The Chemical Equilibrium Problem

Steve and Susan Zumdahl's texts focus on helping students build critical thinking skills through the process of becoming independent problem-solvers. They help students learn to "think like a chemists" so they can apply the problem solving process to all aspects of their lives. In CHEMISTRY: AN ATOMS FIRST APPROACH, 1e, International Edition the Zumdahls use a meaningful approach that begins with the atom and proceeds through the concept of molecules, structure, and bonding, to more complex materials and their properties. Because this approach differs from what most students have experienced in high school courses, it encourages them to focus on conceptual learning early in the course, rather than relying on memorization and a "plug and chug" method of problem solving that even the best students can fall back on when confronted with familiar material. The atoms first organization provides an opportunity for students to use the tools of critical thinkers: to ask questions, to apply rules and models and to

Chemistry 2e is designed to meet the scope and sequence requirements of the two-semester general chemistry course. The textbook provides an important opportunity for students to learn the core concepts of chemistry and understand how those concepts apply to their lives and the world around them. The book also includes a number of innovative features, including interactive exercises and real-world applications, designed to enhance student learning. The second edition has been revised to incorporate clearer, more current, and more dynamic explanations, while maintaining the same organization as the first edition. Substantial improvements have been made in the figures, illustrations, and example exercises that support the text narrative. Changes made in Chemistry 2e are described in the preface to help instructors transition to the second edition.

* The present work is designed to provide a practical introduction to aqueous equilibrium phenomena for both students and research workers in chemistry, biochemistry, geochemistry, and interdisciplin ary environmental fields. The pedagogical strategy I have adopted makes heavy use of detailed examples of problem solving from real cases arising both in laboratory research and in the study of systems occurring in nature. The procedure starts with mathematically complete equations that will provide valid solutions of equilibrium problems, instead of the traditional approach through approximate concentrations and idealized, infinite-dilution assumptions. There is repeated emphasis on the use of corrected, conditional equilibrium constants and on the checking of numerical results by substitution in complete equations and/or against graphs of species distributions. Graphical methods of calculation and display are used extensively because of their value in clarifying equilibria and in leading one quickly to valid numerical approximations. The coverage of solution equilibrium phenomena is not, however, exhaustively comprehensive. Rather, I have chosen to offer funda mental and rigorous examinations of homogeneous step-equilibria and their interactions with solubility and redox equilibria. Many examples are worked out in detail to demonstrate the use of equi librium calculations and diagrams in various fields of investigation.

This 1970 book, the authors derive the equations describing equilibria in different types of system and outline the effect of variation of the parameters of the system on the equilibrium composition by using equilibrium calculations in high temperature, high pressure processes, in rocketry and in explosives technology.

The chemical equilibrium problem--finding the equilibrium composition of a multiphase, multicomponent system--is of interest in the study of chemical systems in general, with many potential applications in biochemistry and biomedicine. The problem can be posed as a nonlinear program, where a convex 'free energy' function is minimized, subject to linear mass balance equations. There is an associated dual chemical problem, equivalent to a geometric program when the system is ideal. This work studies the chemical duality and applies the existing theory of geometric programming to analyze and solve chemical problems. Some general characteristics of free energy functions are developed and are used to analyze the properties of equilibrium solutions. Chemical duality is applied to formulate and solve a class of related problems which are of a different nature than the original chemical equilibrium problem. A dual cutting-plane algorithm is adapted from a method developed for geometric programs and is tested and compared to a standard chemical equilibrium code. Geometric programming theory is extended to include forms having variables as exponents. The resulting 'transcendental geometric programs' are shown to be a generalization of chemical problems, where the system is not ideal.

It has long been known that the problem of determining the equilibrium composition of a solution of chemically reacting species could be formulated as a constrained minimum problem. Previous methods for solving the chemical equilibrium problem in this form have had much success. However, all such methods run into trouble whenever degeneracy or near-degeneracy occurs during the computational procedure. The paper shows that the constrained minimum formulation of the chemical equilibrium problem is equivalent to a generalized linear program which can in turn be replaced by a quadratic program. In these alternative forms, degeneracy is more easily accomodated than in previous methods. (Author).

An investigation of the use of mathematical models to explore the chemical aspects of physiological systems; this deals with the theoretical and computational aspects of understanding the chemistry of human physiological function. The question of existence of solutions to problems having unbounded constraint sets is investigated by relating their existence (or nonexistence) to a property of a solution to an auxiliary chemical equilibrium problem with a bounded constraint set. An example system is selected consisting of gases in contact with an aqueous buffer solution at a uniform total hydrostatic pressure and temperature. The numerical problem of determining the amount of CO2 to be added to achieve a specified partial pressure of CO2 in the gas phase, and its effects on the composition of the total system, is solved by using a procedure suggested by the concept of unbounded constraint sets. Findings may apply to design of artificial life-support systems needed in extraterrestrial environments related to Air Force missions. (Author).

Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn