Chemical Kinetics with Mathcad and Maple

Foreword

Chapter 1. Formally-kinetic description of one- and two-step reactions

1.1 Main concepts of chemical kinetics

1.2 Kinetics of simple reactions

1.3 Reactions, which include two elementary steps

1.3.1 Reversible (two-way) reactions

1.3.2 Consecutive reactions

1.3.3 Parallel reactions

1.3.4 Simplest self-catalyzed reaction

Chapter 2. Multi-step reactions: the methods for analytical solving the direct problem

2.1 Developing a mathematical model of a reaction

2.2 The classical matrix method for solving the direct kinetic problem

2.3 The Laplace transform in kinetic calculations

2.3.1 Brief notes from operational calculus

2.3.2 Derivation of kinetic equations for linear sequences of first-order reactions

2.3.3 Transient regime in a system of flow reactors

2.3.4 Kinetic models in the form of equations containing piecewise continuous functions

2.4 Approximate methods of chemical kinetics

2.4.1 The steady-state concentration method

2.4.2 The quasi-equilibrium approximation. Enzymatic reaction kinetics

Chapter 3. Numerical solution of the direct problem in chemical kinetics

3.1 Given/Odesolve solver in Mathcad system

3.2 Built-in Mathcad integrators

3.3 The Maple system commands dsolve, odeplot in numerical calculations

3.4 Oscillation processes modeling

3.5 Some points on non-isothermal kinetics

Chapter 4. Inverse chemical kinetics problem

4.1 Features of the inverse problem

4.2 Determination of kinetic parameters using data linearization

4.2.1 Hydrolysis of methyl acetate in acidic media

4.2.2 Butadiene dimerization: finding the reaction order and the rate constant

4.2.3 Exclusion of time as an independent variable

4.2.4 Linearization with numerical integration of kinetic data. Basic hydrolysis of diethyl adipate

4.2.5. Estimation of confidence intervals for the calculated constants

4.2.6 Kinetics of α-pinene isomerization

4.3 Inverse problem and specialized minimization methods

4.3.1 Deriving parameters for an empirical rate equation of phosgene synthesis

4.3.2 Kinetics of trans-stilbene isomerization

4.3.3 Kinetics of stepwise ligand exchange in chrome complexes

4.4 Computing kinetic parameters using non-linear approximation tools

4.5 Universal approaches to inverse chemical kinetics problem

4.5.1 Reversible reaction with dimerization of an intermediate

4.5.2 Thermal decomposition of disilane

Chapter 5. Introduction into electrochemical kinetics

5.1 General features of electrode processes

5.2 Kinetics of the slow discharge-ionization step

5.3 Electrochemical reactions with stepwise electron transfer

5.4 Electrode processes under slow diffusion conditions

5.4.1 Relationship between rate and potential under stationary diffusion

5.4.2 Nonstationary linear diffusion to a planar electrode under electrostatic conditions

5.4.3 Nonstationary diffusion to a spherical electrode under potentiostatic conditions

5.4.4 Nonstationary diffusion under galvanostatic conditions

Chapter 6. Interface of Mathcad 15 and Mathcad Prime

6.1 Input/displaying of data

6.2 VFO (Variable-Function-Operator)

6.2.1 Function and operator

6.2.2 Variable name

6.2.3 Invisible variable

Example 1. Invisible addition

Example 2. Zero dimension quantity

Example 3. The Roman arithmetic

Example 4. The sparse matrix

Example 5. Displaying a dimensional value in several units

Example 6. An endless loop

Example 7. A Mathcad user’s dream

6.3 Comments in Mathcad worksheets

6.4 Calculation with physical quantities: problems and solutions

6.5 Three dimensions of Mathcad worksheets

6.6 Mathcad plots

6.7

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.