Gibbs Free Energy Calculator

Q: How does temperature affect spontaneity?

The four spontaneity cases arise from the signs of ΔH and ΔS. If both are negative (ΔH 0, it is spontaneous at all temperatures. If ΔH > 0 and ΔS < 0, it is never spontaneous. This temperature dependence explains phenomena like ice melting only above 0°C and calcium carbonate decomposing only above ~840°C.

Q: What is the relationship between ΔG° and the equilibrium constant K?

ΔG° = -RT ln K, where R = 8.314 J/(mol·K) and T is temperature in Kelvin. This equation shows that a large negative ΔG° corresponds to a large K (product-favored equilibrium), while a large positive ΔG° gives a small K (reactant-favored). For ΔG° = 0, K = 1 exactly. Combining ΔG° = -nFE°cell with this relationship connects electrochemical measurements directly to equilibrium positions.

Q: What is the difference between ΔG and ΔG°?

ΔG° is the standard Gibbs energy change — evaluated at standard conditions (1 mol/L or 1 bar for each species, usually at 25°C). ΔG is the Gibbs energy change under actual conditions. They are related by ΔG = ΔG° + RT ln Q, where Q is the reaction quotient. This equation shows that even a reaction with positive ΔG° can become spontaneous if reactant concentrations are very high (Q ≪ K) and vice versa. At equilibrium, Q = K and ΔG = 0.

Calculate Gibbs free energy (ΔG) from enthalpy (ΔH), entropy (ΔS), and temperature (T). Determine if a reaction is spontaneous.

Thermodynamics

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How to Use

1
Enter enthalpy and entropy changes
Input ΔH (enthalpy change) in kJ/mol and ΔS (entropy change) in J/(mol·K). Be careful with units: ΔH is usually in kJ while ΔS is in J.
2
Specify the temperature
Enter the temperature in Kelvin (K). Convert Celsius by adding 273.15. The tool computes ΔG = ΔH - TΔS at the given temperature.
3
Interpret spontaneity
A negative ΔG indicates a spontaneous reaction at that temperature. The calculator also shows the crossover temperature where ΔG = 0 and the reaction becomes non-spontaneous.

About

Gibbs free energy (ΔG = ΔH - TΔS) is the master equation of chemical thermodynamics, combining enthalpy and entropy into a single criterion for spontaneity under the constant temperature and pressure conditions typical of most chemical processes. Introduced by American physicist Josiah Willard Gibbs in the 1870s, it elegantly resolves the apparent conflict between enthalpy-driven and entropy-driven processes by weighting entropy by temperature.

The equation ΔG = ΔH - TΔS reveals the interplay of the two driving forces of chemistry. Enthalpy change (ΔH) reflects bond-making and bond-breaking: exothermic reactions (ΔH < 0) release heat, while endothermic reactions (ΔH > 0) absorb it. Entropy change (ΔS) measures the dispersal of energy and matter: reactions that increase disorder (ΔS > 0) gain a thermodynamic advantage that grows with temperature. At high temperature, entropy dominates; at low temperature, enthalpy wins.

Gibbs energy calculations appear throughout chemistry, biochemistry, materials science, and chemical engineering. In biochemistry, ATP hydrolysis (ΔG°’ = -30.5 kJ/mol) drives otherwise unfavorable biosynthetic reactions through coupling. In materials science, the temperature dependence of ΔG for phase transitions determines melting points and solubility. In chemical engineering, ΔG diagrams guide reactor design and optimization of equilibrium yields. This calculator provides both the ΔG value and the spontaneity crossover temperature for a complete thermodynamic picture.

FAQ

What does Gibbs free energy measure physically?

Gibbs free energy G represents the maximum non-expansion work obtainable from a system at constant temperature and pressure, or equivalently, the thermodynamic potential that determines the direction of spontaneous change. A negative ΔG means the system can release free energy to do useful work while proceeding spontaneously. At equilibrium, ΔG = 0, and no net work is available. The concept was introduced by Josiah Willard Gibbs in 1876 and underpins all of modern chemical thermodynamics.

Why is Gibbs energy calculated at constant temperature and pressure?

The condition of constant temperature and pressure is the most common situation in laboratory chemistry and in biology (where reactions occur in open vessels at atmospheric pressure and body temperature). Under these conditions, the criterion for spontaneity is ΔG < 0 rather than the more general entropy criterion. In systems at constant volume and temperature, the analogous criterion uses Helmholtz free energy A instead. Industrial reactors often operate at elevated pressure where pressure-composition diagrams become important.

How does temperature affect spontaneity?

The four spontaneity cases arise from the signs of ΔH and ΔS. If both are negative (ΔH < 0, ΔS < 0), the reaction is spontaneous at low temperature but becomes non-spontaneous above the crossover temperature T = ΔH/ΔS. If both are positive, the reaction is spontaneous above T. If ΔH < 0 and ΔS > 0, it is spontaneous at all temperatures. If ΔH > 0 and ΔS < 0, it is never spontaneous. This temperature dependence explains phenomena like ice melting only above 0°C and calcium carbonate decomposing only above ~840°C.

What is the relationship between ΔG° and the equilibrium constant K?

ΔG° = -RT ln K, where R = 8.314 J/(mol·K) and T is temperature in Kelvin. This equation shows that a large negative ΔG° corresponds to a large K (product-favored equilibrium), while a large positive ΔG° gives a small K (reactant-favored). For ΔG° = 0, K = 1 exactly. Combining ΔG° = -nFE°cell with this relationship connects electrochemical measurements directly to equilibrium positions.

What is the difference between ΔG and ΔG°?

ΔG° is the standard Gibbs energy change — evaluated at standard conditions (1 mol/L or 1 bar for each species, usually at 25°C). ΔG is the Gibbs energy change under actual conditions. They are related by ΔG = ΔG° + RT ln Q, where Q is the reaction quotient. This equation shows that even a reaction with positive ΔG° can become spontaneous if reactant concentrations are very high (Q ≪ K) and vice versa. At equilibrium, Q = K and ΔG = 0.

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