diopside + spinel + enstatite. In that reaction the minerals had unique and invariant compositions. In the Earth, things are not quite so simple: these minerals are present as solid solutions*, with substitutions of Fe2+ for Mg, Na for Ca, and Cr and Fe3+ for Al, among others. Indeed, most natural substances are solutions; that is, their compositions vary. Water, which is certainly the most interesting substance at the surface of the Earth and perhaps the most important, inevitably has a variety of substances dissolved in it. These dissolved substances are often of primary geochemical interest. More to the point, they affect the chemical behavior of water. For example, the freezing temperature of an aqueous NaCl solution is lower than that of pure water. You may have taken advantage of this phenomenon by spreading salt to de-ice sidewalks and roads.
In a similar way, the equilibrium temperature and pressure of the plagioclase + olivine ⇌ clinopyroxene + spinel + orthopyroxene reaction depends on the composition of these minerals. To deal with this compositional dependence, we need to develop some additional thermodynamic tools, which is the objective of this chapter. This may seem burdensome at first: if it were not for the variable composition of substances, we would already know most of the thermodynamics we need. However, as we will see in Chapter 4, we can use this compositional dependence to advantage in reconstructing conditions under which a mineral assemblage or a hydrothermal fluid formed.
A final difficulty is that the valance state of many elements can vary. Iron, for example, may change from its Fe2+ state to Fe3+ when an igneous rock weathers. The two forms of iron have very different chemical properties; for example, Fe2+ is considerably more soluble in water than is Fe3+. Another example of this kind of reaction is photosynthesis, the process by which CO2 is converted to organic carbon. These kinds of reactions are called oxidation–reduction, or redox reactions. The energy your brain uses to process the information you are now reading comes from oxidation of organic carbon – carbon originally reduced by photosynthesis in plants. To fully specify the state of a system, we must specify its “redox” state. We treat redox reactions in the final section of this chapter.
Though Chapter 4 will add a few more tools to our geochemical toolbox, and treat a number of advanced topics in thermodynamics, it is designed to be optional. With completion of this chapter, you will have a sufficient thermodynamic background to deal with a wide range of phenomena in the Earth, and most of the topics in the remainder of this book.
3.2 PHASE EQUILIBRIA
3.2.1 Some definitions
3.2.1.1 Phase
Phases are real substances that are homogeneous, physically distinct, and (in principle) mechanically separable. For example, the phases in a rock are the minerals present. Amorphous substances are also phases, so glass and opal would be phases. The sugar that won't dissolve in your iced tea is a distinct phase from the tea, but the dissolved sugar is not. Phase is not synonymous with compound. Phases need not be chemically distinct: a glass of ice water has two distinct phases: water and ice. Many solid compounds can exist as more than one phase. Nor need they be compositionally unique: plagioclase, clinopyroxene, olivine, and so on, are all phases even though their composition can vary. A fossil in which the aragonite (CaCO3) is partially retrograded into calcite (also CaCO3) consists of two phases, which, although they might be chemically identical, have different crystal structures and hence different properties. Systems and reactions occurring within them that consist of a single phase are referred to as homogeneous; those systems consisting of multiple phases, and the reactions occurring within them, are referred to as heterogeneous.
3.2.1.2 Species
Species is somewhat more difficult to define than either phase or component. A species is a chemical entity, generally an element or compound (which may or may not be ionized). The term is most useful in the context of gases and liquids. A single liquid phase, such as an aqueous solution, may contain a number of species. For example, H2O, H2CO3,
3.2.1.3 Component
In contrast to a species, a component need not be a real chemical entity; rather, it is simply an algebraic term in a chemical reaction. The minimum number of components† of a system is rigidly defined as the minimum number of independently variable entities necessary to describe the composition of each and every phase of a system. Unlike species and phases, components may be defined in any convenient manner: what the components of your system are and how many there are depend on your interest and on the level of complexity you will be dealing with. Consider our aragonite–calcite fossil. If the only reaction occurring in our system (the fossil) is the transformation of aragonite to calcite, one component, CaCO3, is adequate to describe the composition of both phases. If, however, we are also interested in the precipitation of calcium carbonate from water, we might have to consider CaCO3 as consisting of two components: Ca2+ and
There is a rule to determine the minimum number of components in a system once you decide what your interest in the system is; the hard part is often determining your interest. The rule is:
(3.1)
where n is the number of species and r is the number of independent chemical reactions possible between these species. Essentially, this equation simply states that if a chemical species can be expressed as the algebraic sum of other components, we need not include that species among our minimum set of components. Let's try the rule on the species we listed above for water. We have six species: H2O, H2CO3,
We can write three reactions relating them:
Equation 3.1 tells us we need 3 = 6 – 3 components to describe this system:
