Spontaneity Calculators

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Spontaneity in chemistry refers to whether a process will occur without continuous external energy input. A spontaneous process is one that proceeds naturally in a given direction. In thermodynamics, spontaneity at constant temperature and pressure is determined by Gibbs free energy change: ΔG = ΔH − TΔS. When ΔG < 0, the process is spontaneous (exergonic); when ΔG > 0, it is non-spontaneous (endergonic) and requires energy input; when ΔG = 0, the system is at equilibrium. Spontaneity depends on both the enthalpy change (ΔH) and entropy change (ΔS), and their interplay with temperature.

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Gibbs Free Energy and Spontaneity

ΔG = ΔH − TΔS

  • ΔG < 0: spontaneous (exergonic) — reaction proceeds forward without external energy
  • ΔG > 0: non-spontaneous (endergonic) — requires energy input to proceed
  • ΔG = 0: equilibrium — no net change occurs

Enthalpy and Entropy Contributions

ΔHΔSSpontaneous at...
−+All temperatures (always spontaneous)
+−Never (always non-spontaneous)
−−Low temperature (enthalpy dominates)
++High temperature (entropy dominates)

Standard Free Energy

ΔG° = standard free energy change (reactants and products at 1 M, 1 atm, 25°C). ΔG° = −RT ln(K_eq). If K_eq > 1: ΔG° < 0 (products favored); if K_eq < 1: ΔG° > 0 (reactants favored). Actual ΔG (non-standard conditions): ΔG = ΔG° + RT ln(Q), where Q = reaction quotient.

Common Examples

Spontaneous: combustion (ΔH << 0, ΔS > 0); dissolving NaCl (entropy driven); ice melting above 0°C (ΔS > 0 at high T). Non-spontaneous: water splitting (ΔH >> 0, ΔS slightly +); photosynthesis (requires light energy input).

Glossary

Spontaneity
A process that occurs without continuous external energy input at constant T and P; determined by ΔG = ΔH − TΔS; ΔG < 0 = spontaneous; ΔG > 0 = non-spontaneous; ΔG = 0 = equilibrium.
Gibbs Free Energy (ΔG)
ΔH − TΔS; the thermodynamic criterion for spontaneity at constant T and P; related to equilibrium by ΔG° = −RT ln(K); actual ΔG = ΔG° + RT ln(Q).
Exergonic / Endergonic
Exergonic: ΔG < 0 (spontaneous, releases usable energy); endergonic: ΔG > 0 (non-spontaneous, requires energy input); distinct from exothermic/endothermic (ΔH terms only).

Frequently Asked Questions

Spontaneity at constant T and P is determined by ΔG = ΔH − TΔS: ΔG < 0 = spontaneous; ΔG > 0 = non-spontaneous. Both enthalpy (ΔH) and entropy (ΔS) contribute. A reaction with ΔH < 0 and ΔS > 0 is always spontaneous (at all temperatures). A reaction with ΔH > 0 and ΔS < 0 is never spontaneous. When ΔH and ΔS have the same sign, temperature determines spontaneity: if ΔH < 0 and ΔS < 0: spontaneous only at low T (where −TΔS is small and positive); if ΔH > 0 and ΔS > 0: spontaneous only at high T (where TΔS dominates).

Yes — an endothermic reaction (ΔH > 0) can be spontaneous if ΔS > 0 and T is high enough that TΔS > ΔH. Example: dissolving ammonium nitrate (NH₄NO₃) in water is endothermic (absorbs heat — the solution cools, as in cold packs) but spontaneous because the entropy increase (solid dissolving into many aqueous ions) is large enough to overcome the unfavorable ΔH. ΔG = ΔH − TΔS: with ΔS large and positive, TΔS > ΔH at room temperature → ΔG < 0 → spontaneous despite being endothermic.

ΔG° = −RT ln(K_eq). R = 8.314 J/mol/K; T = temperature in Kelvin. At 25°C (298 K): ΔG° = −(8.314)(298) ln(K) = −2478 ln(K) J/mol. If K = 1000: ΔG° = −2478 × ln(1000) = −2478 × 6.908 = −17,100 J/mol = −17.1 kJ/mol. Every 5.7 kJ/mol change in ΔG° changes K by 10-fold at 25°C. In the cell: actual ΔG differs from ΔG° because concentrations are not standard (1 M); ΔG = ΔG° + RT ln(Q). ATP hydrolysis in the cell: ΔG ≈ −50 kJ/mol (much more negative than ΔG° = −30.5 kJ/mol) because [ADP] and [Pi] are low.

Spontaneity (thermodynamics) and reaction rate (kinetics) are independent. A spontaneous reaction (ΔG < 0) will eventually proceed but may do so extremely slowly without a catalyst. Examples: diamond → graphite conversion is thermodynamically spontaneous at room temperature (ΔG < 0) but occurs at negligible rate (diamond does not spontaneously convert to graphite in a human lifetime). H₂ + O₂ → H₂O is very spontaneous (ΔG° = −237 kJ/mol) but does not react without a spark or catalyst. Activation energy (Ea) controls rate; catalysts lower Ea but don't change ΔG. Thermodynamics predicts if a reaction can happen; kinetics predicts how fast it does happen.