Gibbs Free Energy
Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work a system can perform at constant temperature and pressure, and determines the spontaneity of a process. A negative ΔG indicates a spontaneous reaction, a positive ΔG indicates a non-spontaneous reaction, and ΔG = 0 indicates a system at equilibrium. It combines enthalpy and entropy into a single criterion for spontaneity, making it one of the most powerful tools in chemical thermodynamics.
Key Formula
ΔG = ΔH − TΔS
LaTeX: \Delta G = \Delta H - T \Delta S
| Symbol | Meaning | Unit |
|---|---|---|
| ΔG | Change in Gibbs free energy | kJ/mol |
| ΔH | Change in enthalpy | kJ/mol |
| T | Absolute temperature | K |
| ΔS | Change in entropy | J/(mol·K) |
Worked Example
Problem
Determine whether the decomposition of calcium carbonate CaCO₃(s) → CaO(s) + CO₂(g) is spontaneous at 900 °C. Given: ΔH = +178 kJ/mol, ΔS = +160 J/(mol·K).
Solution
Step 1: Convert temperature to Kelvin: T = 900 + 273 = 1173 K. Step 2: Convert ΔS to kJ: ΔS = 0.160 kJ/(mol·K). Step 3: Apply ΔG = ΔH − TΔS. ΔG = 178 − (1173 × 0.160) ΔG = 178 − 187.7 ΔG = −9.7 kJ/mol. Step 4: Since ΔG < 0, the reaction is spontaneous at 900 °C.
Answer
ΔG = −9.7 kJ/mol; spontaneous at 900 °C
Spontaneity Prediction from Signs of ΔH and ΔS
| ΔH | ΔS | ΔG | Spontaneous? |
|---|---|---|---|
| Negative (−) | Positive (+) | Always negative | Always spontaneous |
| Positive (+) | Negative (−) | Always positive | Never spontaneous |
| Negative (−) | Negative (−) | Negative at low T | Spontaneous at low T |
| Positive (+) | Positive (+) | Negative at high T | Spontaneous at high T |
| Zero | Zero | Zero | At equilibrium |
Interactive Tools
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Related Terms
Standard Enthalpy
Standard enthalpy refers to the enthalpy change of a process measured under standard conditions: 298.15 K (25 °C) and 1 bar (approximately 1 atm) pressure, with all substances in their standard states. Standard enthalpy values provide a universal reference for comparing thermochemical data across different reactions and sources. The symbol ΔH° (read "delta H naught" or "delta H standard") denotes a standard enthalpy change.
Enthalpy of Formation
The enthalpy of formation (ΔH°f) is the heat change when one mole of a compound is formed from its constituent elements in their standard states at 298 K and 1 atm pressure. Standard enthalpies of formation for elements in their most stable form are defined as zero. These values are tabulated and used extensively with Hess's Law to calculate enthalpy changes for any chemical reaction.
Calorimetry
Calorimetry is the experimental science of measuring the heat exchanged during chemical reactions, physical changes, or heat capacity determinations using an instrument called a calorimeter. The fundamental principle is conservation of energy: heat released by the reaction equals heat absorbed by the calorimeter and its contents. Two main types are constant-pressure calorimetry (coffee-cup calorimeter) and constant-volume calorimetry (bomb calorimeter), each suited to different experimental conditions.
Named after Josiah Willard Gibbs, the American physicist and mathematician who introduced it in his landmark 1875–1878 papers 'On the Equilibrium of Heterogeneous Substances'. The term 'free' refers to energy available to do work.