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 (S_{univ} > 0).

Entropy change of the universe (ΔS_{univ})

Total entropy change: $\triangle S_{univ} = \triangle S_{sys} + \triangle S_{surr};$ spontaneity requires $\triangle S_{univ} > 0.$

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 $\triangle S_{sys}$ 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 $\triangle H < 0$, endothermic have $\triangle H > 0$.

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 S_{sys} > 0; reactions that decrease moles of gas tend to have S_{sys} < 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: $\triangle S_{rxn} = \Sigma nS(products) - \Sigma nS(reactants),$ 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, $\triangle G = \triangle H - T\triangle S$ (system quantities); it packages enthalpy and entropy competition into one criterion.

Gibbs free energy sign criteria

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

Temperature dependence of spontaneity

Because G = H - TS, increasing T increases the importance of the entropy term (-TS), which can flip spontaneity depending on signs of H and S.

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

G^ = -RT ln K; if G^ < 0 then $K > 1$ (products favored), if G^ > 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 $\triangle G$ 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 (G > 0) with a favorable step (G < 0) so the overall process is favorable: G_{overall} = G_{1} + G_{2} < 0 (requires mechanistic linkage in reality).