Gibbs Free Energy & Equilibrium Why Gibbs free energy matters Spontaneous does not mean fast — it means thermodynamically allowed at the given temperature (T) and pressure (P). Gibbs free energy, G, puts two powerful drives on one scale: the heat/enthalpy drive (H) and the disorder/entropy drive (S). At constant T and P, the sign of the change in Gibbs free energy (ΔG) predicts whether a process is spontaneous (ΔG < 0), at equilibrium (ΔG = 0), or non-spontaneous (ΔG > 0). The Gibbs balance: enthalpy (ΔH) vs entropy (TΔS) tug-of-war sets the sign of ΔG. Use it like a mental weighing scale for spontaneity. At constant temperature, the entropy term TΔS competes with enthalpy ΔH to decide ΔG. Master definition (Gibbs-Helmholtz form) Spontaneity test at constant T, P For a process at constant temperature and pressure: - ΔG < 0: spontaneous (exergonic) - ΔG = 0: equilibrium (no net drive) - ΔG > 0: non-spontaneous (endergonic; needs energy input) Think of ΔG as the downhill direction on a free-energy landscape: systems roll towards lower G. Free-energy diagram: one path slopes down (ΔG < 0, spontaneous), one slopes up (ΔG > 0), and the minimum marks equilibrium (ΔG = 0). At equilibrium, Q = K and the net drive ΔG becomes zero. Equilibrium condition (statement form) Equilibrium is the lowest achievable G at given T, P. Systems naturally move towards that minimum, then hover there with no net change. remember Temperature decides the winner: sign analysis of ΔH and ΔS ΔG = ΔH − TΔS is a temperature-tunable competition. The sign of ΔH and ΔS predicts the spontaneity window. Visualise TΔS as a lever whose strength grows with T. < 0 > 0 Always (all T) Both favor spontaneity; ΔG is negative at any T. < 0 < 0 Low T Exothermic helps; at low T the −TΔS penalty is small. > 0 > 0 High T Endothermic opposes; at high T the +TΔS benefit wins. > 0 < 0 Never (no T) Both oppose spontaneity; ΔG stays positive. Case ΔH ΔS Spontaneous when... Reason Spontaneity window from signs of ΔH and ΔS (constant P) Meaningful only when ΔH and ΔS have the same sign (cases 2 and 3). Crossover temperature (where ΔG flips sign) ΔG vs T plots for the four ΔH/ΔS sign-combinations; highlight crossover T where applicable. Four-panel diagram of ΔG vs T lines. Panel A (ΔH<0, ΔS>0): line always below zero. Panel B (ΔH<0, ΔS<0): line crossing ΔG=0 at low T; label T = ΔH/ΔS. Panel C (ΔH>0, ΔS>0): line crossing at high T. Panel D (ΔH>0, ΔS<0): line always above zero. Clean vector style, axes labeled, red zero-line. 2026-05-26T17:04:25.886Z gpt-image-2 Watch units: use J with J (ΔH in J mol⁻¹, ΔS in J mol⁻¹ K⁻¹). If ΔH is in kJ mol⁻¹, convert ΔS to kJ mol⁻¹ K⁻¹ before T = ΔH/ΔS. neet-alert Worked insight: decomposition of calcium carbonate Reaction: CaCO3(s) → CaO(s) + CO2(g). One solid gives a solid + a gas, so entropy increases (ΔS > 0). The reaction absorbs heat (breaking the lattice), so ΔH > 0. This is Case 3: spontaneous at high T. Industry uses high-temperature lime kilns so that TΔS outcompetes ΔH and ΔG becomes negative. ΔG(T) for CaCO3(s) → CaO(s) + CO2(g): positive at low T, crosses zero at high T, then negative. Mark the high-T ‘lime kiln’ region. 2026-05-26T17:04:26.234Z Single ΔG vs T plot for CaCO3 decomposition. Show ΔG decreasing linearly with T, crossing ΔG=0 at a labeled T=ΔH/ΔS. Shade high-T region as 'lime kiln operation'. Simple vector graph, clear labels. gpt-image-2 Standard Gibbs energy, K, and the reaction quotient Q Standard Gibbs energy change (ΔG°) refers to reactants and products in their standard states (usually 1 bar gases, 1 M solutions, pure solids/liquids) at a specified T. It connects cleanly to the equilibrium constant K at that T, and to the non-standard reaction drive through Q, the reaction quotient. ΔG°–K relation Large K (K >> 1) means ΔG° is very negative; small K (K << 1) means ΔG° is very positive. Q has the same form as K but with current, not equilibrium, activities/pressures. When Q < K, ln(Q/K) < 0, so ΔG < 0 and the forward reaction is driven. Reaction drive at non-standard conditions At equilibrium, Q = K and ΔG = 0. This recovers the ΔG°–K equation. Away from equilibrium, the sign and magnitude of ΔG tell you the direction and the strength of the driving force. 2026-05-26T17:04:26.226Z Horizontal gauge with markers for Q and K on a line. Regions labeled: left of K (Q<K, forward driven, ΔG<0), at K (ΔG=0), right of K (Q>K, reverse driven, ΔG>0). Vector infographic, minimal text. gpt-image-2 Driving-force meter: show ΔG sign as Q moves relative to K (Q < K: ΔG < 0 forward; Q = K: ΔG = 0; Q > K: ΔG > 0 backward). ΔG° ln K K value System bias Qualitative map from ΔG° to K at a fixed T Very negative Very positive K >> 1 Products strongly favored K = 1 No bias Very positive Very negative K << 1 Reactants strongly favored Free energy and useful work ΔG tells the maximum non-expansion (non-PV) work obtainable from a process at constant T, P if it proceeds reversibly. Real processes are irreversible, so actual useful work is less in practice. ΔG° is not the heat released — it is the theoretical ceiling on useful (non-PV) work at standard states. Heat flow corresponds to ΔH, not ΔG. remember Preview to Electrochemistry (NTCH07) In galvanic cells, chemical free energy converts to electrical work. Details in Electrochemistry. Drug–receptor binding works only if ΔG for complex formation is negative. Thermodynamics underlies biological efficacy. Industrial choices: Ellingham and temperature compromises Metallurgy uses Ellingham diagrams (ΔG° vs T for oxide formation) to choose the right reductant at the right temperature. Where the carbon line (CO/CO2) lies below a metal-oxide line, carbon can reduce that oxide at that T. For iron, carbothermic reduction becomes favorable at high T in the blast furnace. More reactive oxides may require stronger reductants (e.g., Al in aluminothermic processes) at even higher T. Schematic Ellingham diagram: lines for metal oxide formations and the C/CO and CO/CO2 equilibria; mark regions where carbon reduces specific oxides. gpt-image-2 2026-05-26T17:04:26.395Z Simplified Ellingham plot with ΔG° (y-axis) vs T (x-axis). Include sloped lines for formation of FeO, ZnO, Al2O3, and two carbon lines (C+O2→CO2 and 2C+O2→2CO). Shade regions where carbon reduction is feasible. Clean vector style, labeled intersections. In the Haber process (N2 + 3H2 → 2NH3), ΔH° is negative (exothermic). Lower temperatures make ΔG° more negative (K larger), but the reaction becomes slow. Higher temperatures speed kinetics but reduce K (ΔG° less negative). Industry chooses a compromise temperature (about 700 K) with high pressure and an iron-based catalyst to balance rate and yield. Thermo vs kinetics: a condition can be thermodynamically unfavorable (small K) yet chosen for fast rate, then compensated by pressure, recycling, or continuous removal of product. neet-alert Common pitfalls and how to avoid them Spontaneous (ΔG < 0) means the reaction will be fast. Spontaneity is a thermodynamic criterion. Rate depends on activation energy and mechanism (kinetics). A slow spontaneous reaction is still ΔG < 0. Equilibrium is dynamic: forward and reverse rates are equal, so concentrations remain constant while molecules continue reacting. At equilibrium, reactions stop occurring. Only at standard-state conditions and equilibrium do we connect via ΔG° = −RT ln K. Otherwise use ΔG = ΔG° + RT ln Q to include actual conditions. ΔG equals ΔG° always, regardless of conditions. ΔG° is the actual energy you can always extract from a process. ΔG° is the maximum non-PV work under reversible, standard-state conditions. Real processes give less due to irreversibility and non-standard conditions. Hot mess wins: At high T, entropy (TΔS) dominates. Cold comfort: At low T, enthalpy (ΔH) dominates. NEET traps Mixing kJ and J in T = ΔH/ΔS. Forgetting that ΔG decides direction only at the given Q (non-standard states). Confusing ΔG with activation energy (Ea). Assuming ΔG° negative guarantees high yield even at high T (for exothermic reactions K drops as T rises). Quick practice: tie it all together Mini-drills Given ΔH and ΔS signs, classify the spontaneity window and sketch ΔG vs T. Given ΔG° at 298 K, decide whether K > 1, = 1, or < 1 without calculation. Given Q relative to K, state the sign of ΔG and the spontaneous direction. Explain why CaCO3 decomposition needs a kiln and how raising T changes ΔG. State how ΔG relates to maximum non-PV work and mention one device that uses it (fuel cell). State function combining enthalpy and entropy effects; predicts spontaneity at constant T, P. Gibbs free energy (G) Change in Gibbs free energy; ΔG < 0 spontaneous, ΔG = 0 equilibrium, ΔG > 0 non-spontaneous. ΔG Standard Gibbs energy change at specified T with all species in standard states; linked to K by ΔG° = −RT ln K. ΔG° Thermodynamic tendency to occur without external work at given T, P (not a statement about speed). Spontaneity Ratio of product to reactant activities at equilibrium; temperature-dependent. Equilibrium constant (K) Same form as K but with current activities/pressures; compares the present state to equilibrium. Reaction quotient (Q) Process with ΔG < 0 (free-energy releasing). Exergonic Process with ΔG > 0 (requires free-energy input). Endergonic Plot of ΔG° for oxide formation vs T; used to choose reductants and operating temperatures in metallurgy. Ellingham diagram G vs reaction progress curve showing driving force and equilibrium position. Free-energy diagram Key terms at a glance