Equilibrium and the Second Law of Thermodynamics

Author: John Hutchinson

We have developed an understanding of the concept of equilibrium, both for phase equilibrium and reaction equilibrium. As an illustration, at normal atmospheric pressure, we expect to find H₂O in solid form below 0°C, in liquid form below 100°C, and in gaseous form above 100°C. What changes as we move from low temperature to high temperature cause these transitions in which phase is observed? Viewed differently, if a sample of gaseous water at 120°C is cooled to below 100°C, virtually all of the water vapor spontaneously condenses to form the liquid:

H₂O(g) H₂O(l)    ....spontaneous below 100°C

By contrast, very little of liquid water at 80°C spontaneously converts to gaseous water:

H₂O(l) H₂O(g)    ....not spontaneous below 100°C

As we know, at certain temperatures and pressures, more than one phase can be stable. For example, at 1 atm pressure and 0°C,

H₂O(s) H₂O(l)    ....equilibrium at 0°C.

This analysis leaves unanswered a series of questions regarding the differences between liquids and gases. The concept of a gas phase or a liquid phase is not a characteristic of an individual molecule. In fact, it does not make any sense to refer to the "phase" of an individual molecule. The phase is a collective property of large numbers of molecules. Although we can discuss the importance of molecular properties regarding liquid and gas phases, we have not discussed the factors which determine whether the gas phase or the liquid phase is most stable at a given temperature and pressure.

These same questions can be applied to reaction equilibrium. When a mixture of reactants and products is not at equilibrium, the reaction will occur spontaneously in one direction or the other until the reaction achieves equilibrium. What determines the direction of spontaneity? What is the driving force towards equilibrium? How does the system know that equilibrium has been achieved? Our goal will be to understand the driving forces behind spontaneous processes and the determination of the equilibrium point, both for phase equilibrium and reaction equilibrium.