Gibbs Free Energy Calculator (ΔG)

Determine the spontaneity of a reaction by calculating the change in Gibbs Free Energy (ΔG).

Result

Energetic Contributions to ΔG

Visual comparison of the Enthalpy (ΔH) and Entropy (-TΔS) terms.

What is the Gibbs Free Energy Change (ΔG rxn)?

The Gibbs free energy change (ΔG), often referred to as ‘delta G’ or ‘ΔG rxn’ for reactions, is a thermodynamic potential that measures the maximum “useful” or process-initiating work that can be extracted from a closed system at constant temperature and pressure. In chemistry, its most important function is to predict the spontaneity of a chemical reaction. A spontaneous process is one that occurs naturally without any continuous external energy input.

The sign of ΔG tells us whether a reaction will proceed:

• ΔG < 0 (Negative): The reaction is spontaneous in the forward direction. It is an exergonic process.
• ΔG > 0 (Positive): The reaction is non-spontaneous in the forward direction. Energy must be supplied for it to occur. It is an endergonic process.
• ΔG = 0: The system is at equilibrium, and there is no net change in the forward or reverse direction.

The Formula to Calculate Delta G rxn

The change in Gibbs free energy is calculated using a crucial equation that connects enthalpy (ΔH) and entropy (ΔS) at a given temperature (T). The formula is:

ΔG = ΔH – TΔS

It’s critical to ensure the units are consistent. Since ΔH is typically in kilojoules (kJ) and ΔS is in joules (J), you must convert one to match the other. Our calculator handles this automatically by converting the ΔS term to kJ.

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 2000+
ΔS	Change in Entropy	J/mol·K	-300 to 300

Practical Examples

Example 1: Spontaneous Reaction (Haber-Bosch Process)

Let’s calculate the spontaneity of ammonia synthesis at room temperature (25 °C).

• Inputs:
  • ΔH = -92.2 kJ/mol
  • ΔS = -198.7 J/mol·K
  • T = 25 °C (which is 298.15 K)
• Calculation:
  1. Convert T to Kelvin: 25 + 273.15 = 298.15 K
  2. Convert ΔS to kJ: -198.7 J/mol·K / 1000 = -0.1987 kJ/mol·K
  3. Calculate TΔS: 298.15 K * -0.1987 kJ/mol·K = -59.24 kJ/mol
  4. Calculate ΔG: -92.2 kJ/mol – (-59.24 kJ/mol) = -32.96 kJ/mol
• Result: ΔG is negative, so the reaction is spontaneous at 25°C.

Example 2: Non-Spontaneous Reaction (Decomposition of Water)

Let’s check if water decomposes into hydrogen and oxygen at 25 °C.

• Inputs:
  • ΔH = +286 kJ/mol
  • ΔS = +163 J/mol·K
  • T = 25 °C (298.15 K)
• Calculation:
  1. TΔS term in kJ: 298.15 K * (163 J/mol·K / 1000) = +48.6 kJ/mol
  2. Calculate ΔG: +286 kJ/mol – (48.6 kJ/mol) = +237.4 kJ/mol
• Result: ΔG is positive, so the reaction is non-spontaneous at 25°C.

How to Use This Gibbs Free Energy Calculator

This calculator is designed to be straightforward. Here is a step-by-step guide:

1. Enter Enthalpy Change (ΔH): Input the change in enthalpy. Select the appropriate unit, either kJ/mol or J/mol.
2. Enter Temperature (T): Input the temperature of the reaction. The calculation requires Kelvin (K), but you can conveniently enter the value in Celsius (°C) or Fahrenheit (°F) and the calculator will convert it.
3. Enter Entropy Change (ΔS): Input the change in entropy. This value must be in J/mol·K. The calculator automatically handles the conversion to kJ to match the enthalpy units.
4. Calculate: Click the “Calculate ΔG” button to see the result. The calculator will display the final ΔG, an interpretation of what the result means (spontaneous, non-spontaneous, or at equilibrium), and the intermediate values used in the calculation.

Key Factors That Affect Delta G

The spontaneity of a reaction is a balancing act between enthalpy, entropy, and temperature. Here are the key factors:

• Enthalpy (ΔH): A negative ΔH (exothermic reaction, releases heat) favors spontaneity.
• Entropy (ΔS): A positive ΔS (increased disorder) favors spontaneity.
• Temperature (T): Temperature acts as a weighting factor for the entropy term. At high temperatures, the TΔS term becomes more significant, meaning entropy has a greater influence on ΔG.
• Signs of ΔH and ΔS:
  • ΔH negative, ΔS positive: The reaction is spontaneous at all temperatures (ΔG always negative).
  • ΔH positive, ΔS negative: The reaction is non-spontaneous at all temperatures (ΔG always positive).
  • ΔH negative, ΔS negative: The reaction is spontaneous only at low temperatures (enthalpy-driven).
  • ΔH positive, ΔS positive: The reaction is spontaneous only at high temperatures (entropy-driven).
• Pressure: While this calculator assumes constant pressure, changes in pressure can affect ΔG, especially for reactions involving gases.
• Concentration: The values calculated here are for standard states. The actual free energy change can differ under non-standard concentrations of reactants and products.

Frequently Asked Questions (FAQ)

1. What does ‘spontaneous’ mean in chemistry?

A spontaneous reaction is one that will proceed in the forward direction without a continuous supply of external energy. It does not mean the reaction is fast; the reaction rate is determined by kinetics and activation energy, not thermodynamics.

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

ΔG° (delta G standard) refers to the Gibbs free energy change under standard conditions (1 atm pressure, 298.15 K or 25 °C, and 1 M concentration for solutions). ΔG refers to the free energy change under any non-standard set of conditions.

3. Why must temperature be in Kelvin?

The Kelvin scale is an absolute thermodynamic temperature scale, meaning 0 K is absolute zero. The formula ΔG = ΔH – TΔS is derived based on this absolute scale, and using Celsius or Fahrenheit directly would produce incorrect results.

4. Why do I need to convert the units for ΔS?

Enthalpy (ΔH) is usually reported in kilojoules (kJ), while entropy (ΔS) is in joules (J). To correctly subtract the TΔS term from ΔH, their units must match. You must divide the entropy value in joules by 1000 to convert it to kilojoules.

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

Yes. If a reaction is endothermic (positive ΔH), it can still be spontaneous if the entropy change (ΔS) is positive and the temperature is high enough. The -TΔS term can become more negative than the positive ΔH, resulting in a negative ΔG.

6. What happens if ΔG is zero?

If 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 in the concentrations of reactants and products.

7. What is an exergonic reaction?

An exergonic reaction is a reaction that releases energy and is spontaneous. It corresponds to a negative ΔG value.

8. How does this calculator handle unit conversions?

The calculator automatically converts your temperature input to Kelvin and your enthalpy input to kJ/mol for the final calculation. The entropy (ΔS) term is divided by 1000 internally to convert J/mol·K to kJ/mol·K, ensuring the formula works correctly.