Spontaneity and Equilibrium: Why "?G < 0 Denotes a Spontaneous Process" and "?G = 0 Means the System Is at Equilibrium" Are Incorrect

The fundamental criteria for chemical reactions to be spontaneous in a given direction are generally incorrectly stated as ?G < 0 or ?A < 0 in most introductory chemistry textbooks and even in some more advanced texts. Similarly, the criteria for equilibrium are also misstated as being ?G = 0 or ?A = 0. Following a brief review of the thermodynamic equations related to reaction spontaneity and equilibrium in systems involving a single reaction, this paper addresses the nature of these errors by first discussing the conceptual problems thereby introduced. This qualitative discussion is followed by a quantitative treatment of the 2NO[subscript 2](g) ? N[subscript 2]O[subscript 4](g) reaction conducted both under constant temperature and volume and under constant temperature and pressure conditions. The results provide clear examples of the conceptual problems introduced by using ?G < 0 or ?A < 0 as criteria for reaction spontaneity and ?G = 0 or ?A = 0 as the corresponding criteria for equilibrium. It is shown that ?G < 0 or ?A < 0 are necessary conditions for a transformation from state A to state B to be spontaneous, but they are not sufficient conditions. If ? denotes the reaction coordinate, the correct criteria for a spontaneous forward reaction are (?G/??)[subscript T,p] < 0 or (?A/??)[subscript T,V] < 0 when the process can be characterized by a single reaction coordinate. The correct criterion for equilibrium is either dG = 0 or dA = 0. The paper concludes with some briefly stated recommendations as to the manner in which textbooks should be altered. The pedagogical problem of presenting the correct criteria for spontaneity and equilibrium to beginning students not versed in calculus and thermodynamics is also addressed, and some recommendations are made.