Thermodynamics and Gibbs Free Energy Study Pack
Kibin's free study pack on Thermodynamics and Gibbs Free Energy includes a 6-section study guide, 25 quiz questions, 30 flashcards, and 5 open-ended Explain review questions. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.
Last updated May 27, 2026
Thermodynamics and Gibbs Free Energy Study Guide
Master the core of chemical thermodynamics by working through Gibbs free energy, the ΔG = ΔH − TΔS equation, and how temperature, enthalpy, and entropy together determine spontaneity.
Key Takeaways
- •Gibbs free energy (G) combines enthalpy (H) and entropy (S) into a single value that predicts whether a process will occur spontaneously at constant temperature and pressure, expressed as ΔG = ΔH − TΔS.
- •A negative ΔG indicates a spontaneous (thermodynamically favorable) process, a positive ΔG indicates a nonspontaneous process, and ΔG = 0 indicates the system is at equilibrium.
- •Temperature plays a decisive role when ΔH and ΔS have the same sign, because the TΔS term can flip the sign of ΔG depending on whether temperature is high or low.
- •The standard Gibbs free energy change (ΔG°) is measured under standard conditions (1 atm, 1 M concentrations, 25 °C) and is related to the equilibrium constant K by ΔG° = −RT ln K.
- •Under non-standard conditions, actual free energy change is calculated using ΔG = ΔG° + RT ln Q, where Q is the reaction quotient reflecting current concentrations or pressures.
- •Spontaneity in thermodynamics refers strictly to energetic favorability, not to reaction speed — a spontaneous reaction may still proceed extremely slowly without a catalyst.
Thermodynamic Foundations: Enthalpy, Entropy, and Spontaneity
To understand Gibbs free energy, you first need a firm grasp of the two thermodynamic quantities it unifies: enthalpy, which tracks heat flow, and entropy, which measures disorder or dispersal of energy.
Enthalpy (ΔH) and Heat of Reaction
- •Enthalpy (H) represents the total heat content of a system at constant pressure; ΔH is the heat exchanged with the surroundings during a reaction.
- •An exothermic reaction releases heat to the surroundings and has a negative ΔH; an endothermic reaction absorbs heat and has a positive ΔH.
- •Negative ΔH alone does not guarantee a reaction is spontaneous — many endothermic processes, like dissolving ammonium nitrate in water, occur readily.
Entropy (ΔS) and Disorder
- •Entropy (S) quantifies the number of energetically equivalent arrangements (microstates) available to a system; higher entropy means more dispersal of energy and matter.
- •Processes that increase disorder — gas expansion, dissolving a solid, breaking a molecule into smaller fragments — tend to have a positive ΔS.
- •The Second Law of Thermodynamics states that the total entropy of the universe increases in any spontaneous process, meaning ΔS_universe > 0.
Why Neither ΔH Nor ΔS Alone Is Sufficient
- •Highly exothermic reactions with negative ΔS can still be spontaneous (e.g., water freezing at temperatures below 0 °C).
- •Highly positive ΔS reactions with positive ΔH can also be spontaneous (e.g., melting ice above 0 °C).
- •A combined function is needed — one that weighs both driving forces simultaneously — which is exactly what Gibbs free energy provides.
Gibbs Free Energy: Definition and the Spontaneity Criterion
Gibbs free energy (G) is a thermodynamic state function that combines enthalpy and entropy into a single quantity whose change determines whether a process is spontaneous under conditions of constant temperature and pressure — the conditions typical of laboratory chemistry and biological systems.
The Gibbs Free Energy Equation
- •The fundamental relationship is ΔG = ΔH − TΔS, where T is the absolute temperature in Kelvin.
- •Because ΔG is a state function, its value depends only on initial and final states, not on the pathway between them.
- •The term TΔS represents the energy unavailable to do useful work because it is tied up in increasing the entropy of the system.
Interpreting the Sign of ΔG
- •ΔG < 0: the process is spontaneous (exergonic) — the system releases free energy and can do work on the surroundings without an external energy input.
- •ΔG > 0: the process is nonspontaneous (endergonic) — it requires a continuous input of free energy from outside the system to proceed.
- •ΔG = 0: the system is at chemical equilibrium, meaning the forward and reverse processes occur at equal rates and there is no net change in composition.
Spontaneity vs. Reaction Rate
- •Thermodynamic spontaneity only indicates whether a process is energetically downhill; it says nothing about how fast the reaction occurs.
- •The conversion of diamond to graphite is spontaneous (ΔG < 0 at room temperature) yet proceeds at an immeasurably slow rate because the activation energy barrier is enormous.
- •Kinetic barriers are governed by activation energy and catalysis, which are separate from the thermodynamic criterion of ΔG.
Temperature Dependence and the Four ΔH/ΔS Combinations
Because temperature appears explicitly in ΔG = ΔH − TΔS, it can control whether a reaction is spontaneous, and four distinct combinations of ΔH and ΔS sign produce four qualitatively different behaviors.
Always Spontaneous: Negative ΔH, Positive ΔS
- •When ΔH < 0 and ΔS > 0, the TΔS term is subtracted from a negative ΔH, making ΔG negative at every temperature.
- •Both the release of heat and the increase in disorder drive the reaction forward regardless of T.
Never Spontaneous: Positive ΔH, Negative ΔS
- •When ΔH > 0 and ΔS < 0, ΔG is positive at all temperatures because both the enthalpy and entropy terms oppose spontaneity.
- •Such reactions require continuous external work and do not proceed on their own.
Temperature-Dependent Case 1: Negative ΔH, Negative ΔS
- •When both ΔH and ΔS are negative, the process is spontaneous only at low temperatures, where |ΔH| > |TΔS|.
- •At high temperatures, the −TΔS term becomes large and positive, eventually overwhelming the favorable ΔH and making ΔG positive.
- •Water freezing (ΔH_fus < 0, ΔS < 0) is the classic example: spontaneous below 273 K, nonspontaneous above it.
Temperature-Dependent Case 2: Positive ΔH, Positive ΔS
- •When both ΔH and ΔS are positive, the process is spontaneous only at high temperatures, where TΔS > ΔH.
- •At low temperatures, the unfavorable enthalpy dominates and ΔG is positive.
- •Ice melting (ΔH_fus > 0, ΔS > 0) is spontaneous above 273 K but nonspontaneous below it.
Finding the Crossover Temperature
- •The temperature at which a reaction transitions between spontaneous and nonspontaneous can be estimated by setting ΔG = 0 and solving: T_crossover = ΔH / ΔS.
- •This estimate uses standard-state values of ΔH° and ΔS° and assumes they do not vary significantly with temperature.
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What is the Gibbs free energy equation that combines enthalpy and entropy into a single spontaneity criterion?
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Enthalpy and Entropy as Thermodynamic Driving Forces
Explain what enthalpy and entropy are and why neither one alone is sufficient to predict whether a chemical process will be spontaneous. Use a specific example to support your reasoning.
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