Gibbs free energy helps chemists predict whether a process is spontaneous under constant temperature and pressure. A spontaneous process can occur without continuous outside input, but it may still be slow. The key equation is ΔG = ΔH − TΔS, which combines heat flow, disorder, and temperature into one useful test.
This idea matters for reactions, phase changes, batteries, corrosion, and many biological processes.
The sign of ΔG tells the direction favored by thermodynamics. If ΔG < 0, the process is spontaneous as written, if ΔG > 0, the reverse process is spontaneous, and if ΔG = 0, the system is at equilibrium. Enthalpy change ΔH reflects heat absorbed or released, while entropy change ΔS reflects how energy and matter become more spread out.
Temperature matters because the entropy term TΔS grows larger at higher temperatures, which can change whether a process is spontaneous.
Key Facts
- Gibbs free energy equation: ΔG = ΔH − TΔS
- Spontaneous as written: ΔG < 0
- Nonspontaneous as written: ΔG > 0
- Equilibrium condition: ΔG = 0
- Temperature must be in kelvin when using ΔG = ΔH − TΔS
- For standard conditions: ΔG° = ΔH° − TΔS°
Vocabulary
- Gibbs free energy
- Gibbs free energy is the energy available to do useful work in a system at constant temperature and pressure.
- Spontaneous process
- A spontaneous process is one that is thermodynamically favored to occur in a particular direction without continuous external input.
- Enthalpy change
- Enthalpy change, ΔH, is the heat absorbed or released by a process at constant pressure.
- Entropy change
- Entropy change, ΔS, measures the change in energy dispersal or disorder of a system.
- Equilibrium
- Equilibrium is the state where forward and reverse processes are balanced and ΔG equals zero.
Common Mistakes to Avoid
- Using Celsius instead of kelvin in TΔS is wrong because thermodynamic temperature must start at absolute zero. Always convert using K = °C + 273.15.
- Forgetting to match units for ΔH and ΔS is wrong because ΔH is often in kJ and ΔS is often in J/K. Convert one so both terms use the same energy unit before subtracting.
- Assuming spontaneous means fast is wrong because ΔG predicts thermodynamic favorability, not reaction rate. A reaction can have ΔG < 0 and still need a catalyst to occur quickly.
- Ignoring the sign of ΔS in ΔG = ΔH − TΔS is wrong because subtracting a negative entropy term makes ΔG larger. Carefully keep the algebraic sign of each quantity.
Practice Questions
- 1 A reaction has ΔH = -80.0 kJ/mol and ΔS = -150 J/(mol·K). Calculate ΔG at 298 K and state whether the reaction is spontaneous as written.
- 2 For a process with ΔH = 25.0 kJ/mol and ΔS = 80.0 J/(mol·K), find the temperature in kelvin at which ΔG = 0. Predict whether the process is spontaneous above or below that temperature.
- 3 A reaction has ΔH > 0 and ΔS > 0. Explain how temperature affects spontaneity and give a real-world type of process that could fit this sign pattern.