Gibbs Free Energy (ΔG) Calculator

Determine reaction spontaneity by calculating the change in Gibbs free energy (ΔG rxn).

What is Gibbs Free Energy (ΔG)?

Gibbs free energy, denoted as ‘G’, is a thermodynamic potential that measures the maximum amount of reversible work that can be extracted from a system at a constant temperature and pressure. The change in Gibbs free energy (ΔG) during a reaction is the ultimate indicator of whether that reaction will proceed spontaneously. You might find information in a video or textbook that gives you the values needed to calculate the ΔG of a reaction (often abbreviated as δg rxn).

In simple terms, ΔG tells us if a reaction wants to happen on its own.

• If ΔG is negative, the reaction is spontaneous in the forward direction. It will proceed without external energy input.
• If ΔG is positive, the reaction is non-spontaneous. It requires energy to be added for it to occur. The reverse reaction, however, will be spontaneous.
• If ΔG is zero, the system is at equilibrium, and there is no net change in the amounts of reactants and products.

This calculator is designed to help you quickly calculate the δg rxn using the fundamental relationship between enthalpy, entropy, and temperature.

The Gibbs Free Energy Formula and Explanation

The core of this calculator is the Gibbs-Helmholtz equation, a cornerstone of chemical thermodynamics. The formula is:

ΔG = ΔH – TΔS

This equation beautifully combines the two driving forces of a chemical reaction: the tendency to reach a lower energy state (enthalpy) and the tendency to increase disorder (entropy). Even if you have to find your initial values from a source like an informational video, this formula allows you to calculate the final δg rxn.

Formula Variables

Variables in the Gibbs Free Energy Equation

Variable	Meaning	Unit	Typical Range
ΔG	Change in Gibbs Free Energy	kJ/mol	Negative for spontaneous, Positive for non-spontaneous
ΔH	Change in Enthalpy	kJ/mol	-5000 to +5000 (highly variable)
T	Absolute Temperature	Kelvin (K)	0 to thousands
ΔS	Change in Entropy	J/mol·K	-500 to +500 (highly variable)

One common pitfall is the unit mismatch between enthalpy (usually in kJ/mol) and entropy (usually in J/mol·K). Our calculator automatically handles this conversion to ensure an accurate result.

Practical Examples

Example 1: Melting Ice (Spontaneous at High Temperatures)

Consider the process of ice melting: H₂O(s) → H₂O(l)

• Inputs:
  • ΔH (Enthalpy): +6.01 kJ/mol (endothermic, requires heat)
  • ΔS (Entropy): +22.0 J/mol·K (more disorder as a liquid)
  • Temperature: 25 °C (298.15 K)
• Calculation:
  • TΔS = 298.15 K * 22.0 J/mol·K = 6559.3 J/mol = 6.56 kJ/mol
  • ΔG = 6.01 kJ/mol – 6.56 kJ/mol = -0.55 kJ/mol
• Result: ΔG is negative. At 25°C, ice melting is a spontaneous process. For more on thermodynamics basics, see our guide.

Example 2: Combustion of Methane (Always Spontaneous)

Consider the burning of natural gas: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)

• Inputs:
  • ΔH (Enthalpy): -802 kJ/mol (highly exothermic, releases heat)
  • ΔS (Entropy): -5.1 J/mol·K (slight decrease in disorder)
  • Temperature: 25 °C (298.15 K)
• Calculation:
  • TΔS = 298.15 K * -5.1 J/mol·K = -1520.6 J/mol = -1.52 kJ/mol
  • ΔG = -802 kJ/mol – (-1.52 kJ/mol) = -800.48 kJ/mol
• Result: ΔG is highly negative. The reaction is very spontaneous at room temperature, which is why understanding enthalpy vs entropy is key.

How to Use This Gibbs Free Energy Calculator

1. Enter Enthalpy Change (ΔH): Input the change in enthalpy for your reaction. Use a negative value for exothermic (heat-releasing) reactions and a positive value for endothermic (heat-absorbing) reactions. Select the correct unit (kJ/mol or J/mol).
2. Enter Entropy Change (ΔS): Input the change in entropy. A positive value means the system is becoming more disordered (e.g., solid to liquid), and a negative value means it’s becoming more ordered. The unit is typically J/mol·K.
3. Enter Temperature (T): Provide the temperature at which the reaction occurs. You can use Celsius, Kelvin, or Fahrenheit; the calculator will convert it to Kelvin for the calculation.
4. Interpret the Results: The calculator instantly provides the ΔG value. A negative result indicates a spontaneous reaction, while a positive result indicates a non-spontaneous one. The chart also visualizes how temperature affects spontaneity.

Key Factors That Affect Gibbs Free Energy (ΔG)

• Enthalpy (ΔH): A negative ΔH (exothermic) strongly favors spontaneity, as systems tend to move to a lower energy state.
• Entropy (ΔS): A positive ΔS (increased disorder) favors spontaneity, as systems tend towards randomness.
• Temperature (T): Temperature acts as a weighting factor for the entropy term. At high temperatures, the TΔS term becomes more significant and can overcome an unfavorable enthalpy change (or vice versa).
• Exothermic with Increasing Disorder (Neg ΔH, Pos ΔS): Always spontaneous. ΔG will always be negative.
• Endothermic with Decreasing Disorder (Pos ΔH, Neg ΔS): Never spontaneous. ΔG will always be positive.
• Exothermic with Decreasing Disorder (Neg ΔH, Neg ΔS): Spontaneous only at low temperatures.
• Endothermic with Increasing Disorder (Pos ΔH, Pos ΔS): Spontaneous only at high temperatures. Explore the concept in our article on reaction favorability.

Frequently Asked Questions (FAQ)

What does it mean for a reaction to be spontaneous?

A spontaneous reaction is one that can proceed in the forward direction without a continuous input of external energy. It doesn’t mean the reaction is fast, only that it is thermodynamically favorable. For example, the conversion of diamond to graphite is spontaneous, but it takes millions of years.

Why are the units for enthalpy and entropy different in the calculator?

By convention, standard enthalpy changes (ΔH) are reported in kilojoules per mole (kJ/mol), while standard entropy changes (ΔS) are in joules per mole-kelvin (J/mol·K). This is a crucial detail, and our calculator handles the conversion automatically by converting the TΔS term to kJ/mol.

Can ΔG be zero?

Yes. When ΔG = 0, the reaction is at equilibrium. This means the rate of the forward reaction equals the rate of the reverse reaction, and there is no net change. The temperature at which this occurs is the tipping point between spontaneous and non-spontaneous behavior.

How does pressure affect Gibbs free energy?

This calculator assumes standard and constant pressure. Changes in pressure can affect ΔG, especially for reactions involving gases. The relationship is described by the equation ΔG = ΔG° + RTln(Q), where Q is the reaction quotient, which depends on partial pressures or concentrations.

What is the difference between ΔG and ΔG°?

ΔG° is the standard Gibbs free energy change, calculated when all reactants and products are in their standard state (1 atm for gases, 1 M for solutions). ΔG is the non-standard free energy change, which applies to any set of conditions.

What’s a simple way to remember the enthalpy and entropy relationship?

Think of a messy room. The room “wants” to be messy (high entropy). It takes energy to clean it (enthalpy input). Nature favors low energy and high messiness. Gibbs free energy balances these two tendencies.

Does a catalyst change ΔG?

No. A catalyst speeds up a reaction by lowering the activation energy, but it does not change the initial (reactant) or final (product) energy states. Therefore, a catalyst does not affect ΔH, ΔS, or ΔG. It only helps the system reach equilibrium faster.

Where would I find the data to use in this calculator from a video?

An educational video on thermodynamics might provide a table of standard enthalpy (ΔH°f) and entropy (S°) values for various compounds. You would use these to first calculate the total ΔH and ΔS for the reaction before using our calculator. For a reaction aA + bB → cC + dD, ΔH°rxn = [cΔH°f(C) + dΔH°f(D)] – [aΔH°f(A) + bΔH°f(B)]. You’d do a similar calculation for ΔS°rxn.