ΔrG=(∂G/∂ξ ) at constant p and constant T, where ξ is the extent of reaction.
By Second Law implication, ΔrG= 0= (∂G/∂ξ ) at equilibrium. If we consider a graph of G against ξ, this would mean we have a turning point (where first derivative=0) when ξ is that extent of reaction when equilibrium attained:
So, ΔrG=0 when equilibrium attained.
However, first derivative=0 does not mean minimum point only, it can mean maximum point too! Let's say you do work until you reach Gibbs energy maxima. My question: Does a Gibbs energy maxima correspond to equilibrium state or not?
(a) If yes, doesn't this violate the Second Law which implies that Gibbs energy should be minimized whenever possible? No matter which direction you move, your Gibbs energy will always decrease. Just simply move from the maximum point and you will at least be better than your current state:
(b) If no, then it will mean that we have to move from the maximum point, but in which direction? In case the graph is a symmetrical parabola, where same dξ results in same dG, what will you observe in real life? Shift to reactants or products?