target="_blank" rel="nofollow" href="#ulink_b2423830-e722-59d6-9ec3-b2537bde1824">* We will be using System International Units as much as practicable throughout the book. A list of these units and their abbreviations can be found in the Appendix.
3 † Randomness can affect the outcome of any experiment (though the effect might be slight). By definition, the effect of this randomness cannot be predicted. Where the effects of randomness are large, one performs a large collection, or ensemble, of experiments and then considers the average result.
4 † The motion of Mercury is an exception: its motion differs slightly from predictions based on Newtonian mechanics. But relativity theory does accurately predict its motion. This successful prediction was one of several that led physicists to accept Einstein's new theory.
5 ‡ Dmitri Ivanovich Mendeleyev was born in Tobolsk, Russia in 1834. He became professor of chemistry at St Petersburg in 1866. His periodic table was the sort of discovery that noble prizes are awarded for, but it came before the prize was established. He was honored, however, by having element number 101, Medelevium, named for him. Mendeleyev died in 1906.
6 † By convention, the mass number, which is the sum of protons and neutrons in the nucleus, of an isotope is written as a preceding superscript. However, for historical reasons, it is often pronounced “helium–4.” Note also that the atomic number or proton number can be readily deduced from the chemical symbol (atomic number of He is 2). The neutron number can be found by subtracting the proton number from the mass number. Thus, the symbol 4He gives a complete description of the nucleus of this atom.
7 ‡ The actual mass of an atom depends on the number of electrons and the nuclear binding energy as well as the number of protons and neutrons. However, the mass of the electron is over 1000 times less than the mass of the proton and neutron, which have nearly identical masses, and the effect of nuclear binding energy on mass was too small for nineteenth-century chemists to detect.
8 * It is often convenient to think of the electrons orbiting the nucleus much as the planets orbit the Sun. This analogy has its limitations. The electron's position cannot be precisely specified as can a planet's. In quantum mechanics, the Schrödinger wave function, ψ (or more precisely, ψ2) determines the probability of the electron being located in a given region about the atom. As an example of failure of the classical physical description of the atom, consider an electron in the 1s orbital. Both quantum number specifying angular momentum, l and m, are equal to 0, and hence the electron has 0 angular momentum, and therefore cannot be in an orbit in the classical sense.
Chapter 2 Energy, entropy, and fundamental thermodynamic concepts
2.1 THE THERMODYNAMIC PERSPECTIVE
We defined geochemistry as the application of chemical knowledge and techniques to solve geologic problems. It is appropriate, then, to begin our study of geochemistry with a review of physical chemistry. Our initial focus will be on thermodynamics. Strictly defined, thermodynamics is the study of energy and its transformations. Chemical reactions and changes of states of matter inevitably involve energy changes. By using thermodynamics to follow the energy, we will find that we can predict the outcome of chemical reactions, and hence the state of matter in the Earth. In principle, at least, we can use thermodynamics to predict at what temperature a rock will melt and the composition of that melt, and we can predict the sequence of minerals that will crystallize to form an igneous rock from the melt. We can predict the new minerals that will form when that igneous rock undergoes metamorphism, and we can predict the minerals and the composition of the solution that forms when that metamorphic rock weathers and the nature of minerals that will ultimately precipitate from that solution. Thus, thermodynamics allows us to understand (in the sense that we defined understanding in Chapter 1) a great variety of geologic processes.
Thermodynamics embodies a macroscopic viewpoint, that is, it concerns itself with the properties of a system, such as temperature, volume, and heat capacity, and it does not concern itself with how these properties are reflected in the internal arrangement of atoms. The microscopic viewpoint, which is concerned with transformations on the atomic and subatomic levels, is the realm of statistical mechanics and quantum mechanics. In our treatment, we will focus mainly on the macroscopic (thermodynamic) viewpoint, but we will occasionally consider the microscopic (statistical mechanical) viewpoint when our understanding can be enhanced by doing so. More detailed treatments of geochemical thermodynamics can be found in Anderson and Crerar (1993), Nordstrom and Munoz (1986), and Fletcher (1993).
In principle, thermodynamics is only usefully applied to systems at equilibrium. If an equilibrium system is perturbed, thermodynamics can predict the new equilibrium state, but cannot predict how, how fast, or indeed whether the equilibrium state will be achieved. (The field of irreversible thermodynamics, which we will not treat in this book, attempts to apply thermodynamics to nonequilibrium states. However, we will see in Chapter 5 that thermodynamics, through the principle of detailed balancing and transition state theory, can help us predict reaction rates.)
Kinetics is the study of rates and mechanisms of reaction. Whereas thermodynamics is concerned with the ultimate equilibrium state and not concerned with the pathway to equilibrium, kinetics concerns itself with the pathway to equilibrium. Very often, equilibrium in the Earth is not achieved, or achieved only very slowly, which naturally limits the usefulness of thermodynamics. Kinetics helps us to understand how equilibrium is achieved and why it is occasionally not achieved. Thus, these two fields are closely related, and together form the basis of much of geochemistry. We will treat kinetics in Chapter 5.
2.2 THERMODYNAMIC SYSTEMS AND EQUILIBRIUM
We now need to define a few terms. We begin with the term system, which we have already used. A thermodynamic system is simply that part of the universe we are considering. Everything else is referred to as the surroundings. A thermodynamic system is defined at the convenience of the observer in a manner so that thermodynamics may be applied. While we are free to choose the boundaries of a system, our choice must nevertheless be a careful one as the success or failure of thermodynamics in describing the system will depend on how we have defined its boundaries. Thermodynamics often allows us this sort of freedom of definition. This can certainly be frustrating, particularly for someone exposed to thermodynamics for the first time (and often even the second or third time). But this freedom allows us to apply thermodynamics successfully to a much broader range of problems than otherwise.
A system may be related to its environment in a number of ways. An isolated system can exchange neither energy (heat or work) nor matter with its surroundings. A truly isolated system does not exist in nature, so this is strictly a theoretical concept. An adiabatic system can exchange energy in the form of work, but not heat or matter, with its surroundings, that is to say it has thermally insulating boundaries. Though a truly adiabatic system is probably also a fiction, heat transport in many geologic systems is sufficiently slow that they may be considered adiabatic. Closed systems may exchange energy, in the form of both heat and work, with their surrounding but cannot exchange matter. An open system may exchange both matter and energy across it boundaries. The various possible relationships of a system to its environment are illustrated in Figure 2.1.