Question

We have already looked at in lab one mantle sample from San Carlos in Arizona. This sample might have got you thinking about what minerals are stable in the higher temperature and pressure environment of the Earth’s mantle. Among possible mantle minerals are garnet, spinel, olivine, and pyroxene. With thermodynamics, as in most chemistry courses, keep track of units, and make sure you do conversions so that you are dealing with like units! Also show your work.

temperature and pressure environment or uie Calui smante. Among possible manne minerals are garnet, spinel, olivine, and pyroxene. With thermodynamics, as in most chemistry courses, keep track of units, and make sure you do conversions so that you are dealing with like units! Also show your work. (a) Write a balanced reaction for equilibrium among the magnesian endmembers pyrope garnet (Mg, Al,Si,012), spinel (MgA1,02), forsterite (Mg, SiO2), and enstatite (MgSiO2). (Hint to get started on the balancing: Al bearing minerals will have to be on opposite sides on the equation.) (b) Given the experimental data below, calculate AG for your balanced reaction. Is the forward or reverse reaction favored based on your answer? (C) Now calculate AS for your balanced reaction using the experimental data given below. (d) In lecture, we saw that one form of the Gibbs Free Energy equation is: AG = AH – TAS Knowing AG and AS for the reaction from the previous questions, you will be able to figure out AH for the reaction at 1000°K. You may have to convert units to make sure things cancel (remember 1kJ equals 1000 J). (e) From the experimental data given below, estimate the equilibrium temperature at surface conditions of P=0.1 MPa. Remember that AG=0 at equilibrium. Comment on the significance of your result. (f) Calculate AV for the reaction at 298°K using the experimental data below. (g) Now estimate the equilibrium pressure at T = 1000°K using a new form of the Gibbs Free Energy equation: AGP=0=AG + PAV. If the reaction did come to equilibrium at that P and T, what would be the effect of increasing pressure? Why? (h) We will want to plot an approximate P-T stability diagram for your reaction. Use the Clapeyron Equation to figure out the slope of the equilibrium line. Plot your equilibrium line on a graph of P vs T. Use the previous to plot one point on your equilibrium curve. Make sure you label the stability fields on either side of the equilibrium line with the appropriate assemblage based on your written reaction. Recall that high pressure favors lower volume. Pyrope Spinel Forsterite Enstatite AG®, 1000°K, kJ/mole S', 1000°K, J/deg-mole V, 298°K, J/MPa -5067 730.8 113.17 -1879 264.5 39.71 -1772 277.2 43.79 -1256 192.9 31.47

Answer 1