Entropy, Free Energy, and Spontaneity (AP Chemistry Unit 9)

Entropy

A thermodynamic measure of how widely energy is dispersed among the possible microscopic arrangements of particles; more accessible arrangements (microstates) correspond to higher entropy.

Microstate

A specific microscopic arrangement of particles/energy (positions and energy distribution) that is consistent with a given observable state.

Macrostate

The overall, observable state of a system (e.g., temperature, pressure, volume) that can correspond to many different microstates.

Second Law of Thermodynamics

A process is spontaneous if the entropy of the universe increases (ΔS_univ > 0).

Entropy change of the universe (ΔS_univ)

Total entropy change: ΔSuniv = ΔSsys + ΔSsurr; spontaneity requires ΔSuniv > 0.

System entropy change (ΔS_sys)

Entropy change of the chemicals/process being studied (the “system”).

Surroundings entropy change (ΔS_surr)

Entropy change of everything outside the system; can offset a negative ΔS_sys if heat flows to the surroundings.

Thermodynamic spontaneity

“Spontaneous” means thermodynamically allowed (driven by ΔS_univ or ΔG), not necessarily fast; rate is controlled by kinetics.

Enthalpy (ΔH)

A thermodynamic quantity related to heat flow at constant pressure; exothermic processes have ΔH < 0, endothermic have ΔH > 0.

Phase-change entropy trend

Entropy increases going from solid → liquid → gas (more freedom of motion and more microstates).

Gas-moles entropy heuristic

Reactions that increase the moles of gas tend to have ΔSsys > 0; reactions that decrease moles of gas tend to have ΔSsys < 0 (most useful when gases are present).

Standard molar entropy (S°)

Tabulated absolute entropy of 1 mol of a substance in its standard state (units typically J·mol⁻¹·K⁻¹).

Third Law of Thermodynamics

A perfectly ordered crystal at 0 K has zero entropy; absolute entropies are referenced to this baseline.

Standard reaction entropy change (ΔS°_rxn)

Calculated from tabulated entropies: ΔS°_rxn = Σ nS°(products) − Σ nS°(reactants), where n are stoichiometric coefficients.

Surroundings entropy equation (at constant T)

At constant temperature, ΔSsurr = −(ΔHsys)/T (T in kelvins), linking heat flow (enthalpy) to surroundings entropy.

Gibbs free energy equation

At constant T and P, ΔG = ΔH − TΔS (system quantities); it packages enthalpy and entropy competition into one criterion.

Gibbs free energy sign criteria

At constant T and P: ΔG < 0 spontaneous, ΔG = 0 equilibrium, ΔG > 0 nonspontaneous as written (spontaneous in reverse).

Temperature dependence of spontaneity

Because ΔG = ΔH − TΔS, increasing T increases the importance of the entropy term (−TΔS), which can flip spontaneity depending on signs of ΔH and ΔS.

Reaction quotient (Q)

A ratio built like K but using current (non-equilibrium) concentrations/partial pressures; it indicates how a mixture compares to equilibrium.

Nonstandard free energy equation

Free energy under nonstandard conditions: ΔG = ΔG° + RT ln Q (R is gas constant; T in kelvins).

Standard free energy–equilibrium link

ΔG° = −RT ln K; if ΔG° < 0 then K > 1 (products favored), if ΔG° > 0 then K < 1 (reactants favored).

Thermodynamic vs kinetic control

Thermodynamic control: most stable (lowest G) product favored at equilibrium. Kinetic control: fastest-formed product favored (lowest activation energy).

Activation energy (E_a)

The energy barrier that must be overcome for reaction to occur; controls reaction rate (kinetics), not ΔG or equilibrium position.

Catalyst

A substance that lowers activation energy and increases reaction rate, but does not change ΔG, ΔH, or the equilibrium constant K.

Coupled reaction

Pairing an unfavorable step (ΔG > 0) with a favorable step (ΔG < 0) so the overall process is favorable: ΔG_overall = ΔG₁ + ΔG₂ < 0 (requires mechanistic linkage in reality).