Spontaneity and ΔG

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spontaneity Gibbs free energy ΔG

Core Idea

The Gibbs free energy change (ΔG = ΔH - TΔS) combines enthalpy and entropy to predict spontaneity. A negative ΔG indicates a spontaneous process; positive ΔG indicates non-spontaneous.

Explainer

You have already learned two separate ways to think about whether a reaction "wants" to happen. From thermochemistry, you know that exothermic reactions (negative ΔH) release energy and tend to be favorable. From entropy, you know that processes increasing disorder (positive ΔS) also tend to be favorable. But these two drives can conflict — an endothermic reaction can be spontaneous if it creates enough disorder, and a highly ordered product can form if enough energy is released. Gibbs free energy is the single quantity that settles this tug-of-war.

The equation ΔG = ΔH − TΔS combines both factors into one number. Think of it as a balance sheet: ΔH represents the enthalpy "cost" or "payment" of the reaction, while TΔS represents the entropy contribution scaled by temperature. When ΔG is negative, the combination of energy release and entropy increase (or one overwhelming the other) makes the process spontaneous — it can proceed without external input. When ΔG is positive, the process is non-spontaneous as written, though the reverse reaction would be spontaneous.

The temperature term is crucial and often underappreciated. Notice that T multiplies ΔS, not ΔH. This means entropy becomes more influential at higher temperatures. Consider ice melting: ΔH is positive (you must add heat to break hydrogen bonds) and ΔS is positive (liquid water is more disordered than ice). At low temperatures, the positive ΔH dominates and ΔG is positive — ice does not melt. At high temperatures, TΔS overwhelms ΔH and ΔG becomes negative — ice melts spontaneously. The crossover temperature where ΔG = 0 is exactly the melting point: T = ΔH/ΔS. This framework lets you predict not just *whether* a process is spontaneous but *at what temperature* it becomes spontaneous.

There are four possible sign combinations for ΔH and ΔS, and understanding them provides a powerful diagnostic tool. If ΔH is negative and ΔS is positive, ΔG is always negative — the reaction is spontaneous at every temperature (combustion reactions are a classic example). If ΔH is positive and ΔS is negative, ΔG is always positive — the reaction is never spontaneous under standard conditions. The interesting cases are the mixed signs, where temperature acts as the switch. Recognizing which case you are in lets you immediately predict how temperature will affect spontaneity without doing any arithmetic.

Practice Questions 5 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesThe Electromagnetic SpectrumBlackbody Radiation and Planck's LawPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthHeisenberg Uncertainty PrincipleWavefunction and the Born RuleThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsScattering TheoryIntroduction to Scattering TheoryPartial Wave Analysis in ScatteringSpin Angular MomentumElectron Spin and Intrinsic Magnetic MomentStern-Gerlach Experiment: Spin Quantization and MeasurementElectron Diffraction and Matter Wave PropertiesDavisson-Germer Experiment: Crystal Diffraction of ElectronsElectron Diffraction and Matter Wave InterferenceWavefunctions and Probability Density InterpretationQuantum Superposition and Linear Combinations of StatesQuantum Operators and ObservablesCanonical Commutation Relations and UncertaintyHeisenberg Uncertainty Principle and Measurement LimitsTime-Independent Schrödinger Equation and EigenvaluesHydrogen Atom in Quantum MechanicsSpectral Lines and Energy TransitionsSelection Rules for Atomic TransitionsLS and jj Coupling Schemes in Multi-Electron AtomsPauli Exclusion Principle and Antisymmetric WavefunctionsElectron Configuration and the Aufbau PrincipleThe Periodic Table and Atomic Electronic StructureThe Periodic TableElectron ConfigurationPeriodic TrendsIonization EnergyIonic BondingLewis StructuresResonance Structures and Delocalized ElectronsResonance and Formal ChargeMolecular Polarity and Dipole MomentsIntermolecular ForcesStates of Matter and Phase Changes: Melting, Boiling, and SublimationGas Laws and the Ideal Gas EquationGas Stoichiometry and Volume-Volume CalculationsThermochemistry and EnthalpyHeat Capacity and CalorimetryEntropy and Molecular DisorderSpontaneity and ΔG

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