How it Works
The left panel plots ΔG = ΔH − TΔS as a straight line against temperature, using ΔH in kilojoules per mole and ΔS in joules per mole-kelvin (converted internally to kJ/(mol·K) by dividing by 1000, so the units on both sides of the equation match). Because ΔH sets the line's intercept at T=0 and −ΔS/1000 sets its slope, the four possible sign combinations of ΔH and ΔS produce four qualitatively different lines: always below zero, always above zero, or crossing zero exactly once at a crossover temperature T₀ = ΔH/ΔS.
The right panel is a visual analogy for entropy, not a literal molecular simulation. A set of particles is nudged toward either a tidy, lattice-like arrangement (when ΔS is strongly negative, representing increasing order) or allowed to roam freely across the whole box (when ΔS is strongly positive, representing increasing disorder), while their jostling speed is tied directly to the temperature slider — a nod to how thermal energy actually drives molecular motion.
Crossover temperature: T₀ = ΔH / ΔS (exists only when ΔH and ΔS share the same sign)
Spontaneity: ΔG < 0 spontaneous · ΔG = 0 equilibrium · ΔG > 0 non-spontaneous
Four cases: (ΔH<0,ΔS>0) always · (ΔH>0,ΔS<0) never · (ΔH<0,ΔS<0) low T only · (ΔH>0,ΔS>0) high T only
Frequently Asked Questions
What does Gibbs free energy (ΔG) represent physically?
Gibbs free energy is the maximum energy available from a process to do useful, non-expansion work at constant temperature and pressure. It is the master criterion for spontaneity in chemistry: whenever ΔG is negative for a proposed change, that change can occur on its own, without any continuous external energy input, even if it takes a very long time to actually happen.
What do enthalpy (ΔH) and entropy (ΔS) each contribute to spontaneity?
Enthalpy ΔH tracks the heat released or absorbed by the reaction — an exothermic (ΔH<0) reaction favors spontaneity because it lowers the system's energy. Entropy ΔS tracks the change in disorder, or number of accessible microstates — an increase in disorder (ΔS>0) also favors spontaneity, because the second law of thermodynamics favors states with higher entropy. Gibbs free energy combines both effects into a single number.
Why does temperature matter, and how can it flip spontaneity?
Temperature is the weighting factor on the entropy term: ΔG = ΔH − TΔS. At low T the TΔS term is small and ΔH dominates; at high T, TΔS grows and can dominate ΔH. This is why a reaction that is entropy-favored but enthalpy-opposed can flip from non-spontaneous to spontaneous as temperature rises, and why an enthalpy-favored but entropy-opposed reaction can flip the other way as temperature falls.
What does the crossover temperature T = ΔH/ΔS mean physically?
The crossover temperature is the exact point where ΔG = 0 — the system sits at equilibrium, with the forward and reverse processes equally favored thermodynamically. Below that temperature the sign of ΔG is one way; above it, ΔG flips sign, so the reaction's spontaneous direction reverses. A crossover only exists in the physically accessible range when ΔH and ΔS share the same sign.
Why doesn't spontaneous mean fast?
ΔG is a purely thermodynamic criterion: it tells you whether a reaction can happen on its own, not how quickly it will. The rate is governed separately by kinetics — specifically the activation-energy barrier a reaction must climb over, covered in this site's Activation Energy simulation. The classic example is diamond converting to graphite: ΔG is negative at room temperature and pressure, so it is thermodynamically spontaneous, yet the process is immeasurably slow because the kinetic barrier is enormous.
Why does ice melt above 0°C and water freeze below 0°C?
Melting ice is an endothermic, entropy-increasing process (ΔH>0, ΔS>0): heat must be absorbed to break the ice's ordered hydrogen-bond lattice, but the resulting liquid has far more accessible molecular arrangements. Both ΔH and ΔS are essentially unchanged whether it is 0°C or −10°C — what changes is the TΔS term, which crosses ΔH exactly at 273 K (0°C), flipping ΔG from positive (freezing favored) below that point to negative (melting favored) above it.
What are the four classic ΔH/ΔS combinations, and how does each behave?
(1) ΔH<0, ΔS>0: both terms favor spontaneity, so ΔG is negative at every temperature — always spontaneous. (2) ΔH>0, ΔS<0: both terms oppose spontaneity, so ΔG is positive at every temperature — never spontaneous. (3) ΔH<0, ΔS<0: the enthalpy term favors spontaneity but the entropy term opposes it, so the reaction is spontaneous only below the crossover temperature. (4) ΔH>0, ΔS>0: the entropy term favors spontaneity but the enthalpy term opposes it, so the reaction is spontaneous only above the crossover temperature.
Why does the Haber-Bosch process run at moderate-to-high temperature if low temperature favors it thermodynamically?
Ammonia synthesis (N2 + 3H2 → 2NH3) is exothermic with a large entropy decrease (three gas molecules become two), so it is thermodynamically most favorable at low temperature, where ΔG is most negative. But at low temperature the reaction rate is kinetically far too slow to be useful, because collisions rarely clear the activation-energy barrier. Industrially the process runs at a compromise temperature with an iron catalyst and high pressure, trading some equilibrium yield for a commercially viable reaction rate.
What sign convention is used for ΔG, ΔH and ΔS?
By the standard chemistry convention used throughout this simulator, negative ΔH means the reaction releases heat (exothermic) and negative ΔS means the products are more ordered than the reactants. ΔG follows the same convention: ΔG<0 means the forward reaction is spontaneous, ΔG>0 means the reverse reaction is spontaneous, and ΔG=0 means the system is at equilibrium.
Can a reaction with positive ΔG ever occur?
Not spontaneously and not to completion, but a positive-ΔG reaction can still proceed partway before reaching equilibrium (a small equilibrium constant K is directly related to a positive standard ΔG°), or it can be driven forward by continuously supplying external energy — for example coupling it to a more strongly spontaneous reaction, as cells do when they use ATP hydrolysis to power otherwise non-spontaneous biochemical steps.