Standard Free Energy of Reaction

Core Concept

The standard free energy of reaction (ΔG°rxn) is the free-energy change when reactants in their standard states are converted to products in their standard states (25 °C, 1 atm, 1 M). It is calculated from tabulated standard free energies of formation (ΔG°f) — the ΔG for forming one mole of a compound from its elements in their standard states — using ΔG°rxn = ΣνΔG°f(products) − ΣνΔG°f(reactants). By convention, ΔG°f = 0 for elements in their standard states. A negative ΔG°rxn means the reaction is product-favored under standard conditions.

Key Ideas

• Formation reference. ΔG°f of any element in its standard state is defined as zero — the same convention as ΔH°f.
• Per-mole of compound. ΔG°f is quoted per mole of the compound as written in its formation equation.
• Products minus reactants. Sum the coefficients × ΔG°f for products and subtract the same for reactants.
• Standard ≠ actual. ΔG° applies to standard-state conditions only; real ΔG changes as concentrations/pressures shift (via RT ln Q).
• ΔG° sign = K information. ΔG°rxn < 0 ⇒ K > 1 (product-favored); ΔG°rxn > 0 ⇒ K < 1 (reactant-favored); ΔG°rxn = 0 ⇒ K = 1.

Equations and Variables

ΔG°rxn = ΣνΔG°f(products) − ΣνΔG°f(reactants)

How It Works

1. Write the balanced equation.
2. Look up ΔG°f for every species; use 0 for elements in their standard states.
3. Multiply each ΔG°f by its coefficient and sum over products, then subtract the sum over reactants.
4. Interpret: negative → spontaneous/product-favored under standard conditions; positive → reverse favored.

Worked Example

Calculate ΔG°rxn for the combustion of methane: CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l).

Standard free energies of formation: ΔG°f(CH₄) = −50.8, ΔG°f(CO₂) = −394.4, ΔG°f(H₂O(l)) = −237.1 kJ/mol; ΔG°f(O₂) = 0.

• Products: (−394.4) + 2(−237.1) = −394.4 − 474.2 = −868.6 kJ/mol
• Reactants: (−50.8) + 2(0) = −50.8 kJ/mol
• ΔG°rxn = −868.6 − (−50.8) = −817.8 kJ/mol

Large and negative, so combustion of methane is strongly product-favored — consistent with methane burning readily in air.

How it works

1. Write the balanced equation.
2. Look up ΔG°f for every species; use 0 for elements in their standard states.
3. Multiply each ΔG°f by its coefficient and sum over products, then subtract the sum over reactants.
4. Interpret: negative → spontaneous/product-favored under standard conditions; positive → reverse favored.

Common confusions

• "ΔG°f of O₂(g) is some positive number." — Wrong. Elements in their standard states have ΔG°f = 0 by definition.
• "ΔG°rxn = Σ(reactants) − Σ(products)." — Wrong sign. It is products minus reactants.
• "ΔG° equals ΔG in any real reaction." — Wrong. ΔG° is only the standard-state value; real ΔG = ΔG° + RT ln Q.
• "A negative ΔG°rxn means the reaction happens quickly." — Wrong. It says the reaction is thermodynamically favored, not kinetically fast.
• "Forgetting coefficients." — Wrong. Multiply each ΔG°f by its stoichiometric coefficient before summing.

Quick review

• ΔG°f = 0 for elements in standard states.
• ΔG°rxn = ΣνΔG°f(products) − ΣνΔG°f(reactants).
• Negative ΔG°rxn ⇒ product-favored (K > 1).
• ΔG° is the standard-state value; ΔG depends on actual conditions.
• Units: kJ/mol.