Calculate Gibbs Free Energy (ΔG) to determine reaction spontaneity by entering enthalpy (ΔH), temperature (T), and entropy (ΔS) values. Essential for chemistry, biochemistry, and thermodynamics applications.
ΔG = ΔH - TΔS
Where ΔG is Gibbs free energy, ΔH is enthalpy, T is temperature, and ΔS is entropy
Gibbs Free Energy is a fundamental thermodynamic property that predicts whether chemical reactions and physical processes will occur spontaneously. This free online Gibbs Free Energy Calculator helps scientists, engineers, and students quickly determine reaction feasibility using the proven formula ΔG = ΔH - TΔS.
Named after American physicist Josiah Willard Gibbs, this thermodynamic potential combines enthalpy (heat content) and entropy (disorder) to provide a single value that indicates whether a process will proceed naturally without external energy input. Our calculator delivers instant, accurate results for thermodynamic calculations in chemistry, biochemistry, materials science, and engineering applications.
Key benefits of using our Gibbs Free Energy Calculator:
The Gibbs Free Energy change (ΔG) is calculated using the following equation:
Where:
This equation represents the balance between two fundamental thermodynamic factors:
The sign of ΔG provides crucial information about reaction spontaneity:
It's important to note that spontaneity doesn't necessarily indicate reaction speed—a spontaneous reaction may still proceed very slowly without a catalyst.
Standard Gibbs Free Energy change (ΔG°) refers to the energy change when all reactants and products are in their standard states (typically 1 atm pressure, 1 M concentration for solutions, and often at 298.15 K or 25°C). The equation becomes:
Where ΔH° and ΔS° are the standard enthalpy and entropy changes, respectively.
Our Gibbs Free Energy Calculator is designed for simplicity and ease of use. Follow these steps to calculate the Gibbs Free Energy change for your reaction or process:
Enter the Enthalpy Change (ΔH) in kilojoules per mole (kJ/mol)
Input the Temperature (T) in Kelvin
Enter the Entropy Change (ΔS) in kilojoules per mole-Kelvin (kJ/(mol·K))
View the Result
The calculator performs the following checks on user inputs:
If invalid inputs are detected, an error message will be displayed, and the calculation will not proceed until corrected.
Let's walk through a practical example to demonstrate how to use the Gibbs Free Energy Calculator:
Example: Calculate the Gibbs Free Energy change for a reaction with ΔH = -92.4 kJ/mol and ΔS = 0.0987 kJ/(mol·K) at 298 K.
Enter ΔH = -92.4 kJ/mol
Enter T = 298 K
Enter ΔS = 0.0987 kJ/(mol·K)
The calculator performs the calculation: ΔG = ΔH - TΔS ΔG = -92.4 kJ/mol - (298 K × 0.0987 kJ/(mol·K)) ΔG = -92.4 kJ/mol - 29.41 kJ/mol ΔG = -121.81 kJ/mol
Interpretation: Since ΔG is negative (-121.81 kJ/mol), this reaction is spontaneous at 298 K.
Gibbs Free Energy calculations are essential in numerous scientific and engineering applications:
Chemists use Gibbs Free Energy to predict whether a reaction will occur spontaneously under given conditions. This helps in:
In biochemistry and molecular biology, Gibbs Free Energy helps understand:
Materials scientists and engineers use Gibbs Free Energy calculations for:
Environmental applications include:
In industrial settings, Gibbs Free Energy calculations help optimize:
While Gibbs Free Energy is a powerful thermodynamic tool, other related parameters may be more appropriate in certain situations:
Defined as A = U - TS (where U is internal energy), Helmholtz Free Energy is more appropriate for systems at constant volume rather than constant pressure. It's particularly useful in:
For processes where only heat exchange matters and entropy effects are negligible, enthalpy (H = U + PV) may be sufficient. This is often used in:
When focusing solely on disorder and probability, entropy alone may be the parameter of interest, especially in:
For systems with varying composition, chemical potential (partial molar Gibbs energy) becomes important in:
The concept of Gibbs Free Energy has a rich history in the development of thermodynamics:
Josiah Willard Gibbs (1839-1903), an American scientist and mathematician, first introduced the concept in his groundbreaking work "On the Equilibrium of Heterogeneous Substances," published between 1875 and 1878. This work is considered one of the greatest achievements in physical science of the 19th century, establishing the foundation of chemical thermodynamics.
Gibbs developed this thermodynamic potential while seeking to understand the conditions for equilibrium in chemical systems. He recognized that at constant temperature and pressure, the direction of spontaneous change could be predicted by a single function that combined enthalpy and entropy effects.
Gibbs' work initially received little attention in the United States but was highly regarded in Europe, particularly after being translated into German by Wilhelm Ostwald. Today, Gibbs Free Energy is a cornerstone concept in physical chemistry, chemical engineering, materials science, and biochemistry. The ability to predict reaction spontaneity and equilibrium positions using Gibbs Free Energy calculations has enabled countless scientific advances and technological innovations.
Here are examples of how to calculate Gibbs Free Energy in various programming languages:
1' Excel formula for Gibbs Free Energy
2=B2-(C2*D2)
3
4' Where:
5' B2 contains enthalpy change (ΔH) in kJ/mol
6' C2 contains temperature (T) in Kelvin
7' D2 contains entropy change (ΔS) in kJ/(mol·K)
81def calculate_gibbs_free_energy(enthalpy, temperature, entropy):
2 """
3 Calculate Gibbs Free Energy change
4
5 Parameters:
6 enthalpy (float): Enthalpy change in kJ/mol
7 temperature (float): Temperature in Kelvin
8 entropy (float): Entropy change in kJ/(mol·K)
9
10 Returns:
11 float: Gibbs Free Energy change in kJ/mol
12 """
13 gibbs_energy = enthalpy - (temperature * entropy)
14 return gibbs_energy
15
16# Example usage
17delta_h = -92.4 # kJ/mol
18temp = 298.15 # K
19delta_s = 0.0987 # kJ/(mol·K)
20
21delta_g = calculate_gibbs_free_energy(delta_h, temp, delta_s)
22print(f"Gibbs Free Energy change: {delta_g:.2f} kJ/mol")
23
24# Determine spontaneity
25if delta_g < 0:
26 print("The reaction is spontaneous.")
27elif delta_g > 0:
28 print("The reaction is non-spontaneous.")
29else:
30 print("The reaction is at equilibrium.")
311function calculateGibbsFreeEnergy(enthalpy, temperature, entropy) {
2 // Calculate Gibbs Free Energy change
3 // enthalpy: kJ/mol
4 // temperature: Kelvin
5 // entropy: kJ/(mol·K)
6
7 const gibbsEnergy = enthalpy - (temperature * entropy);
8 return gibbsEnergy;
9}
10
11// Example usage
12const deltaH = -92.4; // kJ/mol
13const temp = 298.15; // K
14const deltaS = 0.0987; // kJ/(mol·K)
15
16const deltaG = calculateGibbsFreeEnergy(deltaH, temp, deltaS);
17console.log(`Gibbs Free Energy change: ${deltaG.toFixed(2)} kJ/mol`);
18
19// Determine spontaneity
20if (deltaG < 0) {
21 console.log("The reaction is spontaneous.");
22} else if (deltaG > 0) {
23 console.log("The reaction is non-spontaneous.");
24} else {
25 console.log("The reaction is at equilibrium.");
26}
271public class GibbsFreeEnergyCalculator {
2 /**
3 * Calculate Gibbs Free Energy change
4 *
5 * @param enthalpy Enthalpy change in kJ/mol
6 * @param temperature Temperature in Kelvin
7 * @param entropy Entropy change in kJ/(mol·K)
8 * @return Gibbs Free Energy change in kJ/mol
9 */
10 public static double calculateGibbsFreeEnergy(double enthalpy, double temperature, double entropy) {
11 return enthalpy - (temperature * entropy);
12 }
13
14 public static void main(String[] args) {
15 double deltaH = -92.4; // kJ/mol
16 double temp = 298.15; // K
17 double deltaS = 0.0987; // kJ/(mol·K)
18
19 double deltaG = calculateGibbsFreeEnergy(deltaH, temp, deltaS);
20 System.out.printf("Gibbs Free Energy change: %.2f kJ/mol%n", deltaG);
21
22 // Determine spontaneity
23 if (deltaG < 0) {
24 System.out.println("The reaction is spontaneous.");
25 } else if (deltaG > 0) {
26 System.out.println("The reaction is non-spontaneous.");
27 } else {
28 System.out.println("The reaction is at equilibrium.");
29 }
30 }
31}
321#include <iostream>
2#include <iomanip>
3
4/**
5 * Calculate Gibbs Free Energy change
6 *
7 * @param enthalpy Enthalpy change in kJ/mol
8 * @param temperature Temperature in Kelvin
9 * @param entropy Entropy change in kJ/(mol·K)
10 * @return Gibbs Free Energy change in kJ/mol
11 */
12double calculateGibbsFreeEnergy(double enthalpy, double temperature, double entropy) {
13 return enthalpy - (temperature * entropy);
14}
15
16int main() {
17 double deltaH = -92.4; // kJ/mol
18 double temp = 298.15; // K
19 double deltaS = 0.0987; // kJ/(mol·K)
20
21 double deltaG = calculateGibbsFreeEnergy(deltaH, temp, deltaS);
22
23 std::cout << "Gibbs Free Energy change: " << std::fixed << std::setprecision(2)
24 << deltaG << " kJ/mol" << std::endl;
25
26 // Determine spontaneity
27 if (deltaG < 0) {
28 std::cout << "The reaction is spontaneous." << std::endl;
29 } else if (deltaG > 0) {
30 std::cout << "The reaction is non-spontaneous." << std::endl;
31 } else {
32 std::cout << "The reaction is at equilibrium." << std::endl;
33 }
34
35 return 0;
36}
371# R function to calculate Gibbs Free Energy
2calculate_gibbs_free_energy <- function(enthalpy, temperature, entropy) {
3 # enthalpy: kJ/mol
4 # temperature: Kelvin
5 # entropy: kJ/(mol·K)
6
7 gibbs_energy <- enthalpy - (temperature * entropy)
8 return(gibbs_energy)
9}
10
11# Example usage
12delta_h <- -92.4 # kJ/mol
13temp <- 298.15 # K
14delta_s <- 0.0987 # kJ/(mol·K)
15
16delta_g <- calculate_gibbs_free_energy(delta_h, temp, delta_s)
17cat(sprintf("Gibbs Free Energy change: %.2f kJ/mol\n", delta_g))
18
19# Determine spontaneity
20if (delta_g < 0) {
21 cat("The reaction is spontaneous.\n")
22} else if (delta_g > 0) {
23 cat("The reaction is non-spontaneous.\n")
24} else {
25 cat("The reaction is at equilibrium.\n")
26}
27Here are some practical examples of Gibbs Free Energy calculations:
For a reaction with ΔH = 15.0 kJ/mol and ΔS = 0.050 kJ/(mol·K), at what temperature will equilibrium occur?
At equilibrium, ΔG = 0, so: 0 = 15.0 - (T × 0.050) T = 15.0 ÷ 0.050 = 300 K
Interpretation: Below 300 K, the reaction is non-spontaneous; above 300 K, it becomes spontaneous.
Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work a system can perform at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) determines whether a chemical reaction or physical process will occur spontaneously. It combines enthalpy (heat content) and entropy (disorder) into a single predictive value.
A negative Gibbs Free Energy change (ΔG < 0) indicates a spontaneous reaction that can proceed without external energy input. This means the reaction releases usable energy and naturally progresses toward equilibrium. The more negative the value, the more thermodynamically favorable the process.
Yes, endothermic reactions with positive enthalpy change (ΔH > 0) can be spontaneous if the entropy increase is large enough and temperature is sufficiently high. When the TΔS term exceeds ΔH in the Gibbs Free Energy equation, the overall ΔG becomes negative, making the process spontaneous.
ΔG refers to Gibbs Free Energy change under any specific conditions, while ΔG° represents the standard Gibbs Free Energy change when all reactants and products are in their standard states (1 atm pressure, 1 M concentration, typically at 298.15 K or 25°C).
Temperature directly impacts the TΔS term in the Gibbs equation. For reactions with positive entropy change (ΔS > 0), higher temperatures make reactions more spontaneous. For reactions with negative entropy change (ΔS < 0), higher temperatures make reactions less favorable.
At chemical equilibrium, ΔG equals zero. The standard Gibbs Free Energy change (ΔG°) relates to the equilibrium constant (K) through: ΔG° = -RT ln(K), where R is the gas constant and T is absolute temperature in Kelvin.
No, Gibbs Free Energy only predicts thermodynamic favorability (whether a reaction is spontaneous), not reaction kinetics or speed. A highly spontaneous reaction (large negative ΔG) may still proceed slowly due to high activation energy barriers.
For non-standard conditions, use the equation: ΔG = ΔG° + RT ln(Q), where Q is the reaction quotient, R is the gas constant (8.314 J/mol·K), and T is temperature in Kelvin. This accounts for actual concentrations and pressures.
Gibbs Free Energy is typically expressed in kilojoules per mole (kJ/mol) or joules per mole (J/mol). When using our calculator, ensure temperature is in Kelvin, enthalpy in kJ/mol, and entropy in kJ/(mol·K) for consistent results.
Josiah Willard Gibbs (1839-1903), an American physicist and mathematician, developed the concept in his groundbreaking work "On the Equilibrium of Heterogeneous Substances" (1875-1878). This established the foundation of chemical thermodynamics and earned him recognition as one of America's greatest scientists.
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Chang, R. (2019). Physical Chemistry for the Chemical Sciences. University Science Books.
Engel, T., & Reid, P. (2018). Physical Chemistry (4th ed.). Pearson.
Levine, I. N. (2015). Physical Chemistry (6th ed.). McGraw-Hill Education.
Smith, J. M., Van Ness, H. C., & Abbott, M. M. (2017). Introduction to Chemical Engineering Thermodynamics (8th ed.). McGraw-Hill Education.
Gibbs, J. W. (1878). On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy of Arts and Sciences, 3, 108-248.
Lewis, G. N., & Randall, M. (1923). Thermodynamics and the Free Energy of Chemical Substances. McGraw-Hill.
IUPAC. (2014). Compendium of Chemical Terminology (Gold Book). Version 2.3.3. Retrieved from http://goldbook.iupac.org/
Sandler, S. I. (2017). Chemical, Biochemical, and Engineering Thermodynamics (5th ed.). Wiley.
Denbigh, K. (1981). The Principles of Chemical Equilibrium (4th ed.). Cambridge University Press.
Ready to calculate Gibbs Free Energy for your chemical reactions and thermodynamic processes? Our free online calculator provides instant, accurate results to help you determine reaction spontaneity and optimize experimental conditions. Whether you're a student learning thermodynamics, a researcher designing new reactions, or an engineer optimizing processes, understanding Gibbs Free Energy is essential for predicting chemical behavior and achieving successful outcomes.
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