# Thermodynamics (Gibbs Free Energy) Calculator

Calculate Gibbs free energy ΔG = ΔH − TΔS, reaction spontaneity, equilibrium temperature, and equilibrium constant K.

> Canonical page: https://elysiatools.com/en/tools/thermodynamics-gibbs-calculator

- **Category:** Math & Numbers

- **Keywords:** gibbs free energy, thermodynamics, enthalpy, entropy, spontaneity, equilibrium constant

## Overview

The Thermodynamics (Gibbs Free Energy) Calculator determines reaction spontaneity, equilibrium temperature, and the equilibrium constant (K) using the fundamental thermodynamic equation ΔG = ΔH − TΔS. By inputting enthalpy change (ΔH), entropy change (ΔS), and temperature, you can instantly analyze chemical reaction feasibility and thermodynamic behavior.

## Inputs

- **Calculation Mode** (select)
- **Enthalpy ΔH (kJ/mol)** (number): Negative = exothermic, positive = endothermic.
- **Entropy ΔS (J/mol·K)** (number): Negative = more ordered, positive = more disordered. Units are J (not kJ).
- **Temperature (K)** (number): Absolute temperature. Used in 'Find ΔG' mode.
- **Temperature Unit** (select)
- **Decimal Places** (number)

## When to use

- When predicting whether a chemical reaction will occur spontaneously at a specific temperature.
- When calculating the exact temperature threshold at which a reaction transitions between spontaneous and non-spontaneous.
- When determining the equilibrium constant (K) for a reaction based on its Gibbs free energy change.

## How it works

- Select the calculation mode: either finding Gibbs free energy (ΔG) and spontaneity, or finding the equilibrium temperature.
- Input the enthalpy change (ΔH) in kJ/mol and the entropy change (ΔS) in J/mol·K.
- Specify the temperature and its unit (Kelvin or Celsius) if calculating ΔG, then set the desired decimal precision.
- Click calculate to compute the Gibbs free energy, determine spontaneity, and estimate the equilibrium constant.

## Use cases

- Chemistry students verifying homework calculations for thermodynamic spontaneity and equilibrium constants.
- Chemical engineers assessing the thermodynamic feasibility of industrial synthesis reactions at varying temperatures.
- Researchers determining the temperature limits required to drive endothermic or entropy-favored reactions.

## Frequently asked questions

### What units should I use for enthalpy (ΔH) and entropy (ΔS)?

Enthalpy (ΔH) must be entered in kilojoules per mole (kJ/mol), while entropy (ΔS) must be entered in joules per mole-Kelvin (J/mol·K). The calculator automatically handles the unit conversion factor of 1000.

### How does the calculator determine if a reaction is spontaneous?

A reaction is spontaneous if the calculated Gibbs free energy change (ΔG) is negative, and non-spontaneous if ΔG is positive.

### What does the equilibrium temperature mode calculate?

It calculates the temperature at which ΔG equals zero, representing the point where the system is at equilibrium and the reaction direction can shift.

### Can I input temperatures in Celsius?

Yes, you can select Celsius as the temperature unit, and the calculator will automatically convert it to Kelvin for the thermodynamic equations.

### How is the equilibrium constant K calculated?

The calculator estimates K using the relationship ΔG = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin.

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