Gibbs Free Energy of Reaction (ΔGrxn) Calculator

Determine a reaction’s spontaneity by calculating the change in Gibbs free energy.

Gibbs Free Energy (ΔG_rxn)

Reaction is Spontaneous

Intermediate Values

Temperature in Kelvin: 298.15 K

TΔS Term: 53.67 kJ/mol

Visual representation of Enthalpy (ΔH) and the Temperature-Entropy term (-TΔS) contributing to the final Gibbs Free Energy (ΔG).

Summary of Inputs and Results

Parameter	Value	Unit
ΔH°rxn	-75	kJ/mol
ΔS°rxn	180	J/(mol·K)
Temperature	298.15	K
ΔGrxn	-128.7	kJ/mol

What is Gibbs Free Energy of Reaction (ΔG_rxn)?

The Gibbs Free Energy of a reaction, denoted as ΔG_rxn, is a thermodynamic potential that measures the “usefulness” or process-initiating work obtainable from a chemical reaction at constant temperature and pressure. Its primary value is in predicting the spontaneity of a reaction. If the change in Gibbs Free Energy is negative, the reaction is spontaneous in the forward direction. If it is positive, the reaction is non-spontaneous and requires energy input to proceed. If ΔG is zero, the system is at equilibrium.

This concept is crucial for chemists, engineers, and scientists. For instance, in understanding a reaction like the decomposition of 2HNO₃ (nitric acid), calculating the Gibbs Free Energy helps determine the conditions (like temperature) under which the decomposition will occur naturally. This calculator helps to easily perform that calculation.

The Gibbs Free Energy Formula and Explanation

The spontaneity of a reaction is determined by the interplay between enthalpy (ΔH) and entropy (ΔS). The formula that connects them is the Gibbs Free Energy equation:

ΔG = ΔH – TΔS

This equation is fundamental in chemical thermodynamics. A negative ΔH (exothermic reaction) and a positive ΔS (increased disorder) both favor a spontaneous reaction, making ΔG more likely to be negative. Our Thermodynamics Calculator provides more tools for these concepts.

Variables in the Gibbs Free Energy Equation

Variable	Meaning	Common Unit	Typical Range
ΔG	Change in Gibbs Free Energy	kJ/mol	-1000 to 1000
ΔH	Change in Enthalpy	kJ/mol	-1000 to 1000
T	Absolute Temperature	Kelvin (K)	0 to >1000
ΔS	Change in Entropy	J/(mol·K)	-300 to 300

Practical Examples

Example 1: Spontaneous at All Temperatures

Consider a reaction where the system becomes more disordered and releases heat.

• Inputs: ΔH = -100 kJ/mol, ΔS = 50 J/(mol·K), T = 298 K (25 °C)
• Calculation: ΔG = -100 – (298 * (50 / 1000)) = -100 – 14.9 = -114.9 kJ/mol
• Result: Since ΔG is negative, the reaction is spontaneous. Because both ΔH is negative and ΔS is positive, this reaction is spontaneous at all temperatures.

Example 2: Spontaneity Depends on Temperature

Consider an endothermic reaction that increases in disorder, like melting ice.

• Inputs: ΔH = 6.01 kJ/mol, ΔS = 22.0 J/(mol·K)
• At a low temperature (T = 270 K or -3.15 °C): ΔG = 6.01 – (270 * (22.0 / 1000)) = 6.01 – 5.94 = +0.07 kJ/mol. The reaction is non-spontaneous (ice doesn’t melt).
• At a high temperature (T = 280 K or 6.85 °C): ΔG = 6.01 – (280 * (22.0 / 1000)) = 6.01 – 6.16 = -0.15 kJ/mol. The reaction is spontaneous (ice melts). The Reaction Rate Calculator can help explore temperature effects further.

How to Use This Gibbs Free Energy Calculator

Follow these steps to determine the spontaneity of your reaction:

1. Enter Enthalpy (ΔH): Input the standard enthalpy of reaction in kilojoules per mole (kJ/mol).
2. Enter Entropy (ΔS): Input the standard entropy of reaction in joules per mole-kelvin (J/(mol·K)). The calculator will automatically handle the unit conversion.
3. Enter Temperature (T): Provide the temperature and select whether it is in Celsius or Kelvin. The calculator converts Celsius to Kelvin for the calculation (K = °C + 273.15).
4. Calculate and Interpret: Click the “Calculate” button. The primary result is the ΔG_rxn value. Below it, a clear message will state if the reaction is spontaneous (ΔG < 0), non-spontaneous (ΔG > 0), or at equilibrium (ΔG = 0).

Key Factors That Affect Gibbs Free Energy

• Enthalpy (ΔH): Exothermic reactions (negative ΔH) release heat and are more likely to be spontaneous. Endothermic reactions (positive ΔH) absorb heat and tend to be non-spontaneous.
• Entropy (ΔS): Reactions that increase disorder (positive ΔS), such as a solid turning into a gas, are more likely to be spontaneous. Reactions that decrease disorder (negative ΔS) are less likely.
• Temperature (T): Temperature acts as a weighting factor for the entropy term. At high temperatures, the TΔS term becomes more significant. This means a reaction with a positive ΔS can become spontaneous at high temperatures even if it has a positive ΔH. Exploring the Equilibrium Constant can provide deeper insights here.
• Concentration and Pressure: While this calculator focuses on standard conditions, the concentrations of reactants and products (measured by the reaction quotient Q) affect the non-standard Gibbs Free Energy (ΔG = ΔG° + RTlnQ).
• Physical State: The entropy of a substance is highly dependent on its state (gas > liquid > solid). A reaction that produces gases from solids or liquids will have a large positive ΔS.
• Stoichiometry: A reaction that increases the number of moles of gas will generally have a positive entropy change. For example, 2H₂O(g) → 2H₂(g) + O₂(g) goes from 2 moles of gas to 3 moles of gas.

Frequently Asked Questions (FAQ)

1. What’s the difference between ΔG and ΔG°?

ΔG° refers to the standard Gibbs free energy change, calculated when all reactants and products are in their standard state (1 atm pressure, 1 M concentration). ΔG is the non-standard value under any other conditions and is used to predict spontaneity in real-world scenarios. A Concentration Calculator can help determine these conditions.

2. Why are the units for enthalpy (kJ) and entropy (J) different?

It is a historical convention. Enthalpy changes are typically large and measured in kilojoules (kJ), while entropy changes are smaller and measured in joules (J). It is a CRITICAL step in the calculation to convert one unit to match the other, usually by dividing the entropy value in J by 1000 to get kJ.

3. What does a negative ΔG mean?

A negative ΔG indicates that a reaction is spontaneous in the forward direction. It will proceed without the net input of external energy. This doesn’t, however, say anything about the speed (kinetics) of the reaction.

4. Can a reaction with a positive ΔH (endothermic) be spontaneous?

Yes. If the change in entropy (ΔS) is positive and the temperature (T) is high enough, the TΔS term can be larger than the positive ΔH, resulting in a negative ΔG. The melting of ice above 0°C is a perfect example.

5. What is the “standard state” temperature?

While standard state pressure and concentration are fixed, temperature is not. However, thermodynamic data is most commonly tabulated at 25 °C (298.15 K), so this is often assumed to be the “standard” temperature unless otherwise specified.

6. How are ΔH°_rxn and ΔS°_rxn determined?

They are typically calculated from the standard heats of formation (ΔH°_f) and standard absolute entropies (S°) of the reactants and products, which can be found in thermodynamic data tables. The formula is: ΔValue = Σ(products) – Σ(reactants).

7. What if the reaction involves something complex like 2HNO₃?

The principle remains the same. You would need to find the standard enthalpy and entropy values for the full, balanced chemical reaction involving nitric acid (HNO₃) and all other reactants and products to calculate the overall ΔH°_rxn and ΔS°_rxn.

8. What does it mean if ΔG is zero?

If ΔG = 0, the reaction is at equilibrium. The rate of the forward reaction is equal to the rate of the reverse reaction, and there is no net change in the concentration of reactants and products. This is a key concept covered by our Chemical Equation Balancer.