0.23 Free energy and thermodynamic equilibrium

Introduction

In the previous study, we observed and applied the Second Law of Thermodynamics to predict when a process will be spontaneous. For example, the melting of solid water at a temperature above 0 ˚C at 1 atm pressure is a spontaneous process, and thermodynamics predicts this very accurately. However, over the course of several Concept Development Studies, we focused on processes at equilibrium, rather than processes occurring spontaneously. These include phase equilibrium, solubility equilibrium, reaction equilibrium, and acid-base equilibrium. Interestingly, we can use our understanding of spontaneous processes to make predictions about equilibrium processes too.

To begin, we need to be clear about what we mean by a “spontaneous process” versus an “equilibrium process.” At equilibrium, the macroscopic properties we observe (temperature, pressure, partial pressures, concentrations, volume) do not change. We have developed a model to describe equilibrium based on the idea of dynamic equilibrium, meaning that at equilibrium, there are forward and reverse reactions occurring at the molecular level at the same rate. However, this is not what we mean by “spontaneous process,” since the forward and reverse reactions exactly offset one another in a dynamic equilibrium. By contrast, in a spontaneous process, we observe macroscopic changes: partial pressures of reactants or products are increasing, concentrations are increasing or decreasing, the temperature or volume is changing, etc. This means that the forward and reverse reactions at the molecular level do not offset one another, and real macroscopic changes occur.

As we have discovered, during a spontaneous process the entropy of the universe increases. When a process comes to equilibrium, there are no spontaneous processes, so a reaction at equilibrium does not increase the entropy of the universe. We can combine these two ideas to say that, as a process spontaneously approaches equilibrium, the entropy of the universe continually increases until equilibrium is reached, at which point the process no longer increases the entropy of the universe. This gives us a way to predict the conditions under which a process will reach equilibrium. We will develop this approach in this Concept Development Study.

We will have to be careful in applying the Second Law of Thermodynamics in calculations. So far, we have only observed and tabulated values of the “absolute entropy,” S˚, at standard pressures and concentrations. We can use these to make predictions about processes at standard pressure and concentrations. But we know that phase transitions and reactions almost always come to equilibrium at partial pressures not equal to 1 atm and concentrations not equal to 1 M. Therefore, we must be careful when we interpret calculations of ∆S using S˚ values. And to understand the conditions at equilibrium, we must determine how to calculate S values for non-standard conditions. Only then will we be able to apply the Second Law of Thermodynamics at equilibrium conditions.