
6. Interactive Simulator: ΔG = ΔH – TΔS
Adjust the sliders for ΔH, ΔS, and temperature to see whether the reaction is spontaneous (green) or non‑spontaneous (red) based on the sign of ΔG.
ΔG = ΔH – TΔS. When ΔG < 0, the reaction is spontaneous. Watch how changing temperature affects spontaneity for endothermic (ΔH>0) or exothermic (ΔH<0) reactions.
7. Applications in Science and Industry
- Battery design: A battery’s voltage is related to ΔG: ΔG = –nFE. The more negative ΔG, the higher the cell potential.
- Predicting reaction favourability: ΔG° determines whether a reaction will proceed to form products under standard conditions.
- Metallurgy: Ellingham diagrams use ΔG vs. T to predict which metal oxides can be reduced by carbon or other metals.
- Biochemistry: Metabolic pathways are driven by coupled exergonic (ATP hydrolysis) and endergonic reactions (e.g., synthesis of macromolecules).
- Environmental chemistry: Assessing whether pollutants will degrade spontaneously or require remediation.
- Phase transitions: Determining melting and boiling points from ΔG = 0 condition.
8. Summary & Key Takeaways
- Spontaneity is determined by ΔG, not by reaction rate.
- Gibbs free energy equation: ΔG = ΔH – TΔS.
- ΔG < 0 → spontaneous; ΔG > 0 → non‑spontaneous; ΔG = 0 → equilibrium.
- Exergonic reactions (ΔG < 0) can be coupled with endergonic ones to drive unfavourable processes.
- Temperature significantly affects spontaneity when ΔH and ΔS have the same sign.
- Applications include batteries, metallurgy, biochemistry, and phase equilibria.
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