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)

• At low temperatures the nuclei of the atoms of a solid vibrate about an equilibrium position but are trapped in their lattice positions, unable to flow or diffuse.
• The intermolecular forces are stronger than the average thermal energy of the system.
• Long range radial and angular order (structure) are usually present in single crystal solids. Even amorphous solids have relatively good spatial ordering, especially over small distances, (10-100 molecules)

• As the binding energy to the lattice site is overcome by thermal energy, the molecules in the solid may slip past each other but maintain close contact.
• The overall substance is fluid, but not very compressible.
• Some long range radial ordering persists, but usually only over the size of a few molecular diameters

• Gases are described by the Kinetic Theory of Gases. In this limit, gas molecules have negligible size, have no appeciable intermolecular forces, and are in continous, random motion.
• Gases have mean free paths that are larger than molecular diameters, i.e. they are usually isolated but occasionally have collisions
• The state of a gas is universally, if approximately, described by the Ideal Gas Equation of State.

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:
 

Viscosity:
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.

• Viscosity is a measure of the ease with which molecules move past one another.
• Viscosity depends on the attractive force between the molecules.
• Viscosity of a liquid decreases with increasing temperature - the increasing kinetic energy overcomes the attractive forces and molecules can more easily move past each other.

Some definitions

• Surface is the edge or boundary of a material.
• Interface is the region of contact between two phases.
• Surface tension is the energy required to increase the surface area of a liquid (or solid) by a unit amount, i.e J/m²
• Viscosity is the resistance to the flow of a liquid. Solids don't have viscosity.
• Cohesive forces bind molecules of the same type together
• Adhesive forces bind unlike molecules

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 2 g / r.

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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.

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

• The shape of the Phase Diagram is Different in details depending on the substances.
• There is only one place where all three phases of a pure substance are at equilibrium. This is called the triple point [POINT A on the diagram]. (The aliens, when we meet them, will know the pressure and temperature of the triple point of water, do you?)
• The liquid / vapor equilibrium curve ends at a temperature and pressure where gases and liquids are indistinguishable fluids. This is called the critical point [POINT B on the diagram] and therefore has a critical temperature and a critical pressure.
• At POINT C and POINT D on the diagram, two phases are in equilibrium and off the line entirely there is only one stable phase of the substance.

Liquids can be fleeting...

• Liquid water exists with its vapor at 1 atm pressure, but liquid CO₂ only exists above the pressure of 5.11 atm.
• In the lab (1 atm) we see that solid CO₂ directly dissociates into gaseous CO₂ without making a liquid at all.
• Liquid CO₂ is found in most CO₂ fire extinguishers, but only at a temperature below 31.1 ^oC, (88 F), where the liquid becomes inditinguishible from the gas.
• Liquid water persists to much higher temperatures, over 300 ^oC, but only at great pressure (100's of atm).
• Only water has a liquid / solid equibrium curve that has a negative slope, i.e. it melts when you squeeze it. Water is unique in its highly structured liquid phase (which is why life grows in water)