Nonstandard Free Energy

Core Concept

Real reactions rarely run at standard conditions. The nonstandard free-energy change is given by ΔG = ΔG° + RT ln Q, where Q is the reaction quotient (same form as K, but with actual current concentrations/pressures). When Q < K, ln Q is negative enough that ΔG < 0 and the reaction proceeds forward; when Q > K, ΔG > 0 and it proceeds in reverse; when Q = K, ΔG = 0 and the system is at equilibrium. The term RT ln Q is the correction that moves the standard value to actual conditions.

Key Ideas

• Same form as K. Q = [products]^ν / [reactants]^ν using current (not equilibrium) amounts; gases use partial pressures.
• RT ln Q is the concentration correction. It is zero when Q = 1 (standard-ish conditions) and nonzero otherwise.
• Direction from Q vs. K. Q < K ⇒ ΔG < 0 (forward); Q > K ⇒ ΔG > 0 (reverse); Q = K ⇒ ΔG = 0.
• Spontaneity is now "actual." ΔG, not ΔG°, tells you which way a real reaction mixture moves.
• Units. R = 8.314 J/(mol·K); ΔG° must be in J/mol (convert from kJ) so the terms add.

Equations and Variables

ΔG = ΔG° + RT ln Q

How It Works

1. Compute ΔG° from tables.
2. Write Q from the actual concentrations/pressures.
3. Evaluate RT ln Q (convert ΔG° to J/mol so units match).
4. Add. The sign of ΔG tells the actual spontaneous direction.

Worked Example

For N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g) with ΔG° = −33.0 kJ/mol at 25 °C, find ΔG when P(N₂) = 1.0 atm, P(H₂) = 3.0 atm, P(NH₃) = 0.50 atm.

• Q = P(NH₃)² / [P(N₂) · P(H₂)³] = (0.50)² / [1.0 × (3.0)³] = 0.25 / 27 = 9.26 × 10⁻³
• ln Q = ln(9.26 × 10⁻³) = −4.68
• RT ln Q = 8.314 J/(mol·K) × 298 K × (−4.68) = −11,600 J/mol = −11.6 kJ/mol
• ΔG = ΔG° + RT ln Q = −33.0 + (−11.6) = −44.6 kJ/mol

ΔG < 0, so the mixture is still on the product side of equilibrium and will keep forming NH₃. (Q = 9.26 × 10⁻³ is far less than K ≈ 6 × 10⁵.)

How it works

1. Compute ΔG° from tables.
2. Write Q from the actual concentrations/pressures.
3. Evaluate RT ln Q (convert ΔG° to J/mol so units match).
4. Add. The sign of ΔG tells the actual spontaneous direction.

Common confusions

• "ΔG and ΔG° are the same thing." — Wrong. ΔG° is a fixed standard-state constant; ΔG varies with actual conditions via RT ln Q.
• "Use K instead of Q in ΔG = ΔG° + RT ln Q." — Wrong. Use Q (current amounts); K is used only at equilibrium where ΔG = 0.
• "A positive ΔG° means the reaction can never proceed forward." — Wrong. With Q very small, RT ln Q can be negative enough to make ΔG < 0 even when ΔG° > 0.
• "Include solids and liquids in Q." — Wrong. Pure solids and liquids have activity 1 and are omitted.
• "Forgetting the unit conversion." — Wrong. ΔG° (kJ) and RT ln Q (J) must be reconciled before adding.

Quick review

• ΔG = ΔG° + RT ln Q.
• Q is built from current amounts, not equilibrium amounts.
• Compare Q to K to get the sign of ΔG and the reaction direction.
• RT ln Q = 0 when Q = 1 (standard conditions).
• Watch units: convert ΔG° to J/mol before adding.