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

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)

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

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.

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

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

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

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

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

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

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

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.

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.