Samuel S Butcher and Sharon E Anthony

5.1 Introduction

This chapter applies the physical chemistry taught in the first year of undergraduate chemistry to chemical problems in the natural environment and introduces key chemical concepts to use and keep in mind for the rest of this book. The material in this chapter is especially important to consider when utilizing the modeling techniques presented in Chapter 4.

There are two principal chemical concepts we will cover that are important for studying the natural environment. The first is thermodynamics, which describes whether a system is at equilibrium or if it can spontaneously change by undergoing chemical reaction. We review the main first principles and extend the discussion to electrochemistry. The second main concept is how fast chemical reactions take place if they start. This study of the rate of chemical change is called chemical kinetics. We examine selected natural systems in which the rate of change helps determine the state of the system. Finally, we briefly go over some natural examples where both thermodynamic and kinetic factors are important. This brief chapter cannot provide the depth of treatment found in a textbook fully devoted to these physical chemical subjects. Those who wish a more detailed discussion of these concepts might turn to one of the following texts: Atkins (1994), Levine (1995), Alberty and Silbey (1997).

In many cases one can apply the first principles of thermodynamics and chemical kinetics to natural systems only with caution. The reason has little to do with the shortcomings of the core chemical principles. Rather, the application of thermodynamics (including electrochemistry) can be restricted by the fact that some natural systems have reaction rates so slow that they exist for long periods under non-equilibrium conditions. Moreover, reaction rates can be difficult to characterize when they are sensitive to poorly understood catalytic (including enzymatic) effects or to surface effects. Applications of thermodynamics and kinetics, as they are presented in this chapter, require knowledge of many variables such as concentration, temperature, and pressure. However, in contrast to reactions in a stirred beaker, the natural world may have large gradients of these variables. The natural environment also differs because of the large number of chemical species that coexist and interact concurrently. Therefore, it is important that the limitations of chemical thermodynamics and kinetics be considered before they are applied to biogeochemical systems.

5.2 Thermodynamics

5.2.1 State Functions and Equilibrium Constraints

The laws of thermodynamics are the cornerstones of any description of a system at equilibrium. The First Law, also known as the Law of Conservation of Energy states that energy cannot be created or destroyed, i.e., the energy of the universe is constant. Thus if the internal

Earth System Science ISBN 0-12-379370-X

Copyright V; 2000 Academic Press Limited All rights of reproduction in any form reserved energy of a system decreases in a reaction, the chemical change is accompanied by a release of energy, often in the form of heat. The enthalpy, H, is a property of the system that is equal to E + PV, where E is the internal energy of the system, P is pressure, and V is volume. At constant pressure, the change in H is the energy flow as heat. Enthalpy is a state function of the system, which means that it is a property that depends only on the state of the system and not how it managed to arrive at that state. Other state functions are temperature and pressure. Work and heat are examples of properties that are not state functions.

The Second Law of thermodynamics states that for a chemical process to be spontaneous, there must be an increase in entropy. Entropy (S) can be thought of as a measure of disorder.

Another property of the system, G, the free energy, or the Gibbs free energy, is related to enthalpy and entropy by:

When the temperature of reactants and products are equal, AG is given by

The second law also describes the equilibrium state of a system as one of maximum entropy and minimum free energy. For a system at constant temperature and pressure the equilibrium condition requires that the change in free energy is zero:

We represent a change in a quantity for any chemical reaction as the value of that quantity for the products of the reaction minus the value of that quantity for reactants. It is important to keep in mind that the terms reactant and product refer only to how the chemical equation is written and not to whether or not the substance is actually being formed or is disappearing.

Equation (3) defines the equilibrium condition under the constraint that temperature and pressure are constant. A related consequence of the Second Law is that if AG < 0 the reaction of the reactant to product is thermodynamically spontaneous. Thermodynamic spontaneity means that the system has the potential to react. The more negative AG, the more spontaneous the reaction. The actual time scale for the reaction to occur can vary greatly. A good example of a non-equilibrium system is the ambient pressure of nitrogen oxides in the troposphere, which can greatly exceed their equilibrium values for the equilibrium with N2 and 02. We discuss non-equilibrium systems later in the chapter.

Although AG is the overall determinant of spontaneity, it is convenient to examine the two thermodynamic components of AG. The AH term is largely a function of the strengths of the chemical bonds in reactant and product. To the extent that there are more strong bonds (and strong associations between molecules) in the product than in the reactant, AH will be negative. An examination of Equation (3) shows that a negative AH contributes to the overall spontaneity of the reaction.

The AS term is a measure of the relative degree of disorder in reactant and product. To the extent that the product has greater disorder than the reactant AS will be positive. A positive AS will contribute to the overall spontaneity of the reaction. AS for a reaction can be evaluated from tables of entropy data. Moreover, the sign of AS for gas phase reactions may often be determined without entropy tables. For gas phase systems in which the number of independent molecules and atoms is greater in the product, AS will be positive. If there is no change in the number of atoms and molecules for a gas phase reaction it is difficult to say (without evaluating AS from tables of data) whether AS is positive or negative. In the liquid phase these simple rules for AS are less easily applied because significant entropy effects occur in water and many other solvents. Ionic solutes can cause a relative lowering of entropy of the solution by forming highly ordered associations with water, whereas other solutes may increase the solution entropy by disrupting the structure of water and not replacing it with other low-entropy structures.

In practice, G and H for a substance are defined relative to the G and H for the constituent elements of that substance. These relative values are known as free energy of formation and enthalpy of formation for standard conditions and symbolized as AG0 and AH0. So where we indicated values of G and H in Equations (1) and (2), in practice we would use a free energy and enthalpy of formation, which are themselves a special kind of AG and AH. Values for these functions may be obtained from standard tables of thermodynamic data, usually for the reference temperature of 298.2 K and a pressure of 1.0 bar. The Chemical Rubber Company handbook (Lide, 1998) is one of the more commonly available sources.

More complete sources, including some with data for a range of temperatures, are listed in the references at the end of the chapter. Note that many tabulations (including many contemporary biological sources) still represent these energy functions in calories and that it may be necessary to make the conversion to joules (1 cal = 4.1840 J). Because of the definition of the energy of formation, elements in their standard state (carbon as graphite, chlorine as Cl2 gas at one bar, bromine as Br2 liquid, etc.) have free energies and enthalpies of formation equal to zero. If needed, the absolute entropies of substances (from which AS may be evaluated) are also available in standard sources.

For ions in the aqueous phase there is an additional complication in defining G and H. The change in G and H for the formation of an ion from its constituent element (e.g. jCl2(g) + e~ -> CI (aq)) is defined relative to the change in G and H for the formation of H+ from H2(g). This relative change in G and H is termed the standard free energy or enthalpy of formation for ions. As a result of this definition, AG0 and AH0 for the formation of H+ are zero. In practice, the definitions given above lead to the following algorithm for determining AG0 or AH0 for a reaction. AG0 for a reaction may be obtained by simply adding the AG0 (formation) values for the product species and subtracting the sum of AG0 (formation) for all reactant species. Where an element in its standard state or H+ is involved, substitute zero.

5.2.2 Gas Phase Equilibria

For reactions in the gas phase, the free energy per mole of gas as a function of pressure is given by the following expression:

where P° is the standard reference pressure (commonly 1 bar or (1/1.01325) atmosphere), and P is the pressure of the gas, R is the universal gas constant, which has a value of 8.314 J/mol/K, and T is the temperature of the system in kelvins (°C + 273). For the ideal systems considered here, we will treat the free energy per mole to be the same as the chemical potential. This treatment works best at very low pressures where gases approach ideal behavior.

For the gas phase equilibrium

the change in free energy for this system at equilibrium is

substituting the expression for G° given in Equation (4), we derive the familiar equilibrium constant expression:

AG0 = -RT In /p\J ,! x2 = -RT In KF (5) (j n2 \ / Pq2 \

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