Gibbs Free Energy Calculator

How Gibbs Free Energy Is Calculated

Gibbs Free Energy (G) predicts whether a chemical reaction occurs spontaneously at constant temperature and pressure — the most common conditions in chemistry and biology.

Gibbs Free Energy Formula: ΔG = ΔH − TΔS

Where:

• ΔG = change in Gibbs free energy (kJ/mol)
• ΔH = enthalpy change (kJ/mol), negative means exothermic
• T = temperature in Kelvin (K = °C + 273.15)
• ΔS = entropy change (kJ/mol·K)

Spontaneity Rules:

• ΔG < 0: spontaneous (reaction proceeds forward)
• ΔG > 0: non-spontaneous (requires energy input)
• ΔG = 0: equilibrium (no net change)

Worked Example: Melting Ice at 25°C:

• ΔH = +6.01 kJ/mol (endothermic, absorbs heat)
• ΔS = +22.0 J/mol·K = +0.0220 kJ/mol·K
• T = 25 + 273.15 = 298.15 K
• ΔG = 6.01 − (298.15 × 0.0220) = 6.01 − 6.56 = −0.55 kJ/mol

ΔG < 0 confirms ice melts spontaneously at 25°C. At exactly 0°C (273K): ΔG = 6.01 − (273 × 0.0220) = 6.01 − 6.01 = 0 (equilibrium — ice and water coexist).

Standard Conditions vs Real Conditions: ΔG = ΔG° + RT × ln(Q)

where Q is the reaction quotient, R = 8.314 J/mol·K.

At Equilibrium: ΔG = 0, so ΔG° = −RT × ln(K), allowing calculation of the equilibrium constant K.

The electrochemistry link. For a redox reaction in a battery or fuel cell, Gibbs free energy connects directly to the cell voltage: ΔG° = −nFE°, where n is the moles of electrons transferred per mole of reaction, F is Faraday’s constant (96,485 C/mol), and E° is the standard cell potential in volts. A positive cell voltage means a negative ΔG° — which means the reaction is spontaneous and will deliver electrical work. This is why a fresh AA battery (≈1.5 V) can run a device, and a depleted one (≈0 V) cannot: as the cell discharges, E° drops toward zero, ΔG° rises toward zero, and the chemistry runs out of usable free energy.