In a system at equilibrium, the Gibbs free energy change (ΔG) is indeed zero. When ΔG = 0, it means that the system has reached a state where the forward and reverse reactions are balanced, and there is no net change in the concentrations of reactants and products over time.
At equilibrium, the individual Gibbs energies of the reactants and products do not necessarily become equal to each other. The Gibbs energy (G) is an extensive property, meaning it depends on the amount of substance present. The values of G for reactants and products can differ, but their respective contributions to the overall ΔG cancel each other out, resulting in a net ΔG of zero at equilibrium.
The relationship between the Gibbs energies of reactants and products at equilibrium is given by the following equation:
ΔG = ΣνG(products) - ΣνG(reactants)
Where: ΔG is the Gibbs free energy change ν is the stoichiometric coefficient of each species in the balanced chemical equation G(products) is the Gibbs energy of the products G(reactants) is the Gibbs energy of the reactants
For ΔG to be zero at equilibrium, it is not necessary for the Gibbs energies of individual reactants and products to be equal. The magnitudes and differences in their Gibbs energies determine the direction and extent of the reaction, while the net ΔG being zero indicates equilibrium has been achieved.