GEOL 3041/ GEOL 3041 Igneous & Metamorphic Petrology/GEOL 3041 Answers for Chapter 5: An Introduction to Thermodynamics. 100% Score.

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GEOL 3041 Answers for Chapter 5: An Introduction to Thermodynamics. 1. The molar Gibbs free energy of formation of quartz is the energy change involved in the reaction of Si metal with O2 gas to fo... rm a mole of quartz SiO2: Si (metal) + O2 (gas) = SiO2 (quartz). What does the value = –856.3 kJ/mol tell us about the stability of quartz (as compared to Si metal and O2 gas) at 25oC and 1 atmosphere pressure? Explain. 2. What would be the entropy of any phase at 0K? Explain. Can you explain this on the molecular level? 3. How do we determine the enthalpy of formation of a mineral? 4. In what order would you place crystals, gases, and liquids in terms of increasing (molar) entropy? Explain. 5. In what order would you place crystals, gases, and liquids in terms of increasing (molar) volume? Explain. 6. At constant pressure, dP = 0, so dG = -SdT. We could integrate eq. 5.3 (assuming a constant S) to produce: so that where all properties are molar Explain in words the meaning of equation on the right (think in terms of a slope). 7. Does the equation in question 6 indicate that the molar Gibbs free energy of quartz will increase or decrease with increasing temperature? Explain. . 8. Does the equation in question 6 indicate that the molar Gibbs free energy of a solid or its melt will decrease more for any given rise in temperature? Explain. 9. Again referring to the equation in question 6, would a solid or melt become more stable (relatively) as temperature rises? Explain in terms of the respective Gibbs free energies and your natural intuition/experience. 10. At constant temperature, equation 5.3 can be integrated with respect to pressure: so that where all properties are (again) molar What do we assume in this equation? 11. Does the equation in question 10 indicate that the molar Gibbs free energy of a solid or its melt will increase more for any given rise in pressure? Explain. 12. Will the melt or the solid therefore become more stable as pressure rises? Explain in terms of the respective Gibbs free energies and your natural intuition/experience. 13. For any reaction amongst phases: dG = VdP – SdT (5–11) Both  and d in the equation above refer to a change in some property. What is the difference between  as in V and d, as in dP? 14. The diagram represents a schematic P-T phase diagram for the melting of a mineral. a. Write the melting reaction and express G in terms of the Gibbs free energy of the reactants and products. b. What is the sign or value of G at points A, B, and x in the figure? Explain. c. If we address the change in Gibbs free energy between any two points along the reaction (melting) equilibrium curve, such as points x and y in the figure, what would be the value of dG? Explain. . 15. If dG = 0, then Eq. 5.11 reduces to VdP = SdT, so that Explain in words what this equation means. Use the signs of S and V for the melting reaction to apply it qualitatively to the melting phase diagram in question 14. Is the slope correct? Explain. 16. If the change in volume for the melting reaction in the question 14 diagram were to increase (with no accompanying change in entropy), how would the diagram change? Explain. 17. The diagram on the right is a P-T phase diagram, showing the relative stability fields of the Al2SiO5 polymorphs. Petrology deals extensively with phase equilibrium and phase diagrams, and we will be seeing many such diagrams in subsequent chapters. Each of the three reaction curves shown is determined experimentally. a. How can you tell that this particular system is metamorphic, rather than igneous? b. Does the diagram suggest that kyanite has a lower molar volume than sillimanite or higher? Explain. c. Does the diagram suggest that sillimanite has a lower entropy than andalusite or higher? Explain. d. Would you expect to find andalusite in higher pressure or lower pressure metamorphic terranes than kyanite? What about sillimanite? e. Write the balanced chemical reaction for the transformation of kyanite to sillimanite with increasing metamorphic grade. f. At what temperature would the above reaction occur at 0.6 GPa? How deep is 0.6 GPa? g. What does the diagram suggest about the stability of sillimanite under atmospheric conditions? Why is it possible to have sillimanite samples available in a mineralogy lab? Is it stable, unstable, or metastable? To what should it revert according this phase diagram? Why doesn’t it? 18. The diagram here is another P-T phase diagram showing the position of a stable metamorphic reaction as determined experimentally. a. Write the balanced chemical reaction. b. Do you think albite has a large molar volume or small? Explain. c. What does your answer to part (b) suggest about the stability of plagioclase at great mantle depths? Explain. d. Imagine this system is at equilibrium with coexisting albite, jadeite, and quartz. Where on the diagram would this occur? e. When at a point corresponding to 3-phase equilibrium, what can you say about the rates of the forward (left-to-right) and reverse (right-to-left) directions of the reaction as written in part (a)? f. If you begin to isobarically cool the three-phase equilibrium system will the forward or reverse reaction occur at a faster rate? Use Le Châtelier’s Principle to explain why. Why can’t the temperature vary while all three phases are present at equilibrium? What will eventually limit this situation and permit temperature to fall? g. Where on the diagram is albite stable? Explain. h. If you began to heat the three-phase equilibrium system instead, would the forward or reverse reaction (as written in part (a)) occur at a faster rate? What will eventually limit this situation and permit temperature to rise? Be careful here as you consider this. i. To what extent can you place limits on the stability of jadeite on the diagram? Explain. PROBLEMS. 1. Given the following data, calculate the molar Gibbs free energy of forsterite at 600 and 1200ºC at both 0.1 MPa and 1 GPa (assuming that V and S are constant). 2. If H2O is added to the simple melting reaction S = L and the solid mineral is naturally anhydrous, the liquid will be the only phase that accepts some dissolved H2O. The reaction then becomes: where the subscript means that the phase is aqueous (it contains H2O). Use Le Châtelier’s Principle to qualitatively evaluate the effect of adding H2O to the initial anhydrous melting system. Will it lower or raise the melting point? Explain. 3. If you have access to the Excel Visual Basic program PTGIBBS (Brandelik and Massonne, 2004; available by following from http://www.prenhall.com/winter ...under Min-Pet Links), do the following (you may have to click the Add-Ins tab at the top of Excel 2007): a. Select Calculate energy of a specific phase. Determine the free energy (of formation) of pure andalusite (activity = 1) at 25oC and 0.1 MPa (1 bar). I got -2,617,233 J/mol Is it more stable than the elements from which it is formed? How can you tell from your result? Calculate G at 800oC and 1000 bars (0.1 GPa). How did the change in temperature and pressure affect its stability as compared to the elements? Did thermal expansion or pressure compression have a greater effect on the volume of andalusite between these conditions and the standard state? Calculate G for andalusite, kyanite, and sillimanite at 500oC and 0.2 GPa (2000 bars). Which is most stable? Repeat for 500oC and 0.8 GPa and 700oC and 0.4 GPa. How do your results compare with the phase diagram in Review Question 17? Calculate G for all three polymorphs at 493oC and 3485 bars. Given the precision of the data to about 1%, how can you tell this is close to the point where all three are stable together? b. Select the Calculate 2D option and determine the value of G for QUARTZ-ALPHA from 100 to 1000oC at 1 bar (0.1 MPa). The Gpure(T) option calculates G for the pure phase at various temperatures. Do the values follow a straight or curved line? What does this tell you about the entropy of quartz as temperature is raised [see Equation (5.9)]. c. Calculate a reaction among SiO2 polymorphs. Select Clear Input Data and then enter the following in the first cells of the Input sheet (see the sheet tabs at the bottom). QUARTZ-ALPHA -1 COESITE 1 end Column 2 is contains the stoichiometric coefficients for the reaction. Next click the Calculate Equilibria button at the top and check the box before the reaction, and click OK. You will next see the P-T diagram of the equilibrium boundary separating the stability fields of alpha quartz and coesite (on the PT_PLOT sheet). Select a P and T value anywhere below the curve shown and return to Calculate energy of a specific phase. Determine G for QUARTZ-ALPHA and for COESITE at these conditions. Which is more stable? Explain. Return to the PT_PLOT sheet and select a P and T value above the equilibrium curve and recalculate G for each phase under these conditions. Which polymorph is more stable? Finally, go to the PT_DATA sheet and select any P and T for the equilibrium curve itself. Return to Calculate energy of a specific phase and compare G for the polymorphs. Explain your results. Compare the reaction curve with Figure 6.6. 5. Melting Experiments on Simple Binary Mineral Systems [Show More]

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