Department of Earth and Planetary Sciences

Department of Earth and Planetary Sciences 186-220A Principles of Geochemistry

Home Assignment #3 Due: October 16th.

Fall Term, 2001 Alfonso Mucci and A.E. (Willy) Williams-Jones

1. Calculate and plot three P-T paths of equilibrium (or lines in P-T space where all phases coexist at equilibrium) for the reaction:

NaAlSi3O8 = NaAlSi2O6 + SiO2 (Albite = Jadeite + Quartz)

Use the following data for enthalpy of formation from the oxides and entropy at 1000 K and

assume Cp = 0.

o 1 Phase  Hf (kJ/mol) S (J/K mol) V (J/bar mol)

Albite -65.69 544.38 10.043 Jadeite -75.73 385.43 6.04 Quartz 00.00 115.56 2.2688

Path a.) Assume all phases are pure Path b.) Assume the plagioclase composition is Na0.5Ca0.5Al1.5Si2.5O8 and plagioclase feldspars mix ideally, all other phases are pure. Path c.) Assume the plagioclase is pure albite, but the pyroxene is impure and has the composition Na0.2Ca0.8Al0.2Mg0.8Si2O6. You must determine the mole fraction of jadeite in the pyroxene and use ideal ionic mixing to calculate the activity of jadeite.

2.) Using the plot and calculations from 1c determine if albite, clinopyroxene, and quartz can coexist with water, muscovite (KAl3Si3O10[OH]2), sanidine (KAlSi3O8), and corundum (Al2O3). (Coexistence of all phases occurs when the lines representing the equilibrium reactions intersect in P-T space.) All phases involved in the muscovite reaction are pure. For temperatures between 900 and 1100 K (600 to 800 oC) you may use the following thermodynamic values for the muscovite dehydration reaction (i.e. muscovite on the left-hand-side and water on the right-hand- side of the equation):

Hrxn, 1 bar, T = 98.157 kJ/mol

Srxn, 1 bar, T = 164.01 J/mol K

Vrxn, 1 bar, T, solids = -0.6339 J/bar mol

Use the attached tables for H2O. If all phases cannot coexist with each other then determine which phases in the two reactions can coexist and at what conditions. (Hint: To solve this problem you will have to use successive iterations to find the answers and linear interpolations for the correct

values of H2O. I recommend using a computer for your calculations.)