Inserting the Gibbs free-energy equation and combining like terms produces the following equation: Δ Δ G ‡ ‡ = Δ Δ H 0 ‡ ‡ − − ( T − − β β ) Δ Δ S ‡ ‡ where Δ H 0 is constant regardless of substituents and Δ S is different for each substituent.