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 centers of mass of the atoms in molecules are at the atomic nucleii.  These particles undergo essentially classical motion, either harmonically bound, chaotically quasi-bound or unbound)

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)

• 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, 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.




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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 of the vapor phase, and ths is called an interface, a place where two phases meet. The liquid at the interface hs a special property: it has molecules that only have neightbors on one side, as opposed to 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 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, , with units J/m². Here are some experimental surface tension data:
 

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 you use in your car in the winter is lower than that of the oil you use in the summer when measured at the same 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. If I have a liquid bubble with gas on the inside and outside, the bubble will try to collapse on the gas inside and cause an increase in pressure inside. This increase in pressure is :

Cohesive and adhesive forces give rise to Capillary Action

Our understanding of surface tension can be made more complete by knowing the energetics of making and breaking of molecular neighbors. This can be done by calorimetry, or the measure of the heat flow during an isothermal process.

The heating of a sample of water from -25 to 125 ^oC involves both the heat capacities of the pure phasaes but also the enthalpies of the melting and boiling of the water.

The enthalpy of the melting reaction

Phase Transitions take energy because of the making and breaking of intermolecular forces.

But phase transitions at a given temperature can reach equilibrium. 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 (dependent only of the temperature) equilibrium 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 Clausius-Clapeyron Equation (liquid/gas or solid/gas equilibrium curve):

Solid / Gas and Solid / Liquid equilibria also occur for all substances.

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)