0.22 Entropy and the second law of thermodynamics

Introduction

We have spent much of the previous concept studies finding that chemical and physical processes come to equilibrium. We have observed this in phase equilibrium of pure substances, solution equilibrium, solubility equilibrium, chemical reactions in the gas phase, and acid-base equilibrium. In each case, we have been able to understand equilibrium as a dynamic process. At equilibrium, there are competing processes, forward and reverse, which come to equilibrium when the rates of the competing processes are equal. For example, when liquid and vapor are at equilibrium at the vapor pressure of the liquid, the rate of evaporation of the liquid is equal to the rate of condensation of the vapor.

However, our dynamic equilibrium model does not tell us the conditions at equilibrium. For each liquid, we know that there is one pressure for each temperature at which the liquid can be in equilibrium with its vapor. But we cannot predict or calculate what that pressure is for each temperature for each liquid. We can only make qualitative predictions. Thermodynamics will give us the means to make these predictions and will give us a new physical insight into the nature of equilibrium.

We will begin by developing a means to predict what processes will happen “spontaneously.” This is a term chemists use to refer to processes that are not at equilibrium. It is easiest to explain with an example. We know that, if the pressure of water vapor is 1 atm at 25 ºC, the water vapor will spontaneously condense. On the other hand, we have also seen that, if the pressure of water vapor is below 23 torr at 25 ºC, the liquid water will spontaneously evaporate. These are both examples of spontaneous processes. Note that these are opposite processes. This means that the spontaneity of a process depends on the conditions, in this case, the pressure and the temperature. Any process not at equilibrium is a process occurring spontaneously. One way to understand equilibrium, then, is to understand spontaneity. We will see that the Second Law of Thermodynamics provides us the ability to predict spontaneous processes.

Foundation

We have come a long way to reach this point, so we have a substantial foundation to build on. We know all the elements of the Atomic Molecular Theory, including the models for molecular structure and bonding. We have developed the postulates of the Kinetic Molecular Theory. We have observed and defined phase transitions and phase equilibrium. We have also observed equilibrium in a variety of reaction systems, including acids and bases. We will assume an understanding of the energetics of chemical reactions, including the idea of a “state function” and the concept of Hess’ Law.

Observation 1: spontaneous mixing

We begin by examining common characteristics of spontaneous processes, and for simplicity, we focus on processes not involving phase transitions or chemical reactions. A very clear example of such a process is mixing. Imagine adding a drop of blue ink into a glass of water. At first, the blue dye in the ink is highly concentrated. Therefore, the molecules of the dye are closely congregated. Slowly but steadily, the dye begins to diffuse throughout the entire glass of water, so that eventually the water appears as a uniform blue color. This occurs more readily with agitation or stirring but occurs spontaneously even without such effort. Careful measurements show that this process occurs without a change in temperature, so there is no energy input or released during the mixing.