Question

3. (a) Do problem 5.40 in the text. Assume that the phase boundaries can be represented by straight lines. (b) The Earth's pressure gradient in the lithosphere is VP 300 atm/km (the temperature gradient can be taken from the previous question). At a depth of 50 km, will it be more likely that albite forms or that jadeite+quartz forms? Explain. Problem 5.40. The methods of this section can also be applied to reactions in which one set of solids converts to another. A geologically important example is the transformation of albite into jadeite + quartz: NaAlSi3O8NaAlSi206 Sio2. Use the data at the back of this book to determine the temperatures and pressures under which a combination of jadeite and quartz is more stable than albite. Sketch the phase diagram of this system. For simplicity, neglect the temperature and pressure dependence of both ΔS and Δν.

Answer 1

5.40 Answer:

Gibbs free energy, Entropy and Molar Volumes for Albite, Jadeite, quartz Gibbs free energy Entropy Volume Albite G,--3711-5KJ s. -204-4J/K 100-07cm Jadeite G,-2852-1KJ s,-133-5J/K V,-60.40cm Quartz G,-856-64KJ S,-41-84J/K V,-22-69cm Albite jadeite quartz For this reaction -(-2852 1-856.64+3711-5)kJ 2-76kJ>0

Thus the Albite is more stable under normal conditions. The jadeite quartz combination becomes more stable at high pressures. Change in volume -(100.07-60-40-22-69)cm -16.98cm -1-698x10m kJ kbar kJ kbar AV-1-698

The pressure at which jadeite + quartz becomes stable at standard temperatures AG 2-76 K 1.698 KJ Kbar P-1-6254 Kbar This gives the interest of the coexistence line with P-axis in P-T diagram. The slope from Clausius-Clapeyron equation is dP AS AS-S-S,-S, -(204.4-133-5-41-84)J/K ΔS = 29-06J/K Slope V 29.06J/K 1.698J/bar bar =17-11

Phase Diagram 80T 70 60 50 o 40 30 20 10 Jadeite+Quartz Albite 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Temperature T(K)

The above figure shows the phase diagram the system of Albite, Jadeite+Quartz At room temperature, Jadeite+Quartz is stable at pressure above 1 6254kbar, The slope of the Jadeite& Quartz-Albite phase boundary is 17-11 bar/K. So if temperature is 100K higher than room temperature, then an additional pressure of 1-7kbar to make Jadeite+Quartz stable.