Problem Set #28: Phase Equilibrium and Phase Diagrams

University:
The Pennsylvania State University
Course:
CHEM 450 | Thermodynamics
Academic year:

2024
Views:

375

Pages:

2
Author:

Alexis H.

Problem Set #28 Assigned: March 13, 2024 Due: March 18, 2024 at 2:30 pm 1. Can four different phases of a pure substance (a one component system) be in equilibrium simultaneously at a given temperature and pressure? Explain your answer using the appropriate equation. 2. Consider two phases of a pure substance at a given temperature and pressure. If the chemical potential of the first phase is 7.1 kJ/mol higher than the chemical potential of the second, what is G for transferring 1.00 x 10-3 moles of this substance from the first phase to the second? What is G for transferring 1.00 x 10-3 moles of this substance from the second phase to the first? 3. For a one component system, is the condition P = 1 represented on a phase diagram by a point, a line, or an area? Use the appropriate equation to justify your answer. 4. What are the maximum number of phases that can be in equilibrium in a two component system? Can the mole fraction of the first component be the same in all the phases? 5. Consider the phase diagram for CO2: (a) What phase or phases are present at 250 K and 3 atm? (b) What phase or phases are present at 195 K and 70 atm? (c) What phase or phases is present at 216.8 K and 5.11 atm? (6) Still considering the phase diagram for CO2, (a) describe the phase or phases present at 200 K, as the pressure is increased from 1 atm to 70 atm. (b) Describe the phase or phases present at 67 atm as the sample is heated from 190 K to 300 K. 1. For four di erent phases to be in equilibrium simultaneously at a given temperature and pressure the condition of the equal chemical potential has to be satis ed; they must all be equal to each other 2 µ Mz Ms My µ Gm 7 1 k Mol ΔG 7 1 G 1.00 103moles 2 1 M M G 7 1 3. When P=1 it is represented on the graph by a point because this is at a particular temperature and pressure in which there is only one phase that is stable 4. For a two component system there is a maximum of 4 phases and the mole fraction has to be the same to satisfy the requirements for the chemical potential equation 5. (a) vapor (b) solid (c) vapor, liquid, and solid 6. (a) At 200K and 1 atm the phase is a base but as the pressure increases to 70 atm the phase shifts from a gas into a solid (b) At 67 atm and 190 K it starts out in the solid phase and as it moves to 300 K it the balances on the line between the gas and liquid phase