0.12 Phase equilibrium and intermolecular interactions

Foundation

The "phase" of a substance is the particular physical state it is in. The most common phases are solid, liquid,and gas, each easily distinguishable by their significantly different physical properties. A given substance can exist indifferent phases under different conditions: water can exist as solid ice, liquid, or steam, but water molecules are $H_{2}O$ regardless of the phase. Furthermore, a substance changes phase without undergoing any chemical transformation: the evaporation ofwater or the melting of ice occur without decomposition or modification of the water molecules. In describing the differingstates of matter changes between them, we will also assume an understanding of the principles of the Atomic Molecular Theory and the Kinetic Molecular Theory . We will also assume an understanding of the bonding, structure, and properties of individual molecules.

Goals

We have developed a very clear molecular picture of the gas phase, via the Kinetic Molecular Theory. The gasparticles (atoms or molecules) are very distant from one another, sufficiently so that there are no interactions between theparticles. The path of each particle is independent of the paths of all other particles. We can determine many of the properties of thegas from this description; for example, the pressure can be determined by calculating the average force exerted by collisionsof the gas particles with the walls of the container.

To discuss liquids and solids, though, we will be forced to abandon the most fundamental pieces of the KineticMolecular Theory of Gases. First, it is clear that the particles in the liquid or solid phases are very much closer together than theyare in the gas phase, because the densities of these "condensed" phases are of the order of a thousand timesgreater than the typical density of a gas. In fact, we should expect that the particles in the liquid or solid phases areessentially in contact with each other constantly. Second, since the particles in liquid or solid are in close contact, it is notreasonable to imagine that the particles do no interact with one another. Our assumption that the gas particles do not interact isbased, in part, on the concept that the particles are too far apart to interact. Moreover, particles in a liquid or solid mustinteract, for without attractions between these particles, random motion would require that the solid or liquid dissipate or fallapart.

In this study, we will pursue a model to describe the differences between condensed phases and gases and todescribe the transitions which occur between the solid, liquid, and gas phases. We will find that intermolecular interactions play themost important role in governing phase transitions, and we will pursue an understanding of the variations of these intermolecularinteractions for different substances.

Observation 1: gas-liquid phase transitions

We begin by returning to our observations of Charles' Law . Recall that we trap an amount of gas in a cylinder fitted with a piston, and we apply afixed pressure to the piston. We vary the temperature of the gas, and since the pressure applied to the piston is constant, thepiston moves to maintain a constant pressure of the trapped gas. At each temperature, we then measure the volume of the gas. From ourprevious observations, we know that the volume of the gas is proportional to the absolute temperature in degrees Kelvin. Thus agraph of volume versus absolute temperature is a straight line, which can be extrapolated to zero volume at 0K.