Unit 9 · Applications of Thermodynamics

Entropy (S) ● (core concept) — A measure of the dispersal of matter and energy. Entropy increases when matter spreads out (solid → liquid → gas, gas expansion, more moles of gas in products than reactants) and when energy spreads out (higher temperature).

Standard molar entropy (S°) ● (core concept) — The absolute entropy of one mole of a substance in its standard state.

Standard entropy change ● (core concept) — ΔS°_reaction = ΣS°(products) − ΣS°(reactants), calculated from the absolute entropies of the species involved.

Standard state ● (core concept) — The reference state for thermodynamic quantities: pure substances, solutions at 1.0 M concentration, and gases at 1.0 atm (or 1.0 bar).

Gibbs free energy (ΔG°) ● (core concept) — The thermodynamic quantity that determines favorability at constant temperature and pressure; it can be calculated from enthalpy and entropy: ΔG° = ΔH° − TΔS°.

Thermodynamically favored ● (core concept) — A process with ΔG° < 0; the CED prefers this phrase over 'spontaneous,' since a favored process may still be very slow.

Standard Gibbs free energy of formation (ΔG_f°) ● (core concept) — The free energy change when one mole of a compound forms from its elements in their standard states; ΔG°_reaction = ΣΔG_f°(products) − ΣΔG_f°(reactants).

Predicting favorability from ΔH° and ΔS° ● (core concept) — ΔH° < 0 and ΔS° > 0: favored at all temperatures. ΔH° > 0 and ΔS° < 0: favored at no temperature. ΔH° > 0 and ΔS° > 0: favored at high temperature. ΔH° < 0 and ΔS° < 0: favored at low temperature.

Kinetic control ● (core concept) — A thermodynamically favored process that does not occur at a measurable rate — often because of high activation energy — is said to be under kinetic control; it is not at equilibrium.

Free energy and the equilibrium constant ● (core concept) — ΔG° = −RT ln K (equivalently K = e^(−ΔG°/RT)). ΔG° < 0 means products are favored at equilibrium (K > 1); ΔG° > 0 means reactants are favored (K < 1).

Estimating K from ΔG° ● (core concept) — When ΔG° is near zero, K is close to 1; when ΔG° is much larger or smaller than RT, K deviates strongly from 1.

Free energy of dissolution ● (core concept) — ΔG for dissolving reflects three contributions: breaking the solid's intermolecular interactions, reorganizing the solvent, and solute–solvent interactions. Predicting the total is hard because these terms partially cancel.

Coupled reactions ● (core concept) — A thermodynamically unfavorable reaction can be driven by coupling it to a favorable one (e.g., ATP → ADP in biology); the coupled reactions share intermediates and the overall ΔG° is negative.

Driving unfavorable processes with energy input ● (core concept) — An external energy source can force an unfavorable process to occur — e.g., electrical energy drives an electrolytic cell or recharges a battery, and light drives photosynthesis (CO₂ → glucose).

Galvanic (voltaic) cell ● (core concept) — An electrochemical cell in which a thermodynamically favored redox reaction produces a positive voltage and electric current.

Electrolytic cell ● (core concept) — An electrochemical cell in which a thermodynamically unfavorable redox reaction is driven by an externally applied voltage.

Anode ● (core concept) — The electrode where oxidation occurs in any electrochemical cell.

Cathode ● (core concept) — The electrode where reduction occurs in any electrochemical cell.

Salt bridge ● (core concept) — The component of an electrochemical cell that allows ions to flow between half-cells, completing the circuit while keeping the solutions separate.

Half-cell ● (core concept) — One electrode plus its surrounding solution in an electrochemical cell; the two half-cells host the oxidation and reduction half-reactions.

Electron flow in electrochemical cells ● (core concept) — Electrons flow through the external circuit from the anode, where oxidation occurs, to the cathode, where reduction occurs.

Standard cell potential (E°) ● (core concept) — The voltage of an electrochemical cell under standard conditions, found from the standard reduction potentials of the two half-reactions (E°_cathode − E°_anode).

Standard reduction potential ● (core concept) — The voltage of a half-reaction measured against the standard hydrogen electrode; used to identify which half-reaction is oxidized and which is reduced.

Cell potential and free energy ● (core concept) — ΔG° = −nFE°, where n is moles of electrons and F is Faraday's constant. A positive E° means a thermodynamically favored reaction; a negative E° means an unfavored one requiring external voltage.

Nernst equation (qualitative) ● (core concept) — E = E° − (RT/nF) ln Q. As a cell runs and approaches equilibrium (Q → K), the magnitude of the cell potential decreases, reaching zero at equilibrium.

Concentration cell ● (core concept) — A cell whose voltage comes from a concentration difference between two half-cells of the same species; electrons flow in the direction that moves the system toward equilibrium.

Electrochemical cells are not at equilibrium ● (core concept) — Le Châtelier's principle does not apply to electrochemical cells because they are not at equilibrium; deviations from standard conditions change the cell potential as described by the Nernst equation.

Faraday's laws ● (core concept) — Laws relating the charge flowing through an electrochemical cell to the stoichiometry of the reaction: the number of electrons transferred, the mass deposited on or removed from an electrode (electroplating), the current, the time, and the charge of the ions.

Current equation ● (core concept) — I = q/t: electric current equals charge divided by time.