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Calculate Standard Free Energy Change for The Following Chemical Reaction

Reviewed by Calculator Editorial Team

The standard free energy change (ΔG°) is a fundamental concept in thermodynamics that describes the energy available to do work in a chemical reaction under standard conditions. This calculator helps you determine ΔG° for any given chemical reaction by inputting the standard Gibbs free energies of formation for the reactants and products.

Introduction

The Gibbs free energy (G) is a thermodynamic potential that measures the useful work obtainable from a system at constant temperature and pressure. The standard free energy change (ΔG°) is calculated under standard conditions (25°C and 1 atm pressure) and is used to predict the spontaneity of a chemical reaction.

For a reaction to be spontaneous under standard conditions, ΔG° must be negative. If ΔG° is positive, the reaction is non-spontaneous as written. If ΔG° is zero, the reaction is at equilibrium.

Gibbs Free Energy Formula

The standard free energy change for a chemical reaction is calculated using the following formula:

ΔG° = ΣΔG°products - ΣΔG°reactants

Where:

  • ΔG° is the standard free energy change for the reaction
  • ΔG°products is the sum of the standard Gibbs free energies of formation for all products
  • ΔG°reactants is the sum of the standard Gibbs free energies of formation for all reactants

All values should be in kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).

How to Calculate ΔG°

To calculate the standard free energy change for a chemical reaction:

  1. Identify all reactants and products in the balanced chemical equation
  2. Find the standard Gibbs free energies of formation (ΔG°f) for each compound from a reliable source
  3. Multiply each ΔG°f by the stoichiometric coefficient for that compound in the balanced equation
  4. Sum the ΔG°f values for all products and all reactants separately
  5. Subtract the sum of the reactants' ΔG°f from the sum of the products' ΔG°f to get ΔG°

Note: The standard Gibbs free energies of formation are typically found in thermodynamic tables or databases. Always ensure you're using values at the same temperature and pressure (standard conditions).

Worked Examples

Example 1: Combustion of Methane

Consider the combustion of methane:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

Standard Gibbs free energies of formation:

  • CH4(g): -74.81 kJ/mol
  • O2(g): 0 kJ/mol (element in standard state)
  • CO2(g): -394.39 kJ/mol
  • H2O(l): -285.83 kJ/mol

Calculation:

ΔG° = [1 × (-394.39) + 2 × (-285.83)] - [1 × (-74.81) + 2 × 0] = -856.05 kJ/mol

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

Example 2: Decomposition of Water

Consider the decomposition of water:

2H2O(l) → 2H2(g) + O2(g)

Standard Gibbs free energies of formation:

  • H2O(l): -285.83 kJ/mol
  • H2(g): 0 kJ/mol
  • O2(g): 0 kJ/mol

Calculation:

ΔG° = [2 × 0 + 1 × 0] - [2 × (-285.83)] = +571.66 kJ/mol

The positive value indicates the reaction is non-spontaneous as written.

Interpreting Results

The standard free energy change provides valuable information about a chemical reaction:

  • If ΔG° is negative, the reaction is spontaneous under standard conditions
  • If ΔG° is positive, the reaction is non-spontaneous as written
  • If ΔG° is zero, the reaction is at equilibrium
  • The magnitude of ΔG° indicates the driving force of the reaction

Keep in mind that standard free energy changes are calculated under ideal conditions. In real-world scenarios, factors like temperature, pressure, and concentration can affect the actual free energy change.

FAQ

What is the difference between ΔG and ΔG°?
ΔG is the free energy change for a reaction under specific conditions, while ΔG° is the free energy change under standard conditions (25°C and 1 atm pressure).
How do I find standard Gibbs free energies of formation?
Standard Gibbs free energies of formation can be found in thermodynamic tables, chemistry handbooks, or online databases like the NIST Chemistry WebBook.
What units should I use for ΔG°?
The standard units for ΔG° are kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).
Can ΔG° be negative for an endothermic reaction?
Yes, ΔG° can be negative for an endothermic reaction if the entropy change (ΔS) is sufficiently positive to overcome the positive enthalpy change (ΔH).
How does temperature affect ΔG°?
ΔG° is calculated at 25°C. For other temperatures, you would need to use the temperature-dependent form of the Gibbs free energy equation: ΔG = ΔH - TΔS.