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.
Understanding Chemistry: Predicting Spontaneity with Gibbs Energy
Enthalpy and entropy can support the same direction or compete with each other. A reaction that releases heat and creates greater spreading of particles or energy has two favorable influences. It tends to be favorable over a wide temperature range.
A reaction that absorbs heat while becoming more ordered has two unfavorable influences. It is usually not favorable without being linked to another process. The most interesting cases have one influence in each direction.
Melting ice absorbs heat, yet liquid water has more possible arrangements than solid ice. Above its melting point, the entropy benefit is large enough to favor melting. Below that point, freezing is favored.
Temperature has to be treated carefully because it changes the importance of entropy. The entropy change is multiplied by absolute temperature, so chemists use kelvin rather than degrees Celsius. A temperature difference of one kelvin has the same size as one degree Celsius, but zero kelvin has a physical meaning of the lowest possible temperature.
Zero degrees Celsius does not. Units matter too. Enthalpy change is often reported in kilojoules per mole, while entropy change may be reported in joules per mole per kelvin.
Before combining them, the energy units must match. A missed conversion by a factor of one thousand can reverse a conclusion.
Values measured under standard conditions are useful reference points, not guarantees for every beaker or cell. Real mixtures may have very different concentrations, pressures, or acidity. These conditions affect the tendency of reactants and products to change.
As products build up, making more product often becomes less favorable. As reactants are removed, the forward reaction can become more favorable. At equilibrium, molecules continue reacting in both directions, but the forward and reverse rates are equal.
There is no overall change in the amounts present. A system at equilibrium has reached the lowest Gibbs energy available under those particular conditions.
Thermodynamics predicts whether a change has a driving force. It does not tell how quickly that change happens. Paper can react with oxygen in air to form more stable products, but it does not burst into flame at room temperature because the reaction has a high activation energy.
A spark supplies enough energy to begin it. Cells solve a related problem by using enzymes and coupling unfavorable steps to favorable ones, such as the breakdown of ATP. Batteries use separated chemical reactions to push electrons through a circuit.
When studying Gibbs energy, keep direction, temperature, units, real conditions, and reaction speed separate. They answer different parts of the same chemical story.
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.