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Über dieses Buch

The authors explain at length the principles of chemical kinetics and approaches to computerized calculations in modern software suites

— mathcad and maple. Mathematics is crucial in determining correlations in chemical processes and requires various numerical approaches. Often significant issues with mathematical formalizations of chemical problems arise and many kinetic problems can´t be solved without computers. Numerous problems encountered in solving kinetics´ calculations with detailed descriptions of the numerical tools are given. Special attention is given to electrochemical reactions, which fills a gap in existing texts not covering this topic in detail. The material demonstrates how these suites provide quick and precise behavior predictions for a system over time (for postulated mechanisms).Examples, i.e., oscillating and non-isothermal reactions, help explain the use of mathcad more efficiently. Also included are the results of authors’ own research toward effective computations.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Formally-Kinetic Description of One- and Two-Step Reactions

Abstract
We must accept that in order to describe the chemical system it is urgent for us to know the exact way it follows during the transformation of the reagents into the products of the reaction. Knowledge of that kind gives us a possibility to command chemical transformation deliberately. In other words, we need to know the mechanism of the chemical transformation. Time evolution of the transition of the reactionary system from the unconfigured state (parent materials) to the finite state (products of the reaction) is of great importance too, because it is information of how fast the reaction goes. Chemical kinetics is a self-contained branch of chemical knowledge, which investigates the mechanisms of the reactions and the patterns of their passing in time, and which gives us the answers to questions from above.
Viktor I. Korobov, Valery F. Ochkov

Chapter 2. Multi-Step Reactions: The Methods for Analytical Solving the Direct Problem

Abstract
If a reaction proceeds by a large number of elementary steps and involves many different substances, developing its mathematical model “by hand” turns into a quite exhausting procedure fraught with different possible errors, especially provided complicated reaction stoichiometry. This stage can be considerably simplified by using matrix algebra suits.
Viktor I. Korobov, Valery F. Ochkov

Chapter 3. Numerical Solution of the Direct Problem in Chemical Kinetics

Abstract
Previously discussed analytical methods for solving the direct problem in chemical kinetics are not sufficient for analysis of different reaction kinetic schemes. First, even given the mathematical model represented by an ODE system, it is not always possible to integrate the equations analytically. The reason for that may be just an absence of such a solution. This refers primarily to a large number of kinetic models in which differential equations are non-linear relative to the sought functions. Second, if the analytical solution is obtained, it is often to lengthy and awkward. Finally, there is a large class of real mathematical models that are described by partial differential equation sets, which cannot be integrated numerically. Thus, the series of mathematical problems that can be solved with the previously discussed numerical integration methods is quite narrow. That is why, in order to solve the direct problem, we have to rely on more universal approaches. Such approaches are based on using numerical integration of differential equations and systems.
Viktor I. Korobov, Valery F. Ochkov

Chapter 4. Inverse Chemical Kinetics Problem

Abstract
As opposed to direct chemical kinetics problem, inverse problem consists of finding the kinetic parameters of the reactive system (reaction orders, reaction rates of separate steps, activation energies) based on experimental data. Generally speaking, the goal of solving the inverse problem is to determine the mechanism of a complex chemical process (again, the term “mechanism” is used here in a formal kinetics meaning as opposed to the elementary step mechanism). The problem can be formulated mathematically as the following. A set of kinetic data points is obtained experimentally. Usually it is a set of the concentration values at specific moments of time. Additionally, a kinetic scheme of the process is postulated in a form of hypothesized elementary steps. This scheme is represented with a specific mathematical model that includes the rate constants of separate steps. Consequently, it is necessary to calculate the constants so that they fit the experiment. One can see here the main feature of inverse problems: the initial data is obtained experimentally and, thus, contains measurement errors.
Viktor I. Korobov, Valery F. Ochkov

Chapter 5. Introduction into Electrochemical Kinetics

Abstract
A special kind of chemical reactions are the redox (reduction–oxidation) processes in electrochemical circuits – the systems consisting of two metal electrodes in solution of electrolyte (internal circuit) that are connected using an electronic conductor (external circuit). Electrolytic and Galvanic cells are the examples of electrochemical circuits. The reactions occurring in such cells are called electrochemical reactions to stress out their essential difference from ordinary chemical processes.
Viktor I. Korobov, Valery F. Ochkov

Chapter 6. Interface of Mathcad 15 and Mathcad Prime

Abstract
This is a general way to solve a problem in Mathcad: a user usually types the (new) input data and some operators in the worksheet, using his own or template algorithms and obtains a result. This chapter contains description of the tools for the input and display of data as well as a review of their development and their critical analysis.
Viktor I. Korobov, Valery F. Ochkov

Chapter 7. Problems

Abstract
Show by computer means, that all tangents, drawn to the starting points of kinetic curves for an irreversible first-order reaction with rate constant k, intersect time axis at the same point. What is the physical meaning of the abscissa of the intersection point?
Viktor I. Korobov, Valery F. Ochkov

Backmatter

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