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, which is to say under the conditions almost every reaction in chemistry and biology actually runs.

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. Enter it in J/mol·K, the unit tables use. The formula needs kJ/mol·K, so the calculator divides your value by 1000 before subtracting.

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 273.15 K, which is 0°C, the same arithmetic gives ΔG = 6.01 − (273.15 × 0.0220) = 0.00 kJ/mol. That is equilibrium, and it is why ice and water coexist at exactly that temperature and nowhere else.

The crossover temperature

Set ΔG to zero and the formula rearranges to T = ΔH / ΔS, the single temperature where the reaction flips between spontaneous and not. For the ice numbers above that comes out at 273.2 K, the melting point, which is a satisfying way to see that the melting point is not an arbitrary fact about water but a consequence of its enthalpy and entropy of fusion.

Which side of the crossover is the spontaneous one depends on the signs:

The last two are the interesting ones, and they are where a crossover temperature is worth knowing.

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°, so the reaction is spontaneous and will deliver electrical work.

Watch the degree symbol in that expression, because it is easy to lose. E° and ΔG° are standard values, fixed for a given reaction at a given temperature, and they do not change as a battery runs down. What changes is the actual cell potential E, which the Nernst equation ties to the reaction quotient: E = E° − (RT/nF) ln Q. As a fresh AA cell (≈1.5 V) discharges, products build up, Q climbs, E falls toward zero, and ΔG = −nFE rises toward zero with it. At E = 0 the cell has reached equilibrium and there is no usable free energy left, which is what a dead battery physically is.