Gibbs Free Energy Calculator
Reaction enthalpy (negative for exothermic)
Reaction entropy (in J/(mol·K))
Absolute temperature (25°C = 298.15 K)
What is Gibbs Free Energy?
Gibbs Free Energy (ΔG) is a thermodynamic potential that predicts whether a chemical reaction can occur spontaneously.
Important Rules:
- ΔG < 0: Reaction is spontaneous
- ΔG = 0: System is at equilibrium
- ΔG > 0: Reaction is non-spontaneous
Influencing Factors:
- Enthalpy (ΔH) — energetically favorable
- Entropy (ΔS) — disorder/probability
- Temperature (T) — affects both factors
Practical Application:
- Predict reaction direction
- Equilibrium position
- Cell biology and biochemistry
Formulas
Gibbs-Helmholtz Equation:
ΔG = ΔH - T·ΔS
ΔG = ΔH - T·ΔS
With Equilibrium Constant:
ΔG = -RT·ln(K)
ΔG = -RT·ln(K)
Equilibrium Constant:
K = e-ΔG/RT
K = e-ΔG/RT
Gas Constant:
R = 8.314 J/(mol·K)
R = 8.314 J/(mol·K)
Examples
Water Dissociation (Exothermic but Non-Spontaneous)
H₂O → H⁺ + OH⁻
ΔH ≈ 55.8 kJ/mol
ΔS < 0 (negative entropy)
ΔG > 0 (non-spontaneous)
H₂O → H⁺ + OH⁻
ΔH ≈ 55.8 kJ/mol
ΔS < 0 (negative entropy)
ΔG > 0 (non-spontaneous)
Exothermic, Entropy Favorable Reaction
H₂ + I₂ → 2HI
ΔH < 0, ΔS approximately neutral
ΔG < 0 (spontaneous)
H₂ + I₂ → 2HI
ΔH < 0, ΔS approximately neutral
ΔG < 0 (spontaneous)
Temperature Dependent: Melting Ice
H₂O(s) → H₂O(l)
ΔH > 0 (endothermic)
ΔS > 0 (entropy increases)
Spontaneous above T = 273 K (0°C)
H₂O(s) → H₂O(l)
ΔH > 0 (endothermic)
ΔS > 0 (entropy increases)
Spontaneous above T = 273 K (0°C)
Equilibrium with K = 0.64
ΔG = -RT·ln(0.64) = +1.4 kJ/mol
Non-spontaneous at 298 K
But close to equilibrium
ΔG = -RT·ln(0.64) = +1.4 kJ/mol
Non-spontaneous at 298 K
But close to equilibrium
Technical Background
Gibbs-Helmholtz Equation
The Gibbs-Helmholtz equation relates enthalpy (ΔH), entropy (ΔS), and temperature (T) to Gibbs Free Energy (ΔG):
ΔG = ΔH - T·ΔS
Thermodynamic Potentials
- Enthalpy (ΔH): Heat at constant pressure
- Entropy (ΔS): Measure of disorder or probability
- Gibbs Energy (ΔG): Maximum available work
Spontaneity and Equilibrium
- ΔG < 0: Reaction proceeds spontaneously (forward direction)
- ΔG = 0: System at equilibrium (no net reaction)
- ΔG > 0: Reaction does not proceed spontaneously (reverse direction)
Relationship to Equilibrium Constant
Gibbs Free Energy is directly related to the equilibrium constant:
ΔG° = -RT·ln(K)
- K > 1: ΔG° < 0 (products favored)
- K = 1: ΔG° = 0 (equilibrium)
- K < 1: ΔG° > 0 (reactants favored)
Temperature Dependence
Spontaneity can be temperature-dependent:
- ΔH < 0, ΔS > 0: Spontaneous at all temperatures
- ΔH > 0, ΔS < 0: Never spontaneous
- ΔH < 0, ΔS < 0: Spontaneous at low temperatures
- ΔH > 0, ΔS > 0: Spontaneous at high temperatures
Practical Applications
- Chemical Industry: Optimal reaction conditions
- Biochemistry: Cellular processes and metabolism
- Materials Science: Phase transitions and crystallization
- Electrochemistry: Galvanic cells and electrolysis
- Energy Generation: Maximum work output
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