Chapter 27 Ans

Chapter 27 Ans - Answers for Chapter 27 Thermodynamics of...

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Answers for Chapter 27: Thermodynamics of Metamorphic Reactions 1. Is G for the albite = jadeite + quartz reaction positive or negative at 600 o C and 0.4 GPa? Explain. G must be positive, because albite (the reactant as written) is stable and therefore has the lower G. G is the sum of the product G’s minus the sum of the reactant G’s which is a larger number minus a smaller number, hence positive. 2. Considering Figure 27.1 (below), which has a larger molar volume, albite or jadeite + quartz? Explain your reasoning. Albite must have a larger molar volume than the combined volumes of jadeite + quartz, because it is the low-pressure state. 3. Geologically, where would you expect to find jadeite on the basis of Figure 27.1? (Be careful; this is a tricky question.) In the absence of quartz jadeite would be stable under any conditions according to this diagram. We already learned in an earlier chapter exercise, however, that jadeite will break down to nepheline + quartz at some pressure lower than the reaction drawn, thereby limiting the occurrence of jadeite, but this is another matter. 1
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4. Modify Equation (27.6) for a gas phase by substituting appropriate pressure and/or fugacity coefficient terms, assuming that P o = atmospheric pressure. G G RT n P P P T T o o , ( ) = + (27.6) , ( 100,000) o P T T G G RT n f = + 5. How does the chemical potential of a component relate to the Gibbs free energy of the pure component as a phase at the same pressure and temperature? o i i μ G = for pure i at the standard state of the P and T of interest. Therefore A A i i i μ = G -RT n a 6. Given the reaction Mg 2 SiO 4 + SiO 2 = 2 MgSiO 3 , write an expression of the form of Equation (27.16) for the reaction assuming non-pure Fe-Mg mixtures. Use an ideal solution model for the activities, noting that olivine involves mixing on two octahedral sites. 2 2 Ab Jd SiO Pl Ab Cpx Qtz Jd SiO o o o o G a RT n a a μ = ∆ = - (27–16) En 2 Mg o Ol 2 Mg x G = -RT n x What would be appropriate for the quartz activity expression? Explain. 2 Qtz SiO 1 a = because quartz is pure ( 2 Qtz SiO x = 1, so I left it out of the equation above) 2
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7. What is the difference between the K D expression used in Chapter 9 and the equilibrium constant, K ?
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