Gibbs Free Energy Change (ΔG) Calculator

Determine the spontaneity of a chemical reaction by calculating the change in Gibbs Free Energy (often abbreviated as δgrxn or ΔG).

What is Gibbs Free Energy (δgrxn)?

Gibbs Free Energy, denoted as G, is a thermodynamic potential that measures the maximum amount of reversible work that may be performed by a system at a constant temperature and pressure. The change in Gibbs Free Energy (ΔG, often written as δgrxn) for a reaction is the ultimate arbiter of whether that reaction will proceed on its own. Such a reaction is called a spontaneous reaction.

In simple terms, ΔG tells us if a chemical reaction wants to happen.

• If ΔG is negative, the reaction is spontaneous (exergonic) and will proceed in the forward direction to form products.
• If ΔG is positive, the reaction is non-spontaneous (endergonic) and requires an input of energy to occur. The reverse reaction will be spontaneous.
• If ΔG is zero, the system is at equilibrium, and the rates of the forward and reverse reactions are equal.

The Gibbs Free Energy Formula

The change in Gibbs Free Energy for a reaction (δgrxn) is calculated using a fundamental equation that links enthalpy, entropy, and temperature. The primary formula used by this calculator is:

ΔG = ΔH – TΔS

This equation is a cornerstone of chemical thermodynamics. Let’s break down its components:

Variable	Meaning	Unit (Typical)	Typical Range
ΔG	Change in Gibbs Free Energy	kJ/mol	-3000 to +1000
ΔH	Change in Enthalpy	kJ/mol	-3000 to +1000
T	Absolute Temperature	Kelvin (K)	> 0 K
ΔS	Change in Entropy	J/(mol·K)	-400 to +400

It’s crucial that the units for ΔH and ΔS are compatible. Since ΔS is usually given in Joules and ΔH in kilojoules, a conversion is necessary, which this calculator handles automatically. You may want to check out our Enthalpy vs Entropy article for more details.

Practical Examples

Example 1: The Haber Process

The synthesis of ammonia (NH₃) from nitrogen and hydrogen is a classic industrial reaction. Let’s calculate its δgrxn at 25 °C (298.15 K).

• Inputs:
  • ΔH = -93 kJ/mol
  • ΔS = -198 J/(mol·K)
  • T = 25 °C
• Calculation:
  1. Convert ΔS: -198 J/(mol·K) / 1000 = -0.198 kJ/(mol·K)
  2. Calculate TΔS: 298.15 K * -0.198 kJ/(mol·K) = -59.03 kJ/mol
  3. Calculate ΔG: -93 kJ/mol – (-59.03 kJ/mol) = -33.97 kJ/mol
• Result: ΔG is negative, so the reaction is spontaneous at 25 °C.

Example 2: Decomposition of Calcium Carbonate

When you heat limestone (CaCO₃), it decomposes. Is this spontaneous at 800 °C (1073.15 K)?

• Inputs:
  • ΔH = +178 kJ/mol
  • ΔS = +161 J/(mol·K)
  • T = 800 °C
• Calculation:
  1. Convert T: 800 °C = 1073.15 K
  2. Convert ΔS: +161 J/(mol·K) / 1000 = +0.161 kJ/(mol·K)
  3. Calculate TΔS: 1073.15 K * +0.161 kJ/(mol·K) = +172.78 kJ/mol
  4. Calculate ΔG: +178 kJ/mol – (+172.78 kJ/mol) = +5.22 kJ/mol
• Result: ΔG is slightly positive, suggesting the reaction is close to equilibrium but not quite spontaneous at 800°C. A slightly higher temperature would be needed. This is a great example for a Spontaneous Reaction Calculator.

How to Use This Gibbs Free Energy Calculator

1. Enter Enthalpy Change (ΔH): Input the value for the reaction’s change in enthalpy. Be sure to select the correct units, either kilojoules per mole (kJ/mol) or joules per mole (J/mol).
2. Enter Entropy Change (ΔS): Input the value for the reaction’s change in entropy. The unit is fixed to Joules per mole-Kelvin (J/mol·K) as this is the standard convention.
3. Enter Temperature (T): Input the temperature and select the units (Celsius, Fahrenheit, or Kelvin). The calculator will automatically convert it to Kelvin for the calculation.
4. Interpret the Results: The calculator instantly provides the final Gibbs Free Energy Change (ΔG), along with a clear statement on whether the reaction is spontaneous, non-spontaneous, or at equilibrium. The intermediate values and chart help you understand how the result was derived.

Key Factors That Affect δgrxn

• Enthalpy Change (ΔH): Exothermic reactions (negative ΔH) release heat and tend to be more spontaneous, as this term directly contributes to a more negative ΔG.
• Entropy Change (ΔS): Reactions that increase disorder (positive ΔS) are more likely to be spontaneous. This effect is magnified by temperature.
• Temperature (T): Temperature is a critical factor that moderates the entropy contribution. For reactions with a positive ΔS, increasing the temperature makes the TΔS term larger and more negative, promoting spontaneity. Conversely, for reactions with a negative ΔS, increasing the temperature works against spontaneity.
• Pressure and Concentration: While this calculator uses standard conditions (ΔG°), it’s important to remember that the actual free energy change (ΔG) can be affected by the partial pressures of gases and concentrations of solutions. This is described by the relation to the reaction quotient Q.
• State of Matter: The physical states (solid, liquid, gas) of reactants and products significantly impact entropy and enthalpy, thereby affecting ΔG.
• Stoichiometry: The coefficients in the balanced chemical equation are used when calculating ΔH and ΔS from standard formation values, which in turn are used to calculate the δgrxn using the following information.

Frequently Asked Questions (FAQ)

1. What is the difference between ΔG and ΔG°?

ΔG° (standard Gibbs free energy change) refers to the change under standard conditions (1 atm pressure, 1 M concentration, 298.15 K). ΔG (what this calculator computes for variable temperatures) is the free energy change under any non-standard set of conditions.

2. Can a reaction with a positive ΔH be spontaneous?

Yes. An endothermic reaction (positive ΔH) can be spontaneous if the entropy change (ΔS) is large and positive, and the temperature is high enough. The melting of ice above 0°C is a common example.

3. What does it mean if a reaction is spontaneous?

A spontaneous reaction is one that can proceed without a continuous input of external energy. It doesn’t mean the reaction is fast; the speed of a reaction is governed by chemical kinetics and activation energy, not thermodynamics.

4. Why must I use Kelvin for temperature?

The Kelvin scale is an absolute temperature scale, where 0 K represents absolute zero. The Gibbs free energy equation is derived based on this absolute scale, and using Celsius or Fahrenheit directly will produce an incorrect result.

5. How are the units for enthalpy and entropy handled?

The calculator ensures consistency. Since enthalpy (ΔH) is often in kJ/mol and entropy (ΔS) in J/(mol·K), the entropy value is divided by 1000 to convert it to kJ/(mol·K) before being used in the main formula.

6. What is the relationship between ΔG and the equilibrium constant (K)?

They are related by the equation ΔG° = -RT ln(K), where R is the gas constant. A large negative ΔG° corresponds to a large equilibrium constant K, meaning the reaction strongly favors the products at equilibrium.

7. What is an “entropy-driven” reaction?

This is a term for a reaction that becomes spontaneous primarily because of a large positive change in entropy (ΔS), which makes the `-TΔS` term highly negative, overcoming even a positive (unfavorable) enthalpy change (ΔH).

8. Can I use this calculator for phase changes?

Yes. Phase changes (like melting or boiling) have associated ΔH and ΔS values, and you can use this calculator to find the temperature at which the phase change becomes spontaneous (i.e., where ΔG becomes negative).