Calculate The δg Rxn Using The Following Information

Easily calculate the Gibbs free energy change (ΔG rxn) for a chemical reaction using our ΔG rxn calculator. Input enthalpy change (ΔH), entropy change (ΔS), and temperature (T) to determine reaction spontaneity.

Calculate ΔG rxn

What is ΔG rxn?

The Gibbs free energy change of a reaction, denoted as ΔG rxn (or simply ΔG), is a thermodynamic quantity that represents the maximum amount of non-expansion work that can be extracted from a closed system at constant temperature and pressure. It is a crucial indicator of the spontaneity of a chemical reaction or other process under these conditions. Our ΔG rxn calculator helps you determine this value quickly.

If ΔG is negative, the reaction is spontaneous (exergonic) in the forward direction as written. If ΔG is positive, the reaction is non-spontaneous (endergonic) in the forward direction but spontaneous in the reverse. If ΔG is zero, the system is at equilibrium.

Chemists, biochemists, materials scientists, and engineers frequently use the concept of ΔG to predict the feasibility of reactions, design processes, and understand biological systems. For example, understanding the Gibbs free energy changes is vital in drug design, materials synthesis, and metabolic pathway analysis.

A common misconception is that a spontaneous reaction (negative ΔG) is always fast. Spontaneity only tells us if a reaction *can* occur without external energy input, not how *fast* it occurs. Reaction rate is governed by kinetics, not just thermodynamics (ΔG).

ΔG rxn Formula and Mathematical Explanation

The Gibbs free energy change (ΔG) is related to the enthalpy change (ΔH), entropy change (ΔS), and the absolute temperature (T) by the following fundamental equation:

ΔG = ΔH – TΔS

Where:

• ΔG is the Gibbs free energy change of the reaction.
• ΔH is the enthalpy change of the reaction (heat absorbed or released at constant pressure).
• T is the absolute temperature in Kelvin (K).
• ΔS is the entropy change of the reaction (change in disorder or randomness).

To use this formula with our ΔG rxn calculator and in general:

1. Ensure ΔH and TΔS have the same energy units (e.g., both in kJ/mol or both in J/mol). Typically, ΔH is given in kJ/mol and ΔS in J/(mol·K). So, ΔS is often divided by 1000 to convert TΔS to kJ/mol.
2. Temperature (T) must be in Kelvin (K = °C + 273.15).

The term TΔS represents the energy associated with the change in disorder at a given temperature. Subtracting this from the enthalpy change gives the free energy change available to do work or drive the reaction forward.

Practical Examples (Real-World Use Cases)

Let’s look at how the ΔG rxn calculator can be applied.

Example 1: Synthesis of Ammonia (Haber Process)

N₂(g) + 3H₂(g) → 2NH₃(g)

• ΔH rxn ≈ -92 kJ/mol (exothermic)
• ΔS rxn ≈ -198 J/(mol·K) (decrease in moles of gas, so decrease in entropy)
• Temperature = 25 °C = 298.15 K

Using the formula: ΔG = -92 kJ/mol – (298.15 K * (-198 J/(mol·K)) / 1000) = -92 kJ/mol + 59.03 kJ/mol = -32.97 kJ/mol. At 25°C, the reaction is spontaneous.

Example 2: Melting of Ice

H₂O(s) → H₂O(l)

• ΔH fusion ≈ +6.01 kJ/mol (endothermic)
• ΔS fusion ≈ +22 J/(mol·K) (increase in disorder)
• Temperature = 0 °C = 273.15 K

ΔG = +6.01 kJ/mol – (273.15 K * (22 J/(mol·K)) / 1000) = +6.01 kJ/mol – 6.009 kJ/mol ≈ 0 kJ/mol. At 0°C, ice and water are at equilibrium.

At 10°C (283.15 K): ΔG = +6.01 – (283.15 * 22 / 1000) = +6.01 – 6.229 = -0.219 kJ/mol (spontaneous melting).

How to Use This ΔG rxn Calculator

1. Enter Enthalpy Change (ΔH rxn): Input the standard enthalpy change for your reaction in kilojoules per mole (kJ/mol).
2. Enter Entropy Change (ΔS rxn): Input the standard entropy change in joules per mole Kelvin (J/(mol·K)).
3. Enter Temperature (T): Input the temperature at which the reaction occurs in degrees Celsius (°C). The calculator will convert it to Kelvin.
4. View Results: The calculator automatically updates the ΔG rxn value in kJ/mol, along with intermediate values like temperature in Kelvin and the TΔS term.
5. Interpret ΔG rxn:
   • Negative ΔG: The reaction is spontaneous under the given conditions.
   • Positive ΔG: The reaction is non-spontaneous under the given conditions.
   • ΔG near zero: The reaction is close to equilibrium.

Use the “Reset” button to go back to default values and “Copy Results” to copy the main result and inputs.

Key Factors That Affect ΔG rxn Results

Several factors influence the Gibbs free energy change (ΔG rxn) and thus the spontaneity of a reaction:

• Enthalpy Change (ΔH): A large negative ΔH (exothermic reaction) contributes to a more negative ΔG, favoring spontaneity. Conversely, a positive ΔH (endothermic) makes ΔG more positive. You might find our enthalpy change tool useful.
• Entropy Change (ΔS): A large positive ΔS (increase in disorder) contributes to a more negative TΔS term, thus making ΔG more negative, especially at higher temperatures. A negative ΔS decreases spontaneity. Our entropy change page explains more.
• Temperature (T): Temperature directly scales the TΔS term. For reactions with positive ΔS, increasing temperature makes ΔG more negative (more spontaneous). For reactions with negative ΔS, increasing temperature makes ΔG more positive (less spontaneous).
• Pressure (for gases): While our basic calculator assumes standard or constant pressure, changes in partial pressures of gaseous reactants and products can shift the equilibrium and thus affect ΔG under non-standard conditions (ΔG = ΔG° + RTlnQ).
• Concentration (for solutions): Similar to pressure for gases, changes in concentrations of reactants and products in solution affect ΔG under non-standard conditions.
• Phase of Reactants and Products: The physical state (solid, liquid, gas) of reactants and products significantly impacts their standard enthalpy and entropy values, thereby affecting ΔH and ΔS of the reaction.

Frequently Asked Questions (FAQ)

What does a negative ΔG mean?

A negative ΔG indicates that the reaction is exergonic and spontaneous in the forward direction under the specified conditions (constant temperature and pressure). It can proceed without continuous external energy input.

What does a positive ΔG mean?

A positive ΔG indicates that the reaction is endergonic and non-spontaneous in the forward direction. It requires an input of energy to proceed, or the reverse reaction is spontaneous.

What if ΔG is zero?

If ΔG = 0, the reaction is at equilibrium. The rates of the forward and reverse reactions are equal, and there is no net change in the concentrations of reactants and products.

Can a reaction with a positive ΔH be spontaneous?

Yes, if the TΔS term is positive and large enough to overcome the positive ΔH (i.e., ΔS is positive and T is high enough), making ΔG negative.

Does the ΔG rxn calculator account for non-standard conditions?

This basic ΔG rxn calculator uses the standard ΔH° and ΔS° values to calculate ΔG at a given temperature, assuming pressure and concentrations are standard (or their effect is incorporated in the input ΔH and ΔS). For non-standard conditions, you’d use ΔG = ΔG° + RTlnQ, where Q is the reaction quotient.

How do I find ΔH and ΔS values for my reaction?

Standard enthalpy (ΔH°) and entropy (ΔS°) values for many substances can be found in thermodynamic tables in chemistry textbooks or online databases. For a reaction, ΔH°rxn = ΣΔH°f(products) – ΣΔH°f(reactants) and ΔS°rxn = ΣS°(products) – ΣS°(reactants).

Is ΔG temperature-dependent?

Yes, ΔG is temperature-dependent because of the TΔS term in the equation ΔG = ΔH – TΔS. The chart generated by our ΔG rxn calculator illustrates this dependence.

What is 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 states (1 bar pressure for gases, 1 M concentration for solutions, pure liquids/solids, usually at 298.15 K). ΔG is the Gibbs free energy change under any non-standard conditions.