Phases and Equilibrium

The States of Matter, Molecular Stickiness, and Thermodynamics

The phases of matter represent 'classes' of the type of molecular motion found at different temperatures.  When the temperature is low, the motion of molecules is dominated by the fact that they stick together, and the result is a phase of matter that is rigid and dense. When the termperature is high, the motion of the molecules is dominated by their translational energy, so intermolecular forces can almost be ignored. At intermediate temperatures, molecules translate but still stick together.

Solids  (tightly-bound molecules)

Liquids Gases (free motion)

Surfaces and Interfaces

At the edge of any solid or liquid (condensed phase) is a surface. When two different types of matter are in contact, they share a surface called and interface. An interface is where two phases of matter meet. At a surface, molecules have neighbors of the same type only on one side. Thus surface molecules are different from those in the bulk. Bulk molecules have neighbors in all directions. At an interface between a condensed phase and a gas or a vacuum, the molecules at the surface are unstable with respect to the bulk. Why? Because attractive intermolecular forces must be broken to bring a molecule from the bulk to the surface and there is nothing there to give that energy back. The number of molecules at the surface is proportional to the surface area.

Surface Tension:

It takes energy to create a new surface of a solid or liquid because one must move a molecule from the bulk to a site at the surface and this takes energy. The amount of energy it takes to create one unit of area (1 m2) of new surface is called the surface tension, g, with units J/m2. Here are some experimental surface tension data:

The Surface Tension of Various Interfaces
Interface (Temperature)
Surface Tension [mJ/m2]
Water / Air (20 oC)
Hg / Air (20 oC)
Benzene / Air (20 oC)
Water / Air (100 oC)

Intermolecular forces manifest themselves not only in the surface tension tension of a liquid, but in the way a liquid flows. The resistance to flow of a liquid is called the liquid's viscosity . The greater the viscosity, the "more slowly it flows".   The viscosity of the oil lubricating your car engine is an important part of engine performance and longevity. You change your oil when the viscosity of the engine oil 'breaks down' or decreases. You use in different oil in your car during the winter than in the summer because viscosity is effected by temperature.

Some definitions

Surface tension determines the pressure inside of a bubble. A free standing liquid bubble has gas on the inside and outside; Surface tension will tend to make the bubble collapse on the gas inside and thus cause an increase in pressure inside. This increase in pressure can be derived (can you derive this formula?):

This formula results from the observation that a bubble has two interfaces, the pressure increase inside a drop or cavitation, with only one interface, is only g / r.
Cohesive and Adhesive forces and Curved Surfaces also give rise to the phenomenon of Capillary Action. We will assume a "contact angle" of 0 degrees to gert a simplified expression for capilary rise. The more correct formula can be found here.

Phase Transitions
Our understanding of surface tension was made more complete by our understanding of intermolecular forces, i.e., the energetics of making and breaking of intermolecular bonds between molecular 'neighbors'. Such energies can be determined experimentally by calorimetry, or the measure of the heat flow during a chemical or physical process.

The heating of a sample of water from -25 to 125 oC involves both the heat capacities of the pure phases but also the enthalpies of the melting(fusion) and boiling(vaporization) of the water.

The enthalpy of the melting reaction and the boiling reaction are both positive (endothermic). {Melting is sometimes called fusion}

Phase Transitions take energy because of the breaking (or making) of intermolecular 'bonds'.

Phase Transitions at a given temperature can reach equilibrium, i.e. steady state. If you put any liquid in a sealed vessel and wait long enough, the liquid will come into equilibrium with its vapor, and a constant (steady; dependent only of the temperature) equilibrium vapor pressure will be established.

The equilibrium vapor pressure has an exponential temperature dependence for any given substance. We can see this from the liquid/vapor equilibrium curve:

Why does the vapor pressure increase with temperature so dramatically? Because the fraction of the molecules in the sample with sufficient energy to escape the shackles of their intermolecular forces depends on the energy distribution that we have already seen in our study of gases.

The liquid / vapor equilibrium curve follows a simple relation, because the amount of heat needed to vaporize the gas (molecular stickiness) determines the vapor pressure. The equation governing the pressure of a gas in equilibrium with a solid or a liquid can be derived from the postulates of Thermodynamics and is a milestone in the fundamental understanding of Phase Equilibria.
This relationship is called the Clausius-Clapeyron Equation (applicable to both liquid/gas or solid/gas equilibrium curves) and has the form:

The Phase Diagram
Every substance can exist as a Solid, Liquid, or Gas, and so Solid / Gas and Solid / Liquid and Liquid / Gas equilibria occur for all substances at some temperature and pressure.

The phase diagram is a plot of all the equilibrium curves between any two phases on a pressure temperature diagram:

Comparison of Phase diagrams of Familiar Substances; Water(a) and Dry Ice(b)

Liquids can be fleeting...

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