-85.1
kJ/mol
-14.9
kJ/mol
0
kJ/mol
-0
kJ/mol
2,000
K
8,511
-85.1
kJ/mol
-14.9
kJ/mol
0
kJ/mol
-0
kJ/mol
2,000
K
8,511
The Gibbs Free Energy Calculator determines ΔG, the thermodynamic quantity that predicts whether a process is spontaneous at a given temperature. Gibbs free energy combines enthalpy (ΔH) and entropy (ΔS) effects into a single criterion: if ΔG < 0, the process is spontaneous. This calculator supports three modes: the standard equation (ΔG = ΔH − TΔS), the equilibrium constant method (ΔG° = −RT ln K), and the non-standard conditions method (ΔG = ΔG° + RT ln Q). It also computes the crossover temperature where spontaneity changes. Gibbs free energy is the cornerstone of chemical thermodynamics, biochemistry (ATP hydrolysis), electrochemistry (cell potentials), and phase equilibria.
Mode 1 — Standard Equation:
$$\Delta G = \Delta H - T\Delta S$$
where ΔH is in kJ/mol, T in K, and ΔS in J/(mol·K). Note the unit conversion: TΔS is divided by 1000 to match kJ.
Mode 2 — From Equilibrium Constant:
$$\Delta G^\circ = -RT \ln K$$
where R = 8.314 J/(mol·K). A large K gives a large negative ΔG° (favorable).
Mode 3 — Non-Standard Conditions:
$$\Delta G = \Delta G^\circ + RT \ln Q$$
where Q is the reaction quotient at current conditions.
The crossover temperature is where ΔG = 0:
$$T_{crossover} = \frac{|\Delta H|}{|\Delta S|}$$
ΔG < 0: Spontaneous (thermodynamically favorable) in the forward direction. ΔG > 0: Non-spontaneous (reverse direction is favored). ΔG = 0: System is at equilibrium. The crossover temperature is where spontaneity switches — below this temperature one direction is favored, above it the other direction. Four thermodynamic scenarios exist: (1) ΔH < 0, ΔS > 0: always spontaneous; (2) ΔH > 0, ΔS < 0: never spontaneous; (3) ΔH < 0, ΔS < 0: spontaneous at low T; (4) ΔH > 0, ΔS > 0: spontaneous at high T.
Inputs
Results
ΔG = −100 − 298 × (−50/1000) = −100 + 14.9 = −85.1 kJ/mol. Spontaneous (ΔG < 0). Crossover T = |−100 × 1000|/|−50| = 2000 K. Below 2000 K, the reaction is spontaneous.
Inputs
Results
ΔG° = −8.314 × 298 × ln(1000)/1000 = −8.314 × 298 × 6.908/1000 = −17.11 kJ/mol. Large K gives negative ΔG°, confirming products are favored.
Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work a system can perform at constant temperature and pressure. The change ΔG determines spontaneity: ΔG < 0 means spontaneous.
Spontaneous means the process is thermodynamically favorable — it can occur without external energy input. It does NOT mean fast. A spontaneous reaction may be extremely slow if the activation energy is high.
ΔG° is the standard Gibbs energy (all species at 1 M or 1 atm, 25°C). ΔG is at actual conditions. They are related by ΔG = ΔG° + RT ln Q. At equilibrium, ΔG = 0 and Q = K.
The temperature where ΔG = 0 (ΔH = TΔS). Below this temperature, one sign of ΔG prevails; above it, the other. It only exists when ΔH and ΔS have the same sign.
Nature favors both lower energy (negative ΔH) and higher entropy (positive ΔS). Gibbs free energy combines both driving forces: ΔG = ΔH − TΔS. Temperature determines which factor dominates.
Biochemical reactions are driven by ΔG. ATP hydrolysis (ΔG°' = −30.5 kJ/mol) provides energy to drive non-spontaneous reactions through coupling. The actual ΔG in cells is even more negative due to concentrations.
In electrochemistry: ΔG = −nFE, where n = moles of electrons, F = Faraday's constant (96,485 C/mol), E = cell potential. A positive cell potential means negative ΔG (spontaneous).
No. ΔG tells you whether a reaction is thermodynamically favorable, not how fast it occurs. Reaction rate depends on activation energy (kinetics), not ΔG (thermodynamics).
When ΔG = 0, the system is at equilibrium. No net reaction occurs. The forward and reverse rates are equal. This is the condition Q = K.
For gases, ΔG = ΔG° + RT ln Q, where Q includes partial pressures. Increasing pressure of reactants (decreasing their contribution to Q) makes ΔG more negative, favoring forward reaction.
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