12.109 Problem Set #1 Exchange reactions The Fe-Mg olivine - melt exchange reaction and formation reactions provide useful tools for understanding the conditions of formation of basaltic magmas and for assessing significance of the composition of an olivine-bearing igneous rock. This problem set gives you some experience in using these exchange and formation reactions. 1) The equation for the Fe-Mg exchange reaction (KD Fe-Mg ) is found in the course notes. Simplify the exchange reaction by substituting an ideal model for the activities of Fe and Mg in the olivine and the melt. Thus: aFooliv = XFo oliv and aMgO liq = X MgO liq Now use these expressions. the value of KD Fe-Mg and the relations: XMgO = 1 - XFeO to develop expressions that allow you to predict XFo oliv in terms of X MgO liq and X MgO liq in terms of XFo oliv . 2) With your newly derived expression for olivine and melt Fe-Mg characteristics carry out the following tasks: a) Predict the Mg# (this is a commonly used expression that is = X MgO liq) of a liquid in equilibrium with Fo90 olivine. b). Calculate the Fo content of the liquidus olivine for a melt with an Mg# = 0.83. 3) Table 1 of Baker et al. gives the composition of a lava and the most Fo-rich olivine found in the lava. a) Use the expressions given by Roeder and Emslie to calculate the crystallization temperature.** b) We usually use this temperature as an estimate of the liquidus temperature for the rock. Why is this a good assumption? c) What test should you always perform before you use the olivine and rock composition to calculate a crystallization temperature? ** Note that you will have to use the appropriate units for the Roeder and Emslie expressions. These are mole % of the oxides in mineral and melt. The compositions of the rock and olivine are given in wt. %. Transform to mole % by dividing by gram formula weight of each oxide and renormalizing to 100%.References: Baker et al. “Origin of compositional zonation (high-alumina basalt to basaltic andesite) in the Giant Crater lava field, Medicine Lake volcano, northern Calfornia.” Journal of Geophysical Research 96 (1991), 21819-21842. Roeder, P. L., and R. F. Emslie. "Olivine-liquid equilibrium." Contrib Mineral Petrol 29 (1970):