Molecular Equilibrium in Closed Systems

Without entropy considerations, equilibrium along any given coordinate x is found very simply as that location where the body assumes a minimum potential energy P the body will eventually come to rest at that exact point. Thus, mechanical equilibrium is subject to the simple criterion 

Systems out of equilibrium—generally in the process of moving toward equilibrium—are characterized by [d ldx) 0. A rock tumbling down a mountainside and a positive test charge moving toward the region of lowest electrical potential are both manifestations of the tendency toward simple mechanical equilibrium. 

Molecular equilibrium, by contrast, is complicated by entropy. Entropy, being a measure of randomness, reflects the tendency of molecules to scatter, to diffuse, to assume different energy states, to occupy different phases and positions. It becomes impossible to follow individual molecules through all these conditions, so we resort to describing statistical distributions of molecules, which for our purposes simply become concentration profiles. The molecular statistics are described in detail by the science of statistical mechanics. However, if we need only to describe the concentration profiles at equilibrium, we can invoke the science of thermodynamics. 

A closed system is one with boundaries across which no matter may pass, either in or out, but one in which other changes may occur, including 

By definition, the Gibbs free energy relates to enthalpy H and entropy S by 

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