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This relationship is called the Clausius-Clapeyron equation. Differentiation of the equations above reveals that the slope may be calculated: Sometimes, petrologists have a starting point, perhaps from experimental studies, and only need to know the slope of a reaction in order to plot it on a phase diagram. Activity models vary from being quite simple to very complex and may require computer programs to be useful. So, we use activity models to calculate the activities of the components we care about, so that we may put the values into the equations above. Consequently, the activity of a given component may vary, depending on composition. Other minerals are more variable in composition. Some minerals, like quartz, are so pure that, when present, their activities are 1. Depending on pressure and temperature, the GASP barometer may involve andalusite or sillimanite instead of kyanite. Also shown are the stability fields for andalusite, kyanite, and sillimanite. Given the compositions of coexisting minerals, K, can be calculated and, if metamorphic temperature is know, the metamorphic pressure may be read from this diagram. Phase diagram showing values of the equilibrium constant, K for the GASP reaction 3An = Gr + Ky + 2Q. This equation is the basis for the GASP geobarometer used by some petrologists to calculate metamorphic pressures (see figure). If a mineral assemblage contains kyanite and quartz, they are generally nearly pure, so their activities = 1. The exponents on the activity terms for kyanite and anorthite are because the reaction involves 3 moles of anorthite and 2 moles of kyanite. The equilibrium constant for a reaction ( K) is the product of the activities of the reaction products, divided by the product of the activities of the reactants:įor an example, let's combine the above equations, and consider the reaction:ģ anorthite = grossular + 2 kyanite + quartzįor this reaction, the conditions for thermodynamic equilibrium are:

The basic thermodynamic equation is modified to take this into account by adding a term involving the equilibrium constant( K): However, many minerals are solid solutions, so the effective activity (reactivity) of mineral components is diluted. The result is a curve (often nearly a straight line) in P-T-X space that separates fields of stability for different minerals or mineral assemblages.įor reactions involving pure, end member minerals, the above equation suffices. In either case, the equation above is solved to find the location of the reaction curve, points at which Δ G rxn = 0.

Alternatively, and more commonly, experimental studies may provide a reference point at which a particular reaction is in equilibrium ( Δ G P,T = 0).

BEFORE YOU GO LEWIS FREE

The starting Gibbs Free Energy value, Δ G P1,T1, may be directly obtained from calorimetric studies. The P and T subscripts remind us that the values change with pressure and temperature. The degree superscript reminds us that these values are for pure phases.

Δ G, Δ V, and Δ S refer to the Gibbs Energy, volume and entropy of reaction. The curve can be calculated from a starting point at, for example, 800 degrees and 2 GPa, and extrapolated to higher temperaures.

Before you go lewis