Calculate The Standard Free-Energy Change of The Following Reaction

The standard free-energy change (ΔG°) of a reaction is a fundamental thermodynamic property that measures the energy available to do work under standard conditions. This calculator helps you determine ΔG° using either the Gibbs free energy of formation or the equilibrium constant of the reaction.

What is standard free-energy change?

The standard free-energy change (ΔG°) represents the maximum amount of useful work that can be obtained from a chemical reaction under standard conditions (25°C and 1 atm pressure). It's a key concept in thermodynamics that helps predict whether a reaction will occur spontaneously.

When ΔG° is negative, the reaction is spontaneous and will proceed in the forward direction. When ΔG° is positive, the reaction is non-spontaneous under standard conditions, though it may occur under non-standard conditions.

How to calculate the standard free-energy change

You can calculate ΔG° using two main approaches:

Using the standard Gibbs free energies of formation (ΔG°f) of the reactants and products
Using the equilibrium constant (K) of the reaction

This calculator provides both methods for your convenience.

The formula

Using Gibbs free energies of formation:

ΔG° = Σ(ΔG°f of products) - Σ(ΔG°f of reactants)

Using equilibrium constant:

ΔG° = -RT ln(K)

Where:

R = 8.314 J/(mol·K)
T = temperature in Kelvin (298.15 K at 25°C)
K = equilibrium constant

Example calculation

Let's calculate ΔG° for the reaction:

2H₂(g) + O₂(g) → 2H₂O(g)

Using the Gibbs free energies of formation:

ΔG°f for H₂(g) = 0 kJ/mol
ΔG°f for O₂(g) = 0 kJ/mol
ΔG°f for H₂O(g) = -237.1 kJ/mol

The calculation would be:

ΔG° = [2 × (-237.1 kJ/mol)] - [2 × 0 + 1 × 0] = -474.2 kJ

This negative value indicates the reaction is spontaneous under standard conditions.

Interpreting the result

The sign of ΔG° tells you about the spontaneity of the reaction:

ΔG° < 0: Reaction is spontaneous and will proceed in the forward direction
ΔG° = 0: Reaction is at equilibrium
ΔG° > 0: Reaction is non-spontaneous under standard conditions

The magnitude of ΔG° indicates the driving force of the reaction. Larger absolute values mean stronger driving forces.

FAQ

What are standard conditions for ΔG°?: Standard conditions are typically 25°C (298.15 K) and 1 atm pressure, with all reactants and products in their standard states (usually 1 M concentration for solutions).
Can ΔG° be negative for a non-spontaneous reaction?: No, a negative ΔG° always indicates a spontaneous reaction under standard conditions. If you're getting a negative value for a reaction you think shouldn't occur, check your inputs or the reaction's feasibility.
How does temperature affect ΔG°?: The formula ΔG° = -RT ln(K) shows that ΔG° depends on temperature. As temperature increases, the value of ΔG° becomes less negative (or more positive), making reactions less spontaneous.
What if I don't know the Gibbs free energies of formation?: You can use the equilibrium constant method if you know K. The calculator will convert between the two approaches for you.