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. The 'motion' of the maolecules is described by the position and momenta of the atomic nuclei. The position of the molecule as a whole is derived from the center of mass of the atoms that compose it The molecules undergo classical (not quantum mechanical) motion, either harmonically bound (solid), chaotically quasi-bound (liquid) or unbound (gas)

Solids (harmonically bound nucleii)

At low temperatures the nuclei of the atoms of a solid vibrate about an equilibrium position but are trapped in their lattice positions.
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)

Liquids

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 (free motion)

Gases are described by the Kinetic Theory of Gases, i.e they are molecules of no size or stickiness, and move at random
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.

Surfaces and Interfaces

Surfaces of liquids or solids in contact with gases are less stable than the bulk of the condensed phase. The surface of a liquid is in contact with some other phase, usually at least opartially composed of its own vapor; This surface is thus an interface, a place where two phases meet. The part of a liquid or solid at an interface has a special property: it is composed of molecules that only have neighbors on one side (the molecules in the middle of the liquid that have neighbors on all sides). Each time a 'bond' between neighbors is broken, energy is required. Thus, it takes energy to move liquid molecules from the bulk to the surface. 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)	72.75
Hg / Air (20 ^oC)	472
Benzene / Air (20 ^oC)	28.88
Water / Air (100 ^oC)	58.0

Viscosity:
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 viscocity of the engine oil 'breaks down' or decreases. You use in different oil in your car during the winter than in the summer because viscocity 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 decreases with increasing temperature - the increasing kinetic energy overcomes the attractive forces and molecules can more easily move past each other.

Some definitions

Surface tension is the energy required to increase the surface area of a liquid or solid by a unit amount, i.e J/m²
Cohesive forces bind molecules of the same type together
Adhesive forces bind unlike molecules

Surface tension determines the pressure inside of a bubble. A fee 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 is only 2 g / r.

Cohesive and Adhesive forces and Curved Surfaces also give rise to the phenomenon of Capillary Action

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 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 and boiling 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 give gas. We can see this from the liquid/vapor equilibrium curve:

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:

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.

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

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)

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PJ Brucat // University of Florida