Introduction to Chemical Kinetics

Chapter 1

Introduction

1.1 Chemical kinetics

Chemical kinetics is the branch of chemistry that deals with the rates or velocity, at which a chemical reaction occurs and also the factors affecting the rates. The word “kinetic” means the movement or change; here it refers to the velocity of a reaction, which is the change in the concentration of a reactant or a product with time.

Kinetic investigation of a reaction is usually carried out with two main objectives in mind.

1. Analysis of the sequence of elementary reactions leading to the overall reaction. i.e. To arrive at the plausible reaction mechanism.
2. Determination of absolute rate of the reaction.

There are several reasons for studying the kinetics of a reaction. At the outset, there is an essential curiosity about “why some reactions are fast and some are slow?” Some phenomena, like photosynthesis, hydrocarbon combustion and nuclear reactions, take place on a time scale as short as pico seconds to micro seconds. Other processes like the setting and hardening of cement and the transformation of graphite to diamond, take longer period of time to complete. Practically, a good understanding of reaction rates is useful, in waste water treatment, in pollution control, in drug design and in food processing. Chemists working in industry give more importance to speed up the rate of a reaction and also to increase the productivity.

Chemical kinetics is a tool to understand fundamental aspects of reaction pathways, a subject that continues evolution with ongoing research. The knowledge rate of reaction has many practical applications. The kinetic study provides the valuable information about the rate and mechanism of chemical reaction, which helps out in running a chemical reaction successfully by selecting optimum reaction conditions.

Generally, reactions are represented by following equation

Reactants →Products

This equation indicates that as the reaction proceeds, reactants are consumed and products are formed. Consequently, the progress of the reaction can be followed by monitoring the change in the concentration of reactants (decrease) or products (increase).

The kinetic investigation also helps us to study the factors which have an effect on the rate of reaction like temperature, pressure, substrate concentration, oxidant concentration, dielectric constant, ionic strength and catalyst concentration. For example, kinetic study helps in optimizing reaction conditions for industrial processes, in understanding the complex dynamics of the environmental problems, in understanding the very complicated bio-chemical reactions that are the basis of life. Generally, reactions involving organic reactants have several plausible pathways. Kinetic analysis of atmospheric reactions helps us to understand chemical transformations of pollutants released in the atmosphere. At a more fundamental level, we want to understand what happens to the molecules in a chemical reaction. By understanding this concept we can develop the theories, which can be used to predict the outcome and rate of reactions.

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We presume that in order to react, the colliding molecules must possess a total kinetic energy equal to or greater than the activation energy (Ea). The activation energy is the minimum energy required to start a chemical reaction. When molecules collide, they form an activated complex (also called the transition state or quasi equilibrium state), formed as a result of the collision of reactant molecules before they form the product.

A +B → AB^‡ → C + D

Where AB^‡ denotes an activated complex formed by the collision between A and B. If the products are more stable than the reactants, then the reaction occurs with a release of heat; i.e., the reaction is exothermic. Conversely, if the products are less stable than the reactants, then the reaction occurs with the absorption of heat from the surroundings; i.e., the reaction is endothermic. The plots of potential energy of the reacting system versus the progress of the reaction qualitatively show the potential energy changes as reactants are converted in to products.

The Arrhenius Equation

The Arrhenius equation explains dependence of the rate constant of a reaction on temperature:

k = Ae^-Ea/RT —– (1)

Where,

Ea →activation energy of the reaction (in kJ/mol),

R→ Universal gas constant (8.314 J/K/ mol),

T → absolute temperature

A → frequency factor which represents frequency of collision. It can be treated as a constant for a given reacting system over a reasonably wide temperature range. Equation (1) shows that the rate constant is directly proportional to frequency factor (A) and, therefore, to the collision frequency. Further, due to the negative sign on exponent Ea/RT, the rate constant decreases with increasing activation energy and increases with increasing temperature. This equation can be simplified by taking the natural logarithm on both sides,

ln k = ln Ae^–Ea/RT ——(2)

—— (3)

Rearrangement of equation (3) leads to the following linear equation,

—– (4)

Therefore, a plot of ln k versus 1/T gives a straight line with a slope m and intercept c. The slope m is equal to Ea/RT and the intercept c is equal to ln A.

One of the important uses of chemical kinetics is to provide the information which is required to propose the plausible mechanism of a reaction. The order of a reaction can be used to interpret the reaction on molecular level. The reaction mechanism is predicted in the way in which molecular bonds break and atoms rearrange during the reaction by considering the order of a reaction with respect to different reactive species. Almost all the information regarding reaction mechanism comes by implication of indirect evidence.

It is the responsibility of chemists to plan the proper experimental method to generate most conclusive truths or evidences for the reaction. The main steps in any kinetic study are; (1) measurement of rate constant and reaction order (2) establishment of relationships between the rate and reaction mixture composition (3) identification of intermediates and products and (4) interpretation of the collected data to arrive at plausible reaction mechanism.

If Chemistry is producing new substances out of old substances (i.e., chemical reactions), then there are two basic questions that must be answered:

1. Is the reaction feasible? This is the subject of chemical thermodynamics.
2. If the reaction is feasible then how fast? This is the subject of chemical kinetics.

Kinetic studies constitute an important source of mechanistic information on the reaction, this is well demonstrated with respect to unsaturated acids in both aqueous [[1]–[2]] and non-aqueous media [[3]].

1.1.1 The main importance of kinetic investigations are

1. Product and intermediate identification.
2. Determination of concentration of all reactant species present in the reaction.
3. Deciding the method may be used to determine the rate.
4. The kinetic analysis.
5. Determination of the mechanism.

1.1.2 Applications of kinetics

The chemist uses kinetics to plan new and better ways of achieving desired chemical reactions. This may involve in increasing the yield of desired products or discovering a better catalyst. The mathematical models, which are used by chemists and chemical engineer to predict chemical kinetics, provide information to understand and describe chemical processes such as ozone depletion, waste water treatment, decaying of food and vegetables, microorganism growth, and the chemistry of biological systems. The mathematical models can also be applied in the design and fabrication of chemical reactors for optimization to get good yield, better separation of products, and to eliminate environmentally hazardous by-products.

Kinetics has an ample of applications in the field of medicine. Chemical kinetics plays an important role in the administration of drugs, in addition to respiration and metabolism mechanisms. For example, the mechanisms for the controlled/sustained release of drugs are based on the half-life period of the substances used and sometimes the pH of the body as well. Half life period and pH have an effect on the way in which dosages are determined and prescribed. The reaction rates and the conditions in which the reactions occur are vital for determining certain aspects of environmental protection. For example, the depletion of ozone layer by chlorofluorocarbons (CFCs) is best understood through an analysis of catalyzed chemical reactions.

1.1.3 Kinetic Methods in chemical analysis

For catalyzed reactions the rate of reaction depends on the catalyst concentrations and hence, a kinetic–catalytic method of analysis of the catalytic species becomes available. Thus, a method of analysis can be developed down to the ppm level in several cases [[4]-,[5][6]].

The development of kinetic methods is an inseparable part of modern analytical chemistry. Great demands are placed on the precision, sensitivity, rapidity and possible automation of analytical methods. This necessitates progress in the physico-chemical methods, employing the most varied chemical, physico-chemical and physical properties of substances for their analysis. As reactions from the basis of most analytical methods, it is unimaginable that the dynamic character of chemical reactions would remain unused for analytical purposes. As has been shown recently, kinetic methods often provide the solution to the analytical problems more effectively than is possible using equilibrium methods [[7]].

Certainly, the most widespread use of kinetic methods is in biochemical and clinical laboratories, where analysis is based on kinetics than on thermodynamics.

1.2 Electron transfer reactions

Electron transfer reactions play a key role in physico-chemical and biological processes. Because of the ubiquity of electron transfer processes, the study of electron transfer reactions, perhaps more so than that of any other area of chemistry is characterized by a strong interplay of theory and experiment [[8]]. The significance of electron transfer reaction in transition metal chemistry and in physical-organic chemistry is well documented [[9]–[10]].

Prof. R. A. Marcus received Nobel Prize in the year 1992 for the discovery of “Electron Transfer Reactions” and Prof. Ahmed Zewail received Nobel Prize in the year 1999 for the discovery of “Femtochemistry” and 2001 Nobel prize to Prof. William Knowles, Prof. K. Barry Sharpless and Prof. Royji Noyori for their work on “Chirally Catalyzed Hydrogenation Reactions” and Nobel Prize for the year 2005 to Prof. Robert Grubbs, Richard Schrock, and Yves Chauvin on their contribution to “Metathesis Catalyst Technology” put emphasis on the importance of reaction kinetics.

The research work of Henry Taube [[11]] in redox systems explicitely demonstrated the transport of electron from reductant species to oxidant species. This discovery indeed added many essential features in the syntheses of metal complexes and organo-metallic compounds. An oxidation reaction is always accompanied by a reduction reaction, such reactions are called redox reactions [[12]]. Therefore, redox reaction needs at least two reactants, one capable of gaining electrons (oxidant) and the other capable of losing electrons (reductant), i.e., a reductant by losing electrons, gets oxidized and an oxidant by gaining the electrons gets reduced. Redox reactions are the basis for various biochemical transformations and chemistry of cells, biosynthesis, and regulation [[13]].

Electron transfer reactions may take place through outer or inner sphere mechanisms.

References

[1]. R. Stewart, Oxidation in Organic Chemistry, in K.B. Wiberg (Ed.), Part A., Academic Press, New York, 1965.

[2]. D. G. Lee, E. J. Lee and K. C. Brown, Phase Transfer Catalysis, New Chemistry, Catalysts and Applications, ACS Symposium Series No. 326, American Chemical Society, Washington, DC, 1987.

[3].J. F. Perez-Benito and D. G. Lee, Kinetics and mechanism of the oxidation of unsaturated carboxylic acids by methyl tributyl ammonium permanganate in methylene chloride solutions, J. Org. Chem., Vol. 52, 1987, pp.3239-3243.

[4] . S. M. Tuwar, S. T. Nandibewoor and J. R. Raju, Analysis of Palladium (II) by a kinetic method and Mercury (I) by volumetry. Indian J. Chem., Vol.29A, 1990, pp. 825-826.

[5].S.T.Nandibewoor and V. A. Morab, Chromium(iii)-catalyzed oxidation of antimony(iii) by alkaline hexacyanoferrate(iii) and analysis of chromium(iii) in microamounts by a kinetic method,J. Chem. Soc. Dalton Trans., 1995, pp.483-488.

[6]. P. L. Timmanagoudar, G. A. Hiremath and S. T. Nandibewoor, Osmium(viii) catalyzed oxidation of antimony(iii) by alkaline hexacyanoferrate(iii) and analysis of osmium(viii) in micro amount by a kinetic method, Indian J. Chem.,Vol. 35A, 1996,pp.1084-1090.

[7]. G. Svehla, “Kinetic Methods in Chemical Analysis Application of Computers in Analytical Chemistry”, Elsevier Scientific Publishing Company, New York, Vol. 18, 1983, pp. 19.

[8] . J. J. Zuckerman, “Inorganic Reactions and Methods”, VCH Publishers, Florida, Vol. 15, 1986, pp.1-22.

[9] . Sir. G. Wilkinson, “Comprehensive Coordination Chemistry”, Pergamon Press, Vol. 1, 1987, pp.327-332.

[10] . R. A. Sheldon and J. K. Kochi, “Metal Catalyzed Oxidation of Organic Compounds”, Academic Press, New York, 1981, pp. 387-407.

[11]. H. Taube, Electron Transfer Reactions of Metal Complexes in Solution”, Academic Press, New York, 1967.

[12] . H. J. Price and H. Taube, Reduction of α-carbonylcarboxylic acid complexes of pentaamminecobalt (III) by chromous, vanadous, and hexaammineruthenium(II) ions, Inorg. Chem., Vol. 7 (1), 1968, pp. 1–9.

[13]. J. H. Espenson, Inner-Sphere Reduction of an Azidocobalt(III) Complex by Vanadium(II). Kinetics of Formation and Decomposition of the Metastable Monoazidovanadium (III) Ion, J. Am. Chem. Soc., Vol.89 (5), 1967,pp. 1276–1278.