Lecture 1 Flashcards
What are phases? How do we determine the number of phases in a system?
A phase is a form of matter that is uniform throughout in both chemical composition and physical state. Thus there are solid, liquid, and gas phases.
The number of phases in a system denoted by P is determined by whether the matter is uniform across the chemical composition and physical state.
For example:
- For a mixture of gases, the structure is uniform throughout the chemical composition and physical state therefore in most cases it has 1 phase.
- For a mixture of two completely mixed liquids they have 1 phase.
- For a mixture of two solids that are immiscible in each other then 2 phases, but for a mixture of solids that are miscible (alloy) then 1 phase.
What are phase transitions? What happens to Gibbs Energy at the phase transitions?
Phase transition is the spontaneous conversion of one phase to another at a characteristic transition temperature and constant pressure.
At this transition temperature, the two phases are in an equilibrium so Gibbs energy is at a minimum
How are we able to detect Phase Transitions?
It is always not obvious to detect the phase transition as it might occur between two phases of a solid, therefore we use thermal analysis, where we measure the heat absorbed or evolved during a transition.
For example, if the transition is exothermic and the substance is cooling we know that the transition is from a higher energy phase to a lower energy phase ( like from liquid to solid). Vise vera is true.
What is a metastable phase?
they are thermodynamically unstable phases that persist because the transition is kinetically hindered. This usually happens between transitions of different solid phases.
What is chemical potential?
The chemical potential (μ) for a single substance is very simple another name for the molar Gibbs energy, where it is also based on the following consequence of the second law:
At chemical equilibrium, the chemical potential (μ) of a substance is the same in and throughout every phase present in the system.
The validity of this statement is shown in the notes.
What is a phase diagram? What are coexistence curves?
The phase diagram of pure substances shows the region of pressure and temperature at which its various phases are thermodynamically stable.
The coexistence Curve is the line separating the two regions in the phase diagram, Where (within the line) equilibrium exists between two the phases meaning they have the same chemical potential (μ)
What is the vapour pressure of a liquid? What is the sublimation vapour pressure? What is the boiling temperature? What is the normal and standard boiling point? What are freezing temp and melting temp? What is the normal and standard freezing temp? Whta is the triplet point
The vapour pressure of a liquid is the pressure of a vapour in equilibrium with its liquid.
The sublimation vapour pressure is the pressure of a vapour in equilibrium with its solid.
The pressure on the coexistence curves is the same as the vapour pressure of a liquid and the sublimation vapour pressure, where the higher the temp the larger the pressure
Boling temperature - It is the temp where a liquid in an open vessel has an external pressure equal to its vapour pressure causing vapour to expand freely to the surroundings, the normal b.p is the b.t at 1 a.t.m and the standard b.p is the b.t (boiling temp) at 1 bar
Melting temp - it is the temp at which, under a specified pressure, the liquid and solid phases of a substance coexist at equilibrium ( Freezing = melting temp). The normal freezing point is the f.t at 1 a.t.m and the standard f.p is the f.t at 1 bar.
The triplet point is the point where all the phases of a substance coexist in equilibrium, represented by the intersection of all coexistence curves. The triplet point of a pure substance is characteristic of it and cannot be changed with any alteration made. The Triplet point marks the lowest temperature and pressure at which a liquid can exist
All of the above are illustrated in the notes
What are the critical constants (taken from the thermodynamic course of Q2)
there is a critical temperature that separates two regions of the compound’s behavior.
Below this critical temperature the fluid as we know it is normal. When a certain pressure is applied to compress a liquid it condenses and forms a gas at which the horizontal barrier between the two phases is very clear, but when this compression is applied at a critical temperature or above the densities of the two phases equal each other causing then to merge into one single point known as the critical point of the gas, the molar volume and pressure at that critical point are known as the critical molar volume and the critical pressure.
The sample at Tc and past it is considered to be the same phase which is a gas, but the gas formed is much denser than what gases usually are so this substance is rather called a supercritical liquid.
What are the three representative phase diagrams? Explain their features.
Carbon dioxide - notes page 1
Water - Notes page 3
Helium - out of the scope of our understanding
What is the relation between chemical potential, molar entropy, and molar volume
The relation stems from two definitions:
- dμ = dGm
- dG = Vdp - SdT
Where the second definition also applies for the molar quantities of Gibbs energy:
Gm = Vmdp - SmdT
using this and definition one we get that dμ = Vmdp – Smdt therefore (δμ/δp) = Vm and (δμ/δT) = -Sm.
This is crucial to understanding the coexistence curves
How are phases dependent on temperature?
Notes… Page 2 (some complications happened :,(. )
Before it is important to note that for a closed system Sm > 0 for any temp above zero, so with our relation (δμ/δT) = -Sm) we know that chemical potential will decrease with increasing temp.
how is the melting/freezing point dependent on the pressure?
Notes… page 2
Before it is important to note that Vm>0 for any pure substance, so with our relation (δμ/δp) = Vm we know the chemical potential will increase with increasing pressure.
What is the Clapeyron equation? How can we obtain it?
Notes pages 3 to 4
How is the Clapeyron equation rewritten for the slope of the solid-liquid coexistence curve?
At the coexistence curve of liquid and solid melting/freezing occurs. Melting is accompanied by an enthalpy change of fusion (fus)H at Temp of T. The entropy change at melting is then represented by (fus)H / the transition temp, subbing that in gives us the updated equation
dp/dt = (fus)H/(trs)T*(fus)V
where (fus)H is always positive (except for He-3) and the change in Molar volume is usually positive and small giving us a positive steep slope slightly to the right.
note (fus)V is the change of volume accompanied by melting and (trs)T is the temps where the melting occurs and the transition happens(from solid to liquid)
What is the equation for the coexistence curve of solid-liquid?
notesss page 4
