Chemical Kinetics and Process Dynamics in Aquatic Systems

Patrick L. Brezonik

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9781351461504
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

Chemical Kinetics and Process Dynamics in Aquatic Systems is devoted to chemical reactions and biogeochemical processes in aquatic systems. The book provides a thorough analysis of the principles, mathematics, and analytical tools used in chemical, microbial, and reactor kinetics. It also presents a comprehensive, up-to-date description of the kinetics of important chemical processes in aquatic environments. Aquatic photochemistry and correlation methods (e.g., LFERs and QSARs) to predict process rates are covered. Numerous examples are included, and each chapter has a detailed bibliography and problems sets. The book will be an excellent text/reference for professionals and students in such fields as aquatic chemistry, limnology, aqueous geochemistry, microbial ecology, marine science, environmental and water resources engineering, and geochemistry.

“Iron rusts from disuse, stagnant water loses its purity, and in cold weather becomes frozen; even so does inaction sap the vigors of the mind.”

Notebooks, Leonardo da Vinci

CHAPTER 1

Overview

1.1 INTRODUCTION

Quantitative understanding of the chemistry of natural waters involves the two cornerstones of physical chemistry: thermodynamics and kinetics. The principles of thermodynamics define a system’s composition at equilibrium — the condition toward which it tends to go in the absence of energy inputs. The rate at which systems approach equilibrium is the domain of kinetics. Aquatic chemists have made major advances over the past two decades in explaining the chemistry of natural waters, via thermodynamic concepts and equilibrium models, and many books have been devoted to these topics.¹ The principles of chemical equilibrium were applied to natural waters most thoroughly by Stumm and Morgan,² whose text has served as a conceptual framework for the discipline of aquatic chemistry.

Equilibrium approaches are useful in relating the inorganic composition of lakes, rivers, groundwater, and the oceans to weathering reactions of minerals in watersheds, but the ability of thermodynamics to describe aquatic systems is limited, particularly for organic substances and for waters affected by human activity. Although equilibrium calculations compare favorably with observed concentrations of major and minor ions in some waters, complete chemical equilibrium never occurs in natural waters. Nonequilibrium conditions persist, in part, because many energetically favorable reactions are very slow and, in part, because natural waters are open systems that receive influxes of matter and energy from external sources. The adequacy of equilibrium models thus depends on the relative rates of influxes and reactions for a substance. If influxes are small and reactions are rapid, equilibrium descriptions are adequate; slow reactions and rapid influxes allow nonequilibrium conditions to persist. The fact that the composition of natural waters changes over time also implies that equilibrium descriptions are not always adequate. Moreover, the time-invariant state for open systems is the steady state and not the equilibrium state. This implies that kinetic relationships are important in describing aquatic systems.

A major goal of aquatic chemists is to understand the rate-controlling factors for chemical processes in aquatic systems. Kinetics often is considered an empirical science in which reaction rates are measured rather than predicted. Nonetheless, relationships are available to describe the effects of the major state variables (temperature, pressure) on reaction rates and to predict the kinetic behavior of some compounds from the behavior of related compounds. In addition, sophisticated theories are available to explain the mechanisms and energetics of chemical change. These relationships and theories are the ingredients that make kinetics a science rather than a mere collection of facts and rate constants. The search for other unifying principles and predictive relationships is the source of intellectual stimulation to scientists.

Aquatic chemists have placed increasing emphasis on kinetic and process-oriented models of natural waters over the past 20 years.³ The evolution from static to dynamic models resulted, in part, from concerns about the fate of pollutants in natural waters. As a result, the literature on kinetics in aquatic systems has increased rapidly in recent years. The reactions and processes receiving attention are diverse, ranging from inorganic redox and ligand exchange reactions to organic transformations by biological and photochemical processes, and from reactions in solution to processes at air/water and water/solid interfaces. This literature is scattered widely in journals and books, and a comprehensive treatment of kinetic principles and their application to natural waters has not been available. This book is an effort to fill that void.

The processes of chemical change are studied at three levels in modern chemical kinetics: (1) phenomenological or observational; (2) mechanistic; and (3) statistical mechanical. The first level involves measurement of reaction rates under various physical conditions (e.g., temperature) and interpretation of the data in terms of rate laws based on mass action principles. The second level is concerned with elucidating reaction mechanisms, i.e., the “elementary” steps that comprise a net (stoichiometric) sequence. The third level is concerned with the details of elementary reactions: the ways reactants approach each other and form transition states, mechanisms of bond breaking, and the energetics of these processes. Aquatic chemical kinetics traditionally has focused on phenomenological and, to a lesser extent, mechanistic aspects. As the subject has matured in recent years, chemists have begun to explore the applications of statistical mechanics to understand the detailed mechanisms of some elementary aquatic reactions.

1.2 NATURAL WATERS AS NONEQUILIBRIUM SYSTEMS

Perhaps the most commonly cited example of nonequilibrium in the natural environment is the coexistence of O₂ and N₂ in the atmosphere. If equilibrium prevailed, the atmosphere would be depleted of O₂, and the world’s oceans would be dilute solutions of nitric acid or nitrate salts. As illustrated in Example 1-1, this reaction is feasible energetically; nonetheless, its rate is exceedingly slow because of its high activation energy.

Example 1-1. .

Atmospheric Nonequilibrium

The reaction between N₂ and O₂ to produce nitric acid:

$N_2+2\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.O_2+H_{2}O\to 2H^{+}+2N{O}_3^{-}$

(1-1)

is slightly endergonic under standard conditions. From compiled free energies of formation for the reactants and products,² we find that ∆G°, the Gibbs free energy of reaction under standard conditions, of Equation 1-1 is +14.55 kJ mol⁻¹. Recall that standard conditions are 1-atm pressure, 25°C, and unit concentrations (activities) of all reactants and products. The actual free energy of reaction, ∆G, depends on the activities of the reactants and products:

$\text{Δ}G=\text{Δ}G°+RT\ln Q$

(1-2a)

where Q is the reaction quotient (the product of the activities of the products, each raised to its stoichiometric power, divided by the product of the activities of the reactants, each raised to its stoichiometric power). For reaction 1-1, Equation 1-2a becomes

$\text{Δ}G=\text{Δ}G°+RT\ln \left({\left\{H^{+}\right\}}^2{\left\{N{O}_3^{-}\right\}}^2/P_{N_2}{P}_{O_2}^{2.5}\right)$

(1-2b)

The standard free energy of reaction 1-1 at pH 7, ∆G°₇, is-65.3 kJ mol⁻¹; i.e., it isexergonic. However, to calculate the actual value of ∆G, we must substitute actual concentrations of the products and reactants into Equation 1-2b. At equilibrium, ∆G = 0, and the reaction quotient is given the symbol K, which is called the equilibrium constant of the reaction. It is apparent from Equation 1-2a that ∆G° = −RTlnK. The equilibrium constant for reaction 1-1 is

$\text{K}={10}^{-2.6}=\frac{{\left\{H^{+}\right\}}_{aq}^2{\left\{N{O}_3^{-}\right\}}_{aq}^2}{P_{N_2}{P}_{O_2}^{2.5}}$

(1-3)

where {i} denotes the activity of i, and P_i is the partial pressure of i.

Some extreme statements have been made regarding the global equilibrium conditions implied by reaction 1-1. Lewis and Randall⁴ stated that if the reaction proceeded to equilibrium, the world’s oceans would have a nitric acid concentration greater than 0.1 M, and Hutchinson⁵ repeated this conclusion in a widely cited book. Holland⁶ estimated that nitrate activity {NO₃⁻} in the oceans would be 10^5.7 if the reaction were at equilibrium under present conditions of pH, ${\text{P}}_{{\text{N}}_2}$ and ${\text{P}}_{{\text{O}}_2}$. None of these statements represents the actual equilibrium situation under the constraints of reactant availability on a global basis.

According ...

Table of contents

• Cover
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Chapter 1 Overview
• Chapter 2 Rate Expressions for Chemical Reactions
• Chapter 3 Theoretical Aspects of Kinetics and Effects of Physical Conditions on Reaction Rates
• Chapter 4 Kinetics of Chemical Reactions in Aquatic Systems: From Homogeneous Catalysis to Reactions at Interfaces
• Chapter 5 Reactors, Mass Transport, and Process Models
• Chapter 6 Kinetics of Biochemical Reactions and Microbial Processes in Natural Waters
• Chapter 7 Prediction Methods for Reaction Rates and Compound Reactivity
• Chapter 8 Photochemical Reactions in Natural Waters
• Index