Calculate Delta G Rxn for The Following Reaction

What is ΔG Rxn?

The Gibbs free energy change (ΔG) for a reaction is a measure of the energy available to do work in a chemical reaction. It is calculated using the standard Gibbs free energy of formation (ΔG°f) for the reactants and products.

ΔG is related to the equilibrium constant (K) of the reaction by the equation:

Where:

• ΔG° is the standard Gibbs free energy change (kJ/mol)
• R is the gas constant (8.314 J/mol·K)
• T is the temperature in Kelvin
• K is the equilibrium constant

For a reaction to be spontaneous (ΔG < 0), the products must have a lower Gibbs free energy than the reactants.

How to Calculate ΔG Rxn

To calculate ΔG for a reaction, you need the standard Gibbs free energy of formation (ΔG°f) for each reactant and product. The formula is:

Where:

• ΔG°rxn is the standard Gibbs free energy change for the reaction (kJ/mol)
• ΔG°f(products) is the sum of the standard Gibbs free energies of formation for the products
• ΔG°f(reactants) is the sum of the standard Gibbs free energies of formation for the reactants

For reactions that occur at non-standard conditions, the actual ΔG can be calculated using:

Where Q is the reaction quotient.

Example Calculation

Let's calculate ΔG for the reaction:

Given the standard Gibbs free energies of formation:

Using the formula:

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

Interpretation of Results

The sign of ΔG provides important information about the reaction:

• ΔG < 0: The reaction is spontaneous and will proceed as written.
• ΔG = 0: The reaction is at equilibrium.
• ΔG > 0: The reaction is non-spontaneous as written and will not occur under standard conditions.

Temperature affects ΔG. For exothermic reactions (ΔH < 0), increasing temperature makes ΔG more negative, favoring the reaction. For endothermic reactions (ΔH > 0), increasing temperature makes ΔG more positive, opposing the reaction.