1. Phase Transformations - Vocabulary
Allotropes
Phase Transitions
Phase Diagram
Normal vs Standard Transition Temperatures
Critical Temperature
Triple Point

2. Phase and Allotropes
Phase: Uniform in physical state and chemical composition
Mathematically, a phase has 1 equation of state.
Allotrope: One of at least two different crystalline or molecular structures of a substance
Examples: Ice, Phosphorous (White and Black), Carbon (Graphite and Diamond)

3. Phase Transformations - Vocabulary
Allotropes
Phase Transitions
Normal vs Standard Transition Temperatures
Phase Diagram
Critical Temperature
Triple Point

4. Transition Temperature
Phase Transitions
Spontaneous conversions from one physical state (phase) to another. The phases are in equilibrium during a phase transition.
What does that mean about S?
What about G?
Transition Temperature
The temperature, AT A GIVEN PRESSURE, where a phase transition occurs.
This means that we have a set of temperatures for every phase transition. How do we graphically represent a set of points? A line.

5. Phase Diagram Normal Melting Point Standard Melting Point
A phase diagram is a P vs T diagram.
Normal Melting Point - T(m) at 1 atm
Standard Melting Point - T(m) at 1 bar
From now on, when talking about phases, we are going to refer to the gas phase as the Vapor Phase
We have vapor, which is above liquid, and we have sublimation vapor which is above the solid

6. Phase Diagrams
Phase diagrams give us a general idea about phase stability….
But they don’t tell the whole story.
Example: Allotropes of carbon
C(diamond) C(graphite)
Gibbs Free Energy
Diamond
Graphite
2.9 kJ/Mol
Look up phase diagram for Carbon
Both Carbon and Diamond exist at room temperature.
One of the homework problems we did showed that the heat of formation for diamond was 1.9 kJ, so we know the conversion from diamond to graphite would be exothermic. We know from experience that diamonds don’t burn people when they wear them.
Maybe Entropy explains it - we know that the driving force of the universe is to increase entropy.
-Nope - the gibbs free energy of formation of diamond is also positive
How does Tiffany’s stay in business?
Activation energy. Kinetics plays an equally important role in phase stability

7. Phase Diagram Super Critical Fluid Critical Point Normal Melting Point
Standard Melting Point
Critical Point - What is it? Above T(c) we cannot get a liquid. There’s only one critical point.
Triple Point - Three phases are in equilibrium. Usually (but not always) it is the lowest pressure at which we can get a liquid. What determines whether the Triple point describes that condition?
The other thing the triple point might describe is the highest T that we can get a solid

8. Critical Point
Tc (K)
Pc (atm)
CO2
304.2
72.85
Br2
584
102
H2O
647.4
218.3 O2
154.8
50.14
CH4
190.6
45.6

9. CO2 Notes about CO2 diagram: We cannot get liquid below 5.11 atm
Solid-liquid boundary is positive (melting point increases as you add pressure)
Solid liquid Boundary has a positive slope

10. H2O Ice-I and liquid water boundary has a negative slope
There are 6 different types of Ice (7 triple points)
There is no such thing as Ice IV
Ice VII isn’t shown on this diagram

11. Helium Gas and solid never coexist
Two allotropes (body centered cubic and hexagonal closed packing)
Two liquid forms
A superfluid flows without any viscosity
Quantum effects are relevant 3He and 4He have different phase diagrams.
Scale of x-axis is much smaller

12. Chemical Potential ()
Is a quantitative measure of a substance’s ability to bring about change.
For a pure substance,  is the potential to bring about physical change (a phase change).
Do we have a quantity that sort of describes that kind of potential?
Entropy is the driving force of the universe.
Molar Gibbs free energy is the definition of  for a pure substance.
 Is going to help us quantify how the system changes under the given conditions.

13. Chemical Potential
Any system in equilibrium must have the same chemical potential throughout the entire system
Melting T is the point where the line for the solid intersects with that of the liquid. The boiling point is where the liquid and gas lines intersect.
What is the slope of each of those lines? (Sm)
The chemical potential of a solid phase changes with T differently than that of the liquid phase.  for a liquid changes at a different rate than that of a solid or liquid.