"Chemical Reaction Equilibrium Analysis: Theory and Algorithms", Krieger, 1991

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The text Chemical Reaction Equilibrium Analysis: Theory and Algorithms, W. R. Smith and R. W. Missen, Krieger Publishing, Malabar, Fla, 1991 (a reprint, with corrections, of the same title by Wiley-Interscience, 1982) is one of the most comprehensive treatments of the theory of chemical reaction equilibria and its computation.

It is addressed to chemical engineers, chemists, aquatic chemists, geochemists, metallurgists, physicists, and those in many other fields for which chemical reaction and phase equilibrium is an important modeling tool. It is suitable for senior undergraduate and graduate-level study in these fields, or for the industrial practitioner who wishes to use and understand chemical equilibrium modeling in their work.

In the text, it is shown how chemical equilibrium problems from many fields may be considered as variations of a single formulation. For example, aquatic chemists and geochemists frequently study equilibrium problems from the point of view of sets of chemical reactions and their associated equilibrium constants. On the other hand, combustion scientists study equilibrium problems using species-specific thermochemical data (e.g., free energies of formation). As a result of this historical development, researchers in different fields have typically considered special approaches for each type of problem. This text shows how both problem types may be viewed as being essentially identical, permitting the the use of a single theoretical and numerical approach.

In addition to more standard types of equilibrium problems, many related topics and special problem types are also considered in the text, including:

  • a comprehensive treatment of chemical reaction stoichiometry
  • obtaining species standard free energy data from equilibrium constant data
  • a description of the qualitative and quantitative effects of varying the problem parameters (essentially, the extension of Le Chatelier's Principle to multi-reaction systems)
  • how to treat isomeric forms of a substance as a single species
  • how to treat equilibrium problems with kinetic or other stoichiometric restrictions
  • how to calculate general thermodynamic properties of a reacting system

Table of Contents

  1. Introduction
    • The nature of chemical equilibrium
    • The importance of chemical reaction equilibrium analysis
    • The problem of computation
    • The constraints
    • Applications of chemical equilibrium analysis
    • Historical sketch
  2. The Closed-System Constraint and Chemical Stoichiometry
    • The approach
    • The closed-system constraint
    • Chemical stoichiometry
    • Expressing compositional restrictions in standard form
  3. Chemical Thermodynamics and Equilibrium Conditions
    • Thermodynamic potential functions and criteria for equilibrium
    • Thermodynamic description of a chemical system
    • Two formulations of the equilibrium conditions
    • The stoichiometric formulation
    • The nonstoichiometric formulation
    • Equivalence of the two formulations
    • The chemical potential
    • Implications of the nonnegativity constraint
    • Existence and uniqueness of solutions
    • The stoichiometric formulation in terms of equilibrium constants
    • Electrochemical cells
    • Ways in which standard free-energy information is available
    • Sources of data
  4. Computation of Chemical Equilibrium for Relatively Simple Systems
    • Relatively simple systems and their treatment
    • Remarks on choice of formulation
    • Stoichiometric formulation for relatively simple systems
    • Nonstoichiometric formulation for relatively simple systems
  5. Survey of Numerical Methods
    • Two classes of numerical problem
    • Minimization problems
    • Nonlinear equation problems
    • Step-size parameter and convergence criteria
  6. Chemical Equilibrium Algorithms for Ideal Systems
    • Classification of algorithms
    • Structure of chapter
    • Nonstoichometric algorithms
    • Stoichiometric algorithms
    • Composition variables other than mole fraction
  7. Chemical Equilibrium Algorithms for Nonideal Systems
    • The transition from ideality to nonideality
    • Further discussion of chemical potentials in nonideal systems
    • Algorithms for nonideal systems
  8. The Effects of Problem Parameter Changes (Sensitivity Analysis)
    • Overall effects of parameter changes
    • Effects of problem parameter changes on optimization problems and nonlinear equations
    • Qualitative effects of parameter changes on chemical equilibria
    • Sensitivity matrices for (T,P) problems
    • Effects of errors in free energy data on equilibrium composition
    • Calculation of thermodynamic derivatives for a system at chemical equilibrium
  9. Practical Considerations and Special Topics
    • Initial estimates for equilibrium algorithms
    • Numerical singularities and the nonnegativity constraint
    • The case of C = Rank(A) not equal to M
    • Standard free-energy data from equilibrium constants
    • Species present in small amounts
    • Restricted equilibrium problems
    • Treatment of isomers
    • Treatment of isotopes
    • Thermodynamic constraints other than (T,P)