Experimental Methods

A kinetic study generally proceeds after the reactants, products and stoichiometry of the reaction have been satisfactorily characterized. The more one knows about the chemistry of the reaction, the better the conclusions that one can draw from a kinetic study. The discussion here describes techniques often used in inorganic studies, emphasizes their time range and general area of applicability and gives some examples of their use. Further details can be found in other sources. Any experimental kinetic method must somehow monitor change of concentration with time. Many studies are done under pseudo-first-order conditions, and then one must monitor the deficient reactant or product(s) because the other species undergo small changes in concentration. The kinetic method(s) of choice often will be dictated by the time scale of the reaction. The detection method(s) will be determined by the spectroscopic properties of the species to be monitored. The efficient use of materials can be a significant factor in the choice of method because a kinetic study generally involves a number of runs at different concentrations and temperatures, and conservation of difficult to prepare or expensive reagents may be a critical factor. The detection method should be as species specific as possible, and ideally one would like to measure both reactant disappearance and product formation. The method must not be subject to interference from other reactants and should be applicable under a wide range of concentration conditions so that the rate law can be fully explored. Often there is a practical trade-off between specificity, sensitivity and reaction time. For example, NMR is quite specific but rather slow and has relatively low sensitivity, unless the system allows time for signal accumulation. Spectrophotometry in the UV and visible range often has good sensitivity and speed, but the specificity may be poor because absorbance bands are broad and intermediates may have chromophoric properties similar to those of the reactant and/or product. Vibrational Spectrophotometry can be better if the IR bands are sharp, as in the case of metal carbonyls, but the solvent must be chosen to provide an appropriate spectral window.

Stereochemical Change

The kinetic and mechanistic aspects of this general area tend to be strongly dependent on the particular system. This makes general treatments and explanations impossible, at least at the current stage of understanding. Various aspects of this area have been summarized in some general reviews. Ligands bonded to a metal can undergo a number of structural changes that do not involve complete breaking of the metal-ligand bond(s). Such processes are the subject of the following sections. Many chelate ligands have conformers that can interconvert. For example, the conformers of ethylenediamine interchange by rotation about the carbon-carbon bond, as shown in the following structures: The Ha and Ha' protons are magnetically different from the Hb and Hb' protons, so their interconversion can, in principle, be studied by NMR. These protons may be referred to as exo and endo, respectively. In simple systems, their interconversion is too rapid (k >106 s-1) for this method. However, if there is some constraint (e.g., CH3 groups) or if the coordinating atoms are part of a larger chelate system, then interconversion is slow enough to be detected by NMR. In nonplanar Fe(III)- tetraphenylporphyrinates, the ring inversion rates vary widely, depending on the axial ligand and the substituents on the porphyrin.

Ligand Substitution Reactions

In ligand substitution reactions, one or more ligands around a metal ion are replaced by other ligands. In many ways, all inorganic reactions can be classified as either substitution or oxidation-reduction reactions, so that substitution reactions represent a major type of inorganic process. Some examples of substitution reactions follow: The operational approach was first expounded in 1965 in a monograph by Langford and Gray. It is an attempt to classify reaction mechanisms in relation to the type of information that kinetic studies of various types can provide. It delineates what can be said about the mechanism on the basis of the observations from certain types of experiments. The mechanism is classified by two properties, its stoichiometric character and its intimate character. The Stoichiometric mechanism can be determined from the kinetic behavior of one system. The classifications are as follows: 1. Dissociative (D): an intermediate of lower coordination number than the reactant can be identified. 2. Associative (A): an intermediate of larger coordination number than the reactant can be identified. 3. Interchange (I): no detectable intermediate can be found. The intimate mechanism can be determined from a series of experiments in which the nature of the reactants is changed in a systematic way. The classifications are as follows: 1. Dissociative activation (d): the reaction rate is more sensitive to changes in the leaving group. 2. Associative activation (a): the reaction rate is more sensitive to changes in the entering group. This terminology has largely replaced the SN1, SN2 and so on type of nomenclature that is still used in physical organic chemistry. These terminologies are compared and further explained as follows: Dissociative [D = SN1 (limiting)]: there is definite evidence of an intermediate of reduced coordination number. The bond between the metal and the leaving group has been completely broken in the transition state without any bond making to the entering group. Dissociative interchange (1d= SN1): there is no definite evidence of an intermediate. In the transition state, there is a large degree of bond breaking to the leaving group and a small amount of bond making to the entering group.

Inorganic Photochemistry

Electromagnetic radiation in the form of UV and visible light has long been used as a reactant in inorganic reactions. The energy of light in the 200- to 800-nm region varies between 143 and 36 kcal mol-1, so it is not surprising that chemical bonds can be affected when a system absorbs light in this readily accessible region. Systematic mechanistic studies in this area have benefited greatly from the development of lasers that provided intense monochromatic light sources and from improvements in actinometers to measure the light intensity. Prior to the laser era, it was necessary to use filters to limit the energy of the light used to a moderately narrow region or to just cut off light below a certain wavelength. Pulsed-laser systems also allow much faster monitoring of the early stages of the reaction and the detection of primary photolysis intermediates. The systems discussed in this chapter have been chosen because of their relationship to substitution reaction systems discussed previously. For a broader assessment of this area, various books and review articles should be consulted. Mechanistic photochemistry incorporates features of both electron-transfer and substitution reactions, but the field has some of its own terminology, which is summarized as follows: The quantum yield,F , is the number of defined events, in terms of reactant or product, that occur per photon absorbed by the system. An einstein, E, is defined as a mole of photons, and if n is the moles of reactant consumed or product formed, then F = n/E. For simple reactions F£ 1 but can be >1 for chain reactions. An actinometer is a device used to measure the number of einsteins emitted at a particular wavelength by a particular light source. Photon-counting devices are now available and secondary chemical actinometers have been developed, such as that based on the Reineckate ion, Cr(NH3)2(NCS)4-, as well as the traditional iron(III)-oxalate and uranyl-oxalate actinometers. An early problem in this field was the lack of an actinometer covering the 450- to 600-nm range and the Reineckate actinometer solved this problem.

Oxidation-Reduction Reactions

For most purposes, inorganic reactions can be classified as either substitution reactions or oxidation-reduction reactions. The latter involve the transfer of at least one electron from the reducing agent to the oxidizing agent. Such reactions are widely used in analytical procedures and are important in many biological processes. One of the mechanistic types in this area is unique in having a fairly simple theoretical basis for predicting rate constants in solution from measurable input parameters. Oxidation-reduction reactions have been classified in two general ways; the first, historically, is by stoichiometry and the second is by mechanism. The Stoichiometric classification only requires a knowledge of the reaction stoichiometry but has limited kinetic applicability. The change in oxidation state of the reducing agent is the same as the change in oxidation state of the oxidizing agent.

Reaction Mechanisms of Organometallic Systems

The general principles discussed in Chapter 3 also apply to reactions of organometallic complexes. Because these systems do not have a wide range of structurally similar complexes with different metal atoms for comparative studies across the Periodic Table, comparisons are usually made down a particular group. However, there is a wide range of ligands available for studies of entering and leaving group effects. This area has been the subject of several recent reviews. A major difference from the systems discussed in Chapter 3 is that many of these complexes are soluble in organic solvents, including hydrocarbons. This can minimize the complicating factor of solvent coordination, but these solvents often have quite low dielectric constants so that various types of preassociation are more probable. The metal carbonyl family of compounds is typical of the range of structures and reactivities of organometallic complexes. The rate of CO exchange was examined in early studies, and this work is the subject of a recent review. The order of reaction rates is as follows: Where the rate law has been determined, the reaction is first-order in [M(CO)R] and zero-order in [CO]. This implies a D mechanism, since a solvent intermediate is unlikely for the "noncoordinating" solvents. This mechanism also is probable for other ligand substitutions. The main mechanistic exception to the above generalizations is V(CO)6, which has an Ia mechanism for PR3 substitution reactions. This compound is unique in that it is the only 17-electron metal carbonyl and also is by far the most labile. Some kinetic results for substitution on V(CO)6 in hexane are given in Table 5.1. The substitution rates have rather low ΔH* values, and the negative ΔS* values are typical of an associative process. The rates for various entering groups correlate with the basicity rather than the size, as measured by the cone angle. It has been suggested that formation of a 19-electron associative intermediate from a 17-electron reactant is much more favorable than a 20-electron intermediate from an 18-electron reactant.

Tools of the Trade

This chapter covers the basic terminology and theory related to the types of studies that are commonly used to provide information about a reaction mechanism. The emphasis is on the practicalities of determining rate constants and rate laws. More background material is available from general physical chemistry texts and books devoted to kinetics. The reader also is referred to the initial volumes of the series edited by Bamford and Tipper. Experimental techniques that are commonly used in inorganic kinetic studies are discussed in Chapter 9. As with most fields, the study of reaction kinetics has some terminology with which one must be familiar in order to understand advanced books and research papers in the area. The following is a summary of some of these basic terms and definitions. Many of these may be known from previous studies in introductory and physical chemistry, and further background can be obtained from textbooks devoted to the physical chemistry aspects of reaction kinetics.

Kinetics in Heterogeneous Systems

In this Chapter, a heterogeneous system is one in which the reactants are present in at least two phases. The discussion will concentrate on two such conditions, two-phase gas/liquid systems and three-phase gas/liquid/solid systems. Chemists tend to favor homogeneous conditions, with the reactants all in one phase, because they provide more controlled and reproducible conditions. However, heterogeneous conditions are often preferred in industrial processes because of the ease of separating the catalyst from the products. In many mechanistic studies, heterogeneity adds a complicating feature to be avoided, but there are times when this cannot be done, or when it happens unexpectedly. In gas/liquid systems, the gas often has limited solubility in the liquid which contains the other reagents. As a consequence, there can be problems of mass transport of the gaseous reactant from the gas to the liquid phase. Mass transport can limit the concentration of the gas in the liquid and/or become a rate-limiting feature of the system. These features can confuse interpretations of product distributions and rate laws. The gas/liquid/solid systems generally involve reactants in the gas and liquid phases and a catalyst as the solid phase. In some cases, the solid may be produced from initially homogeneous conditions, and a question arises as to whether the real catalyst is the original species added or the solid product formed under the reaction conditions. There are further questions about the factors that may control the rate of the catalytic process. In the chemistry laboratory, these systems are most often encountered with the gases H2 or CO reacting with substrate and possibly a catalyst in the liquid phase. For the mechanistic interpretation of kinetic observations, an important factor is the rate of mass transfer of the gas to the liquid phase. The rate of gas absorption into the liquid is typically represented as a first order process, driven by the difference between the saturated gas concentration [G(I)]f and the concentration at any time [G(I)], as given by where kLA is an effective first-order rate constant. This constant is taken as a product of an inherent absorption rate constant, kL, and something related to the surface area of the liquid phase, A.

Bioinorganic Systems

The field of bioinorganic chemistry has grown tremendously in the past 25 years. Much of the work is concerned with establishing the coordination site, ligand geometry and metal oxidation state in biologically active systems. The field also extends to the preparation and characterization of simpler model complexes that mimic the spectroscopic properties and perhaps some of the reactivity of the biological system. Much of this characterization work must precede meaningful mechanistic studies. Williams has provided an interesting overview of metal ions in biology from an inorganic perspective. There are several early review series and specialized journals devoted to the subject, and a recent issue of Chemical Reviews is devoted to the area. There also are several books covering general aspects of the subject. The field is so large and the systems are so individualistic that it is necessary, for the purposes of a text such as this, to choose a few sample systems as illustrative of the mechanistic achievements and problems. Studies of bioinorganic systems inevitably use some terminology from biochemistry which may be unfamiliar to an inorganic chemist. The examples in this Chapter are all metalloenzymes which catalyze some process. Clearly they contain a metal, but there are other components of an enzyme, and terms used to describe these are summarized as follows: An apoenzyme is a polypeptide whose composition, peptide sequence and structure depend on the biological source of the metalloenzyme. Typically, the molar mass of the polypeptide is in the range of 1.5-5xl05 daltons. The polypeptide is folded into coils and sheets whose shape is determined by electrostatics and hydrogen bonding. These terms designate the same type of component, but one or the other is used more commonly for a particular system. This is a nonprotein component which binds to the apoenzyme to produce the active catalyst. It is not covalently bonded to the apoenzyme and can be removed by relatively mild denaturation of the polypeptide. Common bioinorganic examples are coenzyme B12, discussed in Section 8.3, and Zn(II) in carbonic anhydrase, discussed in Section 8.4. A prosthetic group is analogous to a coenzyme except that a prosthetic group is believed to be covalently bonded to the apoenzyme.

Rate Law and Mechanism

Once the experimental rate law has been established, the next step is to formulate a mechanism that is consistent with the rate law. The rate law will not uniquely define the mechanism but will limit the possibilities. The proposed mechanism will lead to predictions of trends in reactivity and other types of experiments that can be done to test the proposal. These aspects will be described in later chapters for specific types of reactions. Except for the simplest cases, the development of the rate law from the mechanism can be a messy exercise. The following sections describe some of the assumptions and tricks that can be used. Further discussions can be found in standard textbooks on kinetics. The problem is to determine the most reasonable mechanism(s) which will predict a rate law that is consistent with the observations. Very often this is done by analogy to previous studies on related systems, but there are some general guidelines that can be useful for writing a mechanism that will produce the desired form of the rate law. The mechanism is composed of elementary reactions whose rate laws are implied from the stoichiometry of each reaction. The elementary mechanistic steps are usually unimolecular or bimolecular reactions; termolecular reactions are very rare because of the improbability of bringing three species together. The form of the experimental rate law provides some guidelines for the construction of a mechanism. The following generalizations assume that the reaction is monophasic, but they may apply to individual steps in a multiphasic reaction. It also should be remembered that the experimental rate law may be incomplete because of experimental constraints. Then, the predicted rate law may contain terms not observed experimentally, but it should be possible to show that the extra terms are minor contributors under the conditions of the experiment. For the simplest cases, in which rate = kexp[A][B] or rate = kexp[A], the kinetics only requires a one step mechanism involving the species in the rate law. In the second case, the solvent also may be involved because its concentration will be constant and may be included in kexp .