Geochemistry and environmental chemistry

Summary

Introduction

Normal seawater contains about 2660 ppm (0.028m) of sulfur in the form of sulfate. Sulfur in this form has a valence of +6, meaning that it has six fewer electrons per atom than has native sulfur, which exists (though not in the ocean) as a yellow crystalline solid. In some parts of the ocean, however, sulfur exists in the form of dissolved hydrogen sulfide, H2S(aq). Sulfur in this form has a valence of -2, meaning that it has two extra electrons compared with native sulfur, and in this form it is a deadly poison. Those parts of the ocean containing this electron-rich form of sulfur contain no living organisms other than a few kinds of bacteria. Obviously, the number of electrons that each sulfur atom has is not a question of interest only to atomic physicists. Changing sulfate-sulfur to H2S-sulfur or vice versa involves transferring electrons from one to the other, and this electron transfer is the basic element of redox (reduction–oxidation) reactions.

Many naturally occurring elements in addition to sulfur show similar variations in their number of electrons, with similarly large differences in their chemical properties. It would be difficult to overemphasize the importance to us of these variations in valence, or numbers of electrons per atom. Biochemistry, for example, is in large part a study of redox reactions. Because natural environments show great variability in their redox state, we need to develop some kind of measurement, an index, which will be useful in characterizing these redox states, much as we use pH as a measurement or index to characterize the acidity of various states, or temperature as a measurement or an index of the hotness of states. In this chapter we develop two such indexes of redox state.

Electron Transfer Reactions

You may not have noticed it, but we have considered two kinds of reactions in previous chapters. In some, such as (9.3),

all elements on the right side have the same number of electrons that they have on the left side – there is no change in valence of any element. In others, such as (9.16),

there is such a change. For example, the carbon in CH4 is C4-, and the carbon in CO2 is C4+.

Summary

Fugacity and activity are the composition terms, adjusted for non-ideality, that relate composition to Gibbs energy. The defintion of activity varies for solids, solutes and gases.

Summary

Temperature and Pressure Scales

Temperature

One of the early milestones in the development of thermodynamics was the demonstration that there is an absolute zero of temperature. Nevertheless there are several different temperature scales, for historical reasons. All you need to know about this is that the Kelvin scale (named after William Thompson, Lord Kelvin) has an absolute zero of 0K and a temperature of 273.16K at the triple point where water, ice, and water vapor are at equilibrium together. The melting point of ice at one atmosphere pressure is 0.01 degrees less than this, at 273.15K (Figure 3.1). The Celsius scale (named after Anders Celsius, a Swedish astronomer) has a temperature of 0 ◦C at the ice point (273.15 K) and absolute zero at -273.15 ◦C. This gives almost exactly 100 ◦C between the freezing and boiling points of water at one atmosphere, so water boils at 100 ◦C (373.15 K). Thus the numerical conversion between the two scales is

T K = T ◦C + 273.15

Remember that all equations in thermodynamics use the absolute or Kelvin temperature scale, so that, if you have temperatures in ◦C, you must convert them to the Kelvin scale before using them in equations. The “standard” temperature of 25 ◦C for example is 298.15 K. Standard IUPAC usage is to refer to temperatures on the Kelvin scale as so many kelvins, not degrees kelvin or ◦K. One kelvin is defined as the fraction 1/273.16 of the temperature of water at the triple point. More detail on temperature scales can be found in Anderson and Crerar (1993, Section 4.3).

Pressure

Force is measured in newtons (N), where 1 newton will give a mass of 1 kg an acceleration of 1 ms-2. Pressure is defined as force per unit area, and a pressure of 1 newton per square meter (1 Nm-2) is called 1 pascal (1 Pa). This is a very small pressure, and older, larger pressure units are still in use. The bar, for example, is 105 Pa and is almost equal to the standard atmosphere (1 atm = 1.01325 bar).

Summary

Introduction

In this chapter we will see how equilibrium thermodynamics is used in dealing with reacting systems, rather than just systems at equilibrium. Realistically, this should mean including the science of chemical kinetics with our thermodynamics, and we should also include other factors, such as fluid flow, temperature and pressure gradients, and adsorption on mineral surfaces, to build increasingly realistic models of complex natural phenomena involving the movement and chemical reactions of fluids in soils and rocks in the Earth's crust.

That is all a bit too ambitious for this book. Computational models including all these subjects are at the forefront of research in several areas. What we will attempt in this chapter is to show how equilibrium thermodynamics simulates chemically reacting systems without using kinetics. Process modeling in thermodynamics has some points in common with kinetics, because both sciences consider the problem of chemical reactions proceeding from start to finish, and both use the extent of reaction variable. But although thermodynamics uses the extent of reaction variable it does not use a real time variable, with which it is closely connected in kinetics. The use of a real time variable is what distinguishes kinetics from thermodynamics.

Quasistatic Processes

The term thermodynamic constraint is particularly appropriate for the extent of reaction variable, because for any equilibrium state of a system which does not appear on the stable equilibrium G–T–P surface, the question arises as to what prevents that system from spontaneously changing toward the stable equilibrium state. In real systems the reason is usually that there is a kinetic barrier, an activation energy which must be overcome for the change to take place (see Lambert (1998) for an entertaining discussion of this point). However, there is no term or variable in thermodynamics for activation energy. Activation energy as well as the enthalpy and entropy of activation are variables in transition state theory and reaction kinetics, but these quantities are not relevant to the present discussion.

Summary

Something Is Missing

We mentioned in Chapter 1 that an early idea for understanding chemical reactions held that spontaneous reactions would always be accompanied by the loss of energy, because the reactants were at a higher energy level than the products, and they wanted to go “downhill.” This energy was thought to be in the form of heat, but this idea received a setback when it was found that some spontaneous reactions in fact absorb heat. Also, there are some processes, such as the mixing of gases, where the energy change is virtually zero yet the processes proceed very strongly and are highly nonreversible. Obviously, something is missing. If the ball-in-valley analogy is right, that is, if reactions do proceed in the direction of decreasing chemical energy of some kind, something more than just heat is involved.

To learn more about chemical reactions, we have to become a bit more precise in our terminology and introduce some new concepts. In this chapter, we will define certain kinds of systems, because we need to be careful about what kinds of matter and energy transfers we are talking about; equilibrium states, the beginning and ending states for processes; state variables, the properties of systems that change during reactions; processes, the reactions themselves; and phases, the different types of matter within the systems. All these terms refer to real systems, but they also refer to the equivalent things in our models of these systems. To be quite clear about thermodynamics, it is a good idea to keep the distinction in mind.

Systems

Real-Life Systems

In real life, a system is any part of the universe that we wish to consider. If we are conducting an experiment in a beaker, then the contents of the beaker is our system. For a petrologist, a crystallizing magma could be the system. In considering geochemical, biological, or environmental problems here on Earth, the choice of system is usually fairly obvious, and depends on the kind of problem in which you are interested.

Summary

How themodynamics and thermochemical data are used to understand phase rlations in systems having only pure phases, no solutions.

Summary

Answers to the End-of-Chapter Exercises

Summary

This book is intended as an introduction to thermodynamics. To give instructors the option of including other aspects of particular thermodynamic topics, several chapters and sections from the second edition (Anderson, 2005) are available on the Cambridge University Press website for this book, www.cambridge.org/thermodynamics.

These sections are as follows.

Summary

Real Problems

We have now completed our survey of the thermodynamic principles required to model natural systems. It only remains to gain practice in formulating problems involving natural systems in thermodynamic terms. Quite often, that is the hardest part. Once the problem has been set up in terms of relevant reactions and components, the equations can be solved by anyone who has absorbed the previous chapters. However, choosing the appropriate components and setting up the relevant balanced reactions only comes from experience. In this chapter we explore a few situations that have been investigated by thermodynamic methods.

Is the Sea Saturated with Calcium Carbonate?

If you have ever been to Florida or the Bahamas, you may be aware that there are vast areas adjacent to the coasts where the sea bottom at shallow levels is a white mud, which turns out to be made of almost pure aragonite. Carbonate muds extend well out to the deep sea as well; in fact, a fairly large proportion of the sea bottom is composed of calcium carbonate. There are also countless calcitic atolls and reefs throughout the tropical zones of the world. Given this amount of contact between the sea and calcium carbonate, both calcite and aragonite, plus the fact that there are vigorous oceanic currents stirring things up constantly, plus the fact that things have not changed drastically for millions of years, you would think that there would be little doubt that the system consisting of the oceans plus their bottom sediments must have reached equilibrium by now. If these were the only factors involved, perhaps they would have, but the situation is quite a bit more complicated. Why would anyone want to know? Reactions involving carbonate in the oceans are fundamental to an understanding of the global CO2 cycle, which in turn is linked to climate change and other things we would like to understand.

How Do You Tell If a Solution Is Saturated?

To explore this problem further, we must first find out how to determine whether a solution is saturated, undersaturated, or supersaturated with a given mineral or compound. One answer would be to just observe the solution in contact with the mineral.

Summary

What Is a Phase Diagram?

A phase diagram in the general sense is any diagram that shows what phase or phases are stable as a function of some chosen system variable or variables. Therefore, the Eh–pH, log f O2–pH, and activity–activity diagrams we have been looking at are a kind of phase diagram. However, if you mention the subject of phase diagrams to a petrologist, a metallurgist, or a ceramic scientist, they will immediately think of a particular type of diagram that is of great usefulness in these subjects. In these sciences, the compositions of phases and their relationships during phase changes, particularly solid→liquid and liquid→solid changes, are of particular importance, so diagrams that depict this information as a function of temperature and pressure have come to be the subject of “phase diagrams.”

Thermodynamics and Phase Diagrams

Though it is true that phase relations can always be described in terms of the thermodynamic principles and equations we have been discussing, and that any phase diagram can in principle be calculated given the appropriate data, the emphasis in this chapter changes from one of calculating what we want to know from numbers in tables of data, to one of simply representing experimentally derived facts in diagrammatic form. The reason for this is that once we get into systems more complex than a single component, and especially when high-temperature melt phases are involved, the calculations are often not possible because the data are not available, or, even if they are available, the results are not very accurate, because they are very sensitive to small inaccuracies in the data. Therefore, in this book, although we will show the relationship between functions such as G and our diagrams, this will be in an illustrative rather than a quantitative way.

Phase Diagrams as Models

Metallurgists and ceramicists quite often deal with simple two- and three-component systems and use phase diagrams to represent their experimental results on the phase relations in these systems. The diagrams therefore truly represent their systems. Petrologists, on the other hand, are interested in the origins of natural rocks, which commonly have 10 or more important components.

Non-biomineralizing Ediacaran macrofossils are rare in carbonate facies, but they offer valuable information about their three-dimensional internal anatomy and can broaden our view about their taphonomy and palaeoecology. In this study, we report a new Ediacaran fossil, Curviacus ediacaranus new genus and species, from bituminous limestone of the Shibantan Member of the Dengying Formation in the Yangtze Gorges area of South China. Curviacus is reconstructed as a benthic modular organism consisting of serially arranged and crescent-shaped chambers. The chambers are confined by chamber walls that are replicated by calcispars, and are filled by micritic sediments. Such modular body construction is broadly similar to the co-occurring Yangtziramulus zhangii and other Ediacaran modular fossils, such as Palaeopascichnus. The preservation style of Curviacus is similar to Yangtziramulus, although the phylogenetic affinities of both genera remain unresolved. The new fossil adds to the diversity of Ediacaran modular organisms.

Summary

Introduction

Thermodynamics is the branch of science that deals with relative energy levels and transfers of energy between systems and between different states of matter. Because these subjects arise in virtually every other branch of science, thermodynamics is one of the cornerstones of scientific training. Various scientific specialties place varying degrees of emphasis on the subject areas covered by thermodynamics – a text on thermodynamics for physicists can look quite different from one for chemists, or one for mechanical engineers. For chemists, biologists, geologists, and environmental scientists of various types, the thermodynamics of chemical reactions is of course a central concern, and that is the emphasis to be found in this book. Let us start by considering a few simple reactions and the questions that arise in doing this.

What Is the Problem?

Some Simple Chemical Reactions

A chemical reaction involves the rearrangement of atoms from one structure or configuration to another, normally accompanied by an energy change. Let's consider some simple examples.

Summary

Introduction

We have had quite enough theoretical discussion for now. Let's see how to get some numbers into our equations so as to be able to calculate something useful. Welcome to the world of experimental thermochemistry.

In this chapter we will have a look at a few of the ways in which the thermodynamic parameters we have derived are measured; i.e., where the numbers in the tables and databases come from. A deep knowledge of this subject is not necessary in order to use thermodynamics to model chemical, geological, or environmental systems, in the same sense that a knowledge of a composer's life and times is not necessary to enjoy his or her music. But it does enrich the experience, and in the case of using thermodynamics, such knowledge does serve to make the user conscious of the many reasons why his or her data might be incorrect.

Thermochemical data are produced for the most part by dedicated scientists, who devote a good part of their lives to tracking down elusive sources of error, and devising ever-improved methods for determining nature's fundamental parameters as defined by thermodynamic theory. When determined by independent methods and/or independent laboratories, the results are often satisfyingly in agreement, but almost as often they are not, meaning that there is some source of error, and identifying it can take a lot of discussion (perhaps argument would be a better term) and a long time.

Beginning with the establishment of the Geophysical Laboratory in Washington in 1905, scientists primarily interested in geological processes have contributed to our knowledge of these thermodynamic properties, especially, as might be expected, those of the rock and soil-forming minerals, liquid–solid phase relationships of these minerals, and aqueous solutions such as sea water and hydrothermal solutions. In addition to the measurement of mineral and solution properties, collecting these data into databases for use by computer programs and the testing of these databases for internal consistency have become increasingly important.

The experimental part and the self-consistent database part of using thermodynamics in the Earth sciences today have both become large and complex subjects, each worthy of separate study.

Thermodynamics deals with energy levels and energy transfers between states of matter, and is therefore fundamental to all branches of science. This new edition provides an accessible introduction to the subject, specifically tailored to the interests of Earth and environmental science students. Beginning at an elementary level, the first four chapters explain all necessary concepts via a simple graphical approach. Throughout the rest of the book, the author emphasizes the importance of field observations and demonstrates that, despite being derived from idealized circumstances, thermodynamics is crucial to understanding ore formation, acid mine drainage, and other real-world geochemical and geophysical problems. Exercises now follow each chapter, with answers provided at the end of the book. An associated website includes extra chapters and password-protected answers to additional problems. This textbook is ideal for undergraduate and graduate students studying geochemistry and environmental science.

Summary

Introduction

The first sentence of Gibbs’ (1961a) classic memoir “On the Equilibrium of Heterogeneous Substances” is

The comprehension of the laws which govern any material system is greatly facilitated by considering the energy and entropy of the system in the various states of which it is capable.

Given the fact that virtually all of equilibrium thermodynamics can be derived by doing exactly that, as Gibbs did, this must rank as one of the world's great understatements. In this chapter, we begin to explore what Gibbs was referring to. By considering “the laws which govern any material system,” we should be able to find out the answers to the questions we posed in Chapter 1.

The Entropy Paradox

In this chapter we introduce a thermodynamic parameter called entropy. Entropy is often described in the following way:

The entropy of an isolated system continuously increases during a spontaneous, irreversible process until it reaches a maximum value at equilibrium.

However, if at the same time we consider the fact that in classical thermodynamics entropy is defined only in equilibrium states we have a paradox, stated for example by Tisza (1966, pp. 120–121):

The nature of this problem is illustrated by the following paradox: How are we to give a precise meaning to the statement that entropy tends toward a maximum, whereas entropy is defined only for systems in equilibrium? Thus in an isolated system, the entropy is constant, if it is defined at all.

The discussion of constraints and metastable equilibrium states in this chapter will provide an answer to this paradox.

The Problem Restated

Having taken a couple of chapters to get our terminology settled and to get used to discussing energy changes in systems, we must now get back to our main problem – what determines whether chemical processes will go or not go? Our method of determining this might be considered a bit simple-minded – we will simply determine the “chemical energy” differences between equilibrium states. Processes can take place spontaneously if they are in the direction of lowering the chemical energy. They cannot take place spontaneously in the opposite direction.

Summary

The equilibrium constant is the most useful variable in all of thermodynamics. How it is defined, and how it varies with temperature and pressure.

Summary

Introduction

If the world were made of pure substances, our development of the thermodynamic model would now be complete. We have developed a method, based on measurements of heat flow, that enables predictions to be made about which way reactions will go in given circumstances. But one of the reasons why the world is so complex is that pure substances are relatively rare, and strictly speaking they are nonexistent (even “pure” substances contain impurities in trace quantities). Most natural substances are composed of several components, and the result is called a solution. Therefore, we need to develop a way to deal with components in solution in the same way that we can now deal with pure substances – we have to be able to get numerical values for the Gibbs energies, enthalpies, and entropies of components in solutions. We will then be able to predict the outcome of reactions that take place entirely in solution, such as the ionization of acids and bases, and reactions that involve solids and gases as well as dissolved components, such as whether minerals will dissolve or precipitate. Our thermodynamic model will then be complete.

In this chapter we have a look at how to deal with dissolved substances – solutes. When we mix two substances together, sometimes they dissolve into one another, like sugar into coffee or alcohol into water, and sometimes they do not, like oil and water. In the former case, if we thought about it at all, we would probably expect that the properties of the mixture or solution would be some kind of average of the properties of the two separate substances. This is more or less true for some properties, but decidedly not true for the most important one, Gibbs energy.

After making sure we understand how to express the composition of solutions, we begin by considering properties of ideal solutions, which are, as you might expect, the simplest possible properties that solutions might have. As you might also expect, no real solutions are in fact ideal, although some come fairly close.

Geochemistry and environmental chemistry

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11 - Redox Reactions

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8 - Fugacity and Activity

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3 - The First Law of Thermodynamics

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13 - Affinity and Extent of Reaction

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2 - Defining Our Terms

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6 - Some Simple Applications

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Appendix C - Answers to Exercises

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Online Resources and Exercises

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APPENDICES

10 - Rock–Water Systems

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Contents

12 - Phase Diagrams

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A new modular palaeopascichnid fossil Curviacus ediacaranus new genus and species from the Ediacaran Dengying Formation in the Yangtze Gorges area of South China

1 - What Is Thermodynamics?

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5 - Getting Data

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References

Thermodynamics of Natural Systems

4 - The Second Law of Thermodynamics

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9 - The Equilibrium Constant

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7 - Solutions

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Thermodynamics of Natural Systems

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