Part I : Preliminaries (Thermodynamics and Kinetics)
Module 1: Gibbs free energy and equilibria
 
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The stable, metastable and unstable equlibria are called equilibria because, as is clear from the gures, these points correspond to the extrema (minima in the case of stable and metastable equilibria and maxima in the case of unstable equilibria), and hence the first derivatives are zero at these extreme points.