Gibbs Free Energy Calculator
Calculate Gibbs free energy change, spontaneity, and equilibrium for chemical reactions
Gibbs Free Energy (ΔG)
Reaction Spontaneity
Calculation Steps
Additional Information
🌡️ Temperature Effects
What is Gibbs Free Energy?
Gibbs free energy (G), also called Gibbs energy or free enthalpy, is a thermodynamic potential that measures the maximum reversible work that may be performed by a thermodynamic system at constant temperature and pressure. The change in Gibbs free energy (ΔG) determines whether a chemical reaction will occur spontaneously and is fundamental to understanding chemical equilibrium.
Fundamental Equations:
ΔG = ΔH - TΔS
Gibbs-Helmholtz equation (standard conditions)
ΔG° = -RT ln(K)
Relationship with equilibrium constant
ΔG = ΔG° + RT ln(Q)
Non-standard conditions (with reaction quotient)
- • ΔG = Change in Gibbs free energy (kJ/mol)
- • ΔH = Change in enthalpy (kJ/mol)
- • ΔS = Change in entropy (J/mol·K)
- • T = Absolute temperature (K)
- • R = Gas constant (8.314 J/mol·K)
- • K = Equilibrium constant
- • Q = Reaction quotient
Spontaneity Criteria
| ΔG Value | Spontaneity | Meaning |
|---|---|---|
| ΔG < 0 | Spontaneous (Exergonic) | Reaction proceeds forward |
| ΔG = 0 | At Equilibrium | No net change, K = Q |
| ΔG > 0 | Non-spontaneous (Endergonic) | Reverse reaction favored |
Combined Effects of ΔH and ΔS
The spontaneity of a reaction depends on both enthalpy (ΔH) and entropy (ΔS) changes, as well as temperature. The table below shows all possible combinations:
| ΔH | ΔS | ΔG Sign | Spontaneity | Example |
|---|---|---|---|---|
| - | + | Always - | Spontaneous at all T | Combustion reactions |
| + | - | Always + | Non-spontaneous at all T | Formation of ozone |
| - | - | - at low T, + at high T | Spontaneous at low T | Exothermic condensation |
| + | + | + at low T, - at high T | Spontaneous at high T | Endothermic melting |
Key Insight:
Temperature can make the difference! When ΔH and ΔS have the same sign, temperature determines spontaneity. The crossover temperature where ΔG = 0 is T = ΔH/ΔS.
Worked Examples
Example 1: Calculate ΔG from ΔH and ΔS
Problem: For the reaction 2H₂(g) + O₂(g) → 2H₂O(l) at 298 K:
ΔH° = -571.66 kJ/mol, ΔS° = -326.8 J/mol·K
Calculate ΔG° and determine if the reaction is spontaneous.
Step 1: Convert units
ΔS° = -326.8 J/mol·K = -0.3268 kJ/mol·K
Step 2: Apply ΔG = ΔH - TΔS
ΔG° = -571.66 - (298.15 × -0.3268)
ΔG° = -571.66 + 97.42 = -474.24 kJ/mol
Step 3: Interpret result
ΔG° < 0, therefore the reaction is spontaneous
Answer: ΔG° = -474.24 kJ/mol (spontaneous)
Example 2: Calculate K from ΔG°
Problem: A reaction has ΔG° = -33.0 kJ/mol at 298 K. Calculate the equilibrium constant K.
Step 1: Use ΔG° = -RT ln(K)
Rearrange: ln(K) = -ΔG°/RT
Step 2: Convert and substitute
ΔG° = -33,000 J/mol
ln(K) = -(-33,000)/(8.314 × 298.15) = 13.31
Step 3: Solve for K
K = e^13.31 = 6.02 × 10⁵
Answer: K = 6.02 × 10⁵ (products strongly favored)
Example 3: Non-Standard Conditions
Problem: For a reaction with ΔG° = -20 kJ/mol at 298 K, calculate ΔG when Q = 0.01.
Step 1: Use ΔG = ΔG° + RT ln(Q)
Step 2: Calculate RT ln(Q)
RT ln(Q) = 8.314 × 298.15 × ln(0.01)
= 2478.8 × (-4.605) = -11,414 J/mol = -11.41 kJ/mol
Step 3: Calculate ΔG
ΔG = -20 + (-11.41) = -31.41 kJ/mol
Answer: ΔG = -31.41 kJ/mol (even more spontaneous at low Q)
Applications of Gibbs Free Energy
Chemical Equilibrium
Predicting equilibrium position and calculating equilibrium constants for chemical reactions. Understanding product vs. reactant favorability.
Electrochemistry
Relating cell potential to Gibbs free energy (ΔG = -nFE°) for batteries, fuel cells, and electrolysis processes.
Biochemistry
Understanding energy coupling in metabolic pathways, ATP hydrolysis, and enzyme-catalyzed reactions in living systems.
Phase Transitions
Predicting melting points, boiling points, and sublimation temperatures where ΔG = 0 at the phase transition.
Material Science
Designing synthesis routes, predicting crystal structures, and understanding alloy formation and stability.
Environmental Chemistry
Assessing pollutant degradation, predicting chemical speciation in natural waters, and understanding atmospheric chemistry.
References
Gibbs free energy calculations are based on fundamental thermodynamic principles:
Note: This calculator uses the gas constant R = 8.314 J/mol·K. Calculations assume ideal behavior and standard state conditions (1 bar pressure, specified temperature, 1 M concentration for solutions) unless otherwise noted. For precise thermodynamic calculations, experimental values of ΔH° and ΔS° should be obtained from reliable databases such as NIST or CRC Handbook. Temperature dependencies of ΔH and ΔS are not accounted for in simple calculations.
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