Gibbs Free Energy Calculator
Calculate ΔG from enthalpy, entropy, and temperature, then interpret whether the process is thermodynamically spontaneous under constant temperature and pressure.
Reaction conditions
Live result
Calculation
ΔG = ΔH – TΔS
– 92.22 kJ/mol – (293.15 K × – 0.19875 kJ/(mol·K)) = – 33.96 kJ/mol
How to use the Gibbs free energy calculator
What this calculator does
This calculator combines the enthalpy change, entropy change, and absolute temperature of a process to estimate the Gibbs free energy change, ΔG. At constant temperature and pressure, the sign of ΔG indicates the thermodynamic direction favored by the stated conditions. A negative value supports a spontaneous forward process, a positive value indicates that the forward process is nonspontaneous, and a value near zero corresponds to equilibrium. This is a thermodynamic criterion, not a prediction of reaction speed: a process can be spontaneous yet proceed extremely slowly because of a kinetic barrier.
When to use it
Use the calculator when comparing reaction feasibility at different temperatures, checking classroom thermodynamics work, evaluating whether entropy can overcome an unfavorable enthalpy term, or preparing a reproducible calculation for a laboratory report. The underlying relationship follows the standard Gibbs energy definition summarized by the IUPAC Gold Book entry for Gibbs energy.
How to calculate
- The calculator opens with a complete ammonia-synthesis demonstration and an immediately available Excel workbook.
- Replace Enthalpy change (ΔH), Entropy change (ΔS), and Temperature (T) with your values. Choose the unit beside each field; changing a unit converts the current value rather than changing only the label.
- Read Gibbs free energy change (ΔG), the temperature in kelvin, the entropy contribution TΔS, and the interpretation.
- Select Download Excel to export the current validated inputs and outputs as an OOXML workbook. Reset clears the demonstration values and disables export until a new complete valid state is entered.
Input guide
Enthalpy change (ΔH) is required and accepts a signed decimal in kJ/mol or J/mol. The startup example is – 92.22 kJ/mol. More negative enthalpy generally lowers ΔG; a common mistake is dropping the negative sign for an exothermic process. Entropy change (ΔS) is required and accepts a signed decimal in J/(mol·K) or kJ/(mol·K). The example is – 198.75 J/(mol·K). A positive entropy change lowers ΔG increasingly as temperature rises, while a negative entropy change raises ΔG increasingly with temperature. Temperature (T) is required and accepts °C, K, or °F, but the calculation always uses kelvin. The example is 20 °C, equal to 293.15 K. Values at or below absolute zero are rejected. Do not multiply entropy by Celsius directly; convert to kelvin first.
Output guide
Gibbs free energy change (ΔG) is displayed in kJ/mol and is an exact result of the entered thermodynamic identity at the shown precision. Temperature reports the converted absolute temperature. Entropy term (TΔS) shows how much the entropy contribution adds to or subtracts from ΔH. The summary pills repeat ΔG, spontaneity, and kelvin temperature for quick scanning. The interpretation labels negative ΔG as spontaneous, positive ΔG as nonspontaneous, and values within a small numerical tolerance of zero as equilibrium. These outputs do not estimate activation energy or rate.
Worked example
For the startup values, ΔH = – 92.22 kJ/mol, ΔS = – 198.75 J/(mol·K) = – 0.19875 kJ/(mol·K), and T = 20 °C = 293.15 K. First calculate TΔS: 293.15 × – 0.19875 = – 58.26 kJ/mol. Then apply ΔG = ΔH – TΔS: – 92.22 – ( – 58.26) = – 33.96 kJ/mol. Because the result is negative, the forward process is thermodynamically spontaneous under the specified conditions.
Understanding the signs
The balance between enthalpy and entropy determines how temperature changes the result. When both ΔH and ΔS are negative, as in the demonstration, the process may be spontaneous at lower temperatures but become nonspontaneous at sufficiently high temperatures. When both are positive, higher temperature can make the entropy term large enough to favor spontaneity. The equilibrium crossover, when it exists, follows T = ΔH/ΔS with consistent units and a physically valid positive kelvin temperature.
The Chemistry LibreTexts overview of Gibbs free energy provides a deeper derivation and discusses how ΔG connects to equilibrium.
Units, precision, and limitations
Enthalpy and Gibbs energy must share energy-per-mole units, while entropy must use energy per mole per kelvin. This calculator converts all entries to kJ/mol and kelvin before applying the formula. Display values are rounded for readability, but the workbook stores typed numeric values from the canonical calculation. Standard thermodynamic data are often reported for defined reference states, so mixing values measured under incompatible conditions can produce a mathematically correct but scientifically misleading result.
For conventions on SI quantities and temperature, consult the NIST Guide for the Use of the International System of Units. For reaction data, the NIST Chemistry WebBook is a widely used source of thermochemical information.