0.6 Equilibrium and the second law of thermodynamics

Foundation

We have observed and defined phase transitions and phase equilibrium. We have also observed equilibrium in avariety of reaction systems. We will assume an understanding of the postulates of the Kinetic Molecular Theory and of the energetics of chemical reactions.

Goals

We have developed an understanding of the concept of equilibrium, both for phase equilibrium and reactionequilibrium. As an illustration, at normal atmospheric pressure, we expect to find $H_{2}O$ in solid form below 0°C, in liquid form below 100°C, and in gaseous form above 100°C. What changes as we movefrom low temperature to high temperature cause these transitions in which phase is observed? Viewed differently, if a sample of gaseouswater at 120°C is cooled to below 100°C, virtually all of the water vapor spontaneously condenses to form theliquid: $$H_{2}O\left(g\right)\to H_{2}O\left(l\right)\text{spontaneous below100°C}$$ By contrast, very little of liquid water at 80°C spontaneously converts to gaseous water: $$H_{2}O\left(l\right)\to H_{2}O\left(g\right)\text{not spontaneous below100°C}$$ We can thus rephrase our question as, what determines which processes are spontaneous and which are not? Whatfactors determine what phase is "stable"?

As we know, at certain temperatures and pressures, more than one phase can be stable. For example, at 1 atmpressure and 0°C, $$H_{2}O\left(s\right)\leftrightarrow H_{2}O\left(l\right)\text{equilibrium at 0°C}$$ Small variations in the amount of heat applied or extracted to the liquid-solid equilibrium cause shifts towardsliquid or solid without changing the temperature of the two phases at equilibrium. Therefore, when the two phases are at equilibrium,neither direction of the phase transition is spontaneous at 0°C. We therefore need to understand what factors determinewhen two or more phases can co-exist at equilibrium.

This analysis leaves unanswered a series of questions regarding the differences between liquids and gases. Theconcept of a gas phase or a liquid phase is not a characteristic of an individual molecule. In fact, it does not make any sense torefer 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 factorswhich 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 isnot 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 spontaneousprocesses and the determination of the equilibrium point, both for phase equilibrium and reaction equilibrium.

Observation 1: spontaneous mixing

We begin by examining common characteristics of spontaneous processes, and for simplicity, we focus on processesnot involving phase transitions or chemical reactions. A very clear example of such a process is mixing. Imagine putting a drop of blueink in a glass of water. At first, the blue dye in the ink is highly concentrated. Therefore, the molecules of the dye areclosely congregated. Slowly but steadily, the dye begins to diffuse throughout the entire glass of water, so that eventually the waterappears as a uniform blue color. This occurs more readily with agitation or stirring but occurs spontaneously even without sucheffort. Careful measurements show that this process occurs without a change in temperature, so there is no energy input or releasedduring the mixing.