MATSCI 204 THERMODYNAMICS & PHASE EQUILIBRIA Winter 2013 ...
MATSCI 204 THERMODYNAMICS & PHASE EQUILIBRIA Winter 2013 Problem Set #6
Problem 1 (30 points) Consider the following phase diagram of a binary system A/B. You can consider AB as a line compound.
We will work at the T=1300K isotherm 1- First assume that all solutions (solid and liquid) are ideal. - plot the activity of A as a function of xB. Be quantitative wherever possible. (pick the equilibrium state of A at T=1300K as the reference state) - calculate the activity of A in AB when AB is in equilibrium with the A-rich liquid solution and with the B-rich liquid solution as well. - estimate the molar melting enthalpy of pure A Δhm at its melting point. Explain the approximations you make.
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2- The terminal B-rich solution now obeys the dilute solution model for solvent and solute throughout the whole composition range at 1300K. Henry’s coefficient for A is 0.25. Furthermore the liquid solution in equilibrium with the terminal B-rich solid is modeled as a regular solution with a molar enthalpy of mixing of the form "hmix = #x A x B . - calculate α. - what’s the activity of A in AB when AB is in equilibrium with the B-rich liquid solution (i.e. right side of the AB line compound)? 3- The liquid in equilibrium with the terminal A-rich solid is not an ideal solution either. Assume it’s a regular solution and the Δgmix at xB=0.15 is -7 kJ/mol. Furthermore, the activity coefficient of B at xB=0.15 is equal to 0.4. What is the activity of A in AB when it’s in equilibrium with the A-rich liquid solution (i.e. left side of the AB line compound)?
Problem 2: (20 points) Consider the reaction SiHCl3(g) + H2(g)
Si(s) +3HCl (g)
a) Briefly explain how the following changes might shift an existing equilibrium of these 4 components (to products or reactants as written above): (6 points) i) an increase in pressure ii) an increase in the amount of Si present. iii) An increase in the temperature. b) A gas mixture consisting of 98.9 mol % H2, 0.1 mol%SiHCl3 and 1 mol% HCl is introduced into a reaction chamber containing a Si single crystal wafer at 1 atm pressure. Will the reaction written above proceed to form products (Si deposition) or to form reactants (Si etching) at 800°C.? Show all work. (14 points) DATA: SiHCl3 (g): Δgof, 1073K = - 810.9 kJ/mol HCl (g): Δgof, 1073K = -292.7 kJ/mol SiHCl3 (g): Δhof, 298K = -125 kcal/mol (assume it does not depend on T) HCl (g): Δhof, 298K = -22 kcal/mol (assume it does not depend on T)
Problem 3 (30 points) Consider a gaseous mixture of 20% CO, 20% CO2, 50% H2 and 10% H2O, which is brought to equilibrium at 700K and 1 atm. of pressure. The equilibration reaction is: CO2 + H 2 " CO + H 2O 1- Using the attached Ellingham diagram and the fact that the Gibbs free-energy is a state function (i.e. ΔGreaction=Gformation(products)-Gformation(reactants)), calculate the ΔG0 of the equilibration reaction at 400°C ! 2- Compute the equilibrium composition of the gas phase at T=400°C and P=1 atm.
Problem 4 (20 points) Consider the attached Au-Sn phase diagram: What is the only compound that melts congruently? Find: 4 peritectics, 2 eutectics, 1 peritectoid and 1 eutectoid. For each one write down the reaction that occurs when the triple point is reached from higher temperatures as well as the reaction temperature and composition of the phases involved. Which Au-Sn compound is the only one that can be cast directly from the melt?
Problem 5: (30 points) Al in Al-Zn alloys exhibits positive deviations from ideality. In the dilute limit, Henry’s coefficient of Al in the alloy is approximately 7. Knowing that the dissociation pressure of ZnO at 700°C is approximately 10-27 atm. and using the Ellingham diagrams given in the notes estimate the dissociation pressure of Al2O3 in a Al-Zn alloy at 700°C with xAl=0.005.
Problem 1 (30 points) Consider the following phase diagram of a binary system A/B. You can consider AB as a line compound.
We will work at the T=1300K isotherm 1- First assume that all solutions (solid and liquid) are ideal. - plot the activity of A as a function of xB. Be quantitative wherever possible. (pick the equilibrium state of A at T=1300K as the reference state) - calculate the activity of A in AB when AB is in equilibrium with the A-rich liquid solution and with the B-rich liquid solution as well. - estimate the molar melting enthalpy of pure A Δhm at its melting point. Explain the approximations you make.
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2- The terminal B-rich solution now obeys the dilute solution model for solvent and solute throughout the whole composition range at 1300K. Henry’s coefficient for A is 0.25. Furthermore the liquid solution in equilibrium with the terminal B-rich solid is modeled as a regular solution with a molar enthalpy of mixing of the form "hmix = #x A x B . - calculate α. - what’s the activity of A in AB when AB is in equilibrium with the B-rich liquid solution (i.e. right side of the AB line compound)? 3- The liquid in equilibrium with the terminal A-rich solid is not an ideal solution either. Assume it’s a regular solution and the Δgmix at xB=0.15 is -7 kJ/mol. Furthermore, the activity coefficient of B at xB=0.15 is equal to 0.4. What is the activity of A in AB when it’s in equilibrium with the A-rich liquid solution (i.e. left side of the AB line compound)?
Problem 2: (20 points) Consider the reaction SiHCl3(g) + H2(g)
Si(s) +3HCl (g)
a) Briefly explain how the following changes might shift an existing equilibrium of these 4 components (to products or reactants as written above): (6 points) i) an increase in pressure ii) an increase in the amount of Si present. iii) An increase in the temperature. b) A gas mixture consisting of 98.9 mol % H2, 0.1 mol%SiHCl3 and 1 mol% HCl is introduced into a reaction chamber containing a Si single crystal wafer at 1 atm pressure. Will the reaction written above proceed to form products (Si deposition) or to form reactants (Si etching) at 800°C.? Show all work. (14 points) DATA: SiHCl3 (g): Δgof, 1073K = - 810.9 kJ/mol HCl (g): Δgof, 1073K = -292.7 kJ/mol SiHCl3 (g): Δhof, 298K = -125 kcal/mol (assume it does not depend on T) HCl (g): Δhof, 298K = -22 kcal/mol (assume it does not depend on T)
Problem 3 (30 points) Consider a gaseous mixture of 20% CO, 20% CO2, 50% H2 and 10% H2O, which is brought to equilibrium at 700K and 1 atm. of pressure. The equilibration reaction is: CO2 + H 2 " CO + H 2O 1- Using the attached Ellingham diagram and the fact that the Gibbs free-energy is a state function (i.e. ΔGreaction=Gformation(products)-Gformation(reactants)), calculate the ΔG0 of the equilibration reaction at 400°C ! 2- Compute the equilibrium composition of the gas phase at T=400°C and P=1 atm.
Problem 4 (20 points) Consider the attached Au-Sn phase diagram: What is the only compound that melts congruently? Find: 4 peritectics, 2 eutectics, 1 peritectoid and 1 eutectoid. For each one write down the reaction that occurs when the triple point is reached from higher temperatures as well as the reaction temperature and composition of the phases involved. Which Au-Sn compound is the only one that can be cast directly from the melt?
Problem 5: (30 points) Al in Al-Zn alloys exhibits positive deviations from ideality. In the dilute limit, Henry’s coefficient of Al in the alloy is approximately 7. Knowing that the dissociation pressure of ZnO at 700°C is approximately 10-27 atm. and using the Ellingham diagrams given in the notes estimate the dissociation pressure of Al2O3 in a Al-Zn alloy at 700°C with xAl=0.005.
