Gibbs free energy connects heat, entropy, and temperature to predict whether a chemical process is thermodynamically favorable. It matters because chemists use ΔG to judge reactions, phase changes, electrochemical cells, and biochemical pathways. A negative ΔG means a process can occur spontaneously under the stated conditions, while a positive ΔG means it is not spontaneous as written.
Understanding Gibbs Free Energy and Thermodynamics
A reaction can be favorable because it releases energy to its surroundings, because it creates more possible arrangements of particles, or for both reasons. Enthalpy tracks heat flow at constant pressure. Entropy tracks how widely energy and matter are spread out.
Melting ice illustrates the competition. Melting absorbs heat, which works against it, yet liquid water has more freedom of motion than solid ice.
Above the melting point, the entropy effect is large enough to make melting favorable. Below that point, freezing is favored instead.
Temperature controls how much entropy affects the result. The temperature term multiplies the entropy change, so a small entropy change can become important at high temperature. Four general patterns help students reason without memorizing isolated examples.
Reactions with negative enthalpy change and positive entropy change are favorable at every temperature. Those with positive enthalpy change and negative entropy change are unfavorable at every temperature. The other two cases depend on temperature.
A reaction that absorbs heat but gains entropy may become favorable when heated. A heat releasing reaction that loses entropy may become favorable only at lower temperatures.
Thermodynamics does not tell how fast a change happens. Diamond can change into graphite under ordinary conditions because graphite is thermodynamically more stable, yet the change is extremely slow. A large activation energy creates this delay.
Rusting, fuel combustion, digestion, and the setting of cement all show the difference between possibility and rate. Free energy describes the overall energy balance between starting materials and products.
Kinetics describes the pathway and the barriers along that pathway. Catalysts lower a barrier and speed a reaction, but they do not change the free energy difference or the final equilibrium position.
Standard free energies of formation provide a practical way to calculate reaction free energy from tables. A formation value refers to making one mole of a substance from its elements in their standard states. Elements in their most stable standard forms have formation free energy values of zero.
To find a reaction value, add the formation values for products after multiplying by their coefficients. Then subtract the similarly weighted total for reactants.
Students should be careful with coefficients because doubling an equation doubles every extensive energy change. A coefficient changes the amount reacting, not the identity of the substance.
Real systems rarely stay at standard conditions. Concentration, gas pressure, acidity, and temperature can shift the actual free energy change. Cells use this fact constantly.
The breakdown of adenosine triphosphate can drive less favorable processes because products are removed or because it is linked to another reaction. Batteries work while a voltage exists because electrons can move through an external circuit toward a lower free energy state. At equilibrium, forward and reverse reactions still occur, but their rates match.
The mixture is dynamic, not frozen. When solving problems, state the conditions, use kelvin for temperature, track units carefully, and separate a claim about favorability from a claim about speed.
Key Facts
- ΔG = ΔH - TΔS, where T must be in kelvin.
- If ΔG < 0, the process is spontaneous in the forward direction.
- If ΔG > 0, the process is nonspontaneous in the forward direction.
- If ΔG = 0, the system is at equilibrium.
- Standard free energy and equilibrium are related by ΔG° = -RT ln K.
- For electrochemical cells, ΔG° = -nFE°cell.
Vocabulary
- Gibbs free energy
- Gibbs free energy is the energy available to do useful work in a system at constant temperature and pressure.
- Enthalpy
- Enthalpy is the heat content of a system at constant pressure, represented by H.
- Entropy
- Entropy is a measure of how spread out energy and matter are in a system, represented by S.
- Spontaneous process
- A spontaneous process is one that is thermodynamically favored and can occur without continuous outside input.
- Equilibrium
- Equilibrium is the state where the forward and reverse processes have no net change and ΔG equals zero.
Common Mistakes to Avoid
- Using Celsius instead of kelvin for T is wrong because thermodynamic equations require absolute temperature.
- Forgetting to convert entropy units is wrong because ΔH is often in kJ/mol while ΔS is often in J/mol·K, so the units must match before calculating ΔG.
- Assuming negative ΔG means a reaction is fast is wrong because ΔG predicts thermodynamic favorability, not reaction rate.
- Treating ΔG and ΔG° as the same is wrong because ΔG depends on actual concentrations or pressures, while ΔG° applies to standard conditions.
Practice Questions
- 1 A reaction has ΔH = -120 kJ/mol and ΔS = -200 J/mol·K at 298 K. Calculate ΔG and decide whether the reaction is spontaneous.
- 2 For a reaction at 350 K, ΔH = 45 kJ/mol and ΔS = 150 J/mol·K. Calculate ΔG and identify whether products or reactants are thermodynamically favored.
- 3 A reaction is endothermic and has a positive entropy change. Explain why increasing temperature can make the reaction spontaneous.