Chemical Reaction Kinetics in Solution

The kinetics of chemical reactions were first studied in liquid solutions. These experiments involved mixing two liquids and following the change in the concentration of a reactant or product with time. The concentration was monitored by removing a small sample of the solution and stopping the reaction, for example, by rapidly lowering the temperature, or by following a physical property of the system in situ, for example, its color. Although the experiments were initially limited to slow reactions, they established the basic laws governing the rate at which chemical changes occur. The variables considered included the concentrations of the reactants and of the products, the temperature, and the pressure. Thus, the reacting system was examined using the variables normally considered for a system at equilibrium. Most reactions were found to be complex, that is, to be made up of several elementary steps which involved one or two reactants. As the fundamental concepts of chemical kinetics developed, there was a strong interest in studying chemical reactions in the gas phase. At low pressures the reacting molecules in a gaseous solution are far from one another, and the theoretical description of equilibrium thermodynamic properties was well developed. Thus, the kinetic theory of gases and collision processes was applied first to construct a model for chemical reaction kinetics. This was followed by transition state theory and a more detailed understanding of elementary reactions on the basis of quantum mechanics. Eventually, these concepts were applied to reactions in liquid solutions with consideration of the role of the non-reacting medium, that is, the solvent. An important turning point in reaction kinetics was the development of experimental techniques for studying fast reactions in solution. The first of these was based on flow techniques and extended the time range over which chemical changes could be observed from a few seconds down to a few milliseconds. This was followed by the development of a variety of relaxation techniques, including the temperature jump, pressure jump, and electrical field jump methods. In this way, the time for experimental observation was extended below the nanosecond range.

Non-Equilibrium Phenomena in Liquids and Solutions

The topics considered up to this point have involved liquids and solutions at equilibrium. Attention is now turned to systems which are not at equilibrium, and the processes which occur spontaneously in such systems. The physical phenomena involved can be quite complex, so that the task faced in early experiments was to separate the various processes and understand the physical properties of the system which govern them. Consider what happens when a beaker of pure isothermal water is placed on a hot plate. The water near the bottom rises in temperature and a temperature gradient is set up. As a result heat flows from the bottom of the beaker, producing a gradual increase in temperature in the water at a given height above the bottom. In addition, the temperature varies with distance, being highest at the bottom and lowest at the top. Eventually, the temperature of the water in the beaker is uniform and equal to that of the hot plate, assuming that the water does not boil. However, the flow of heat is not the only process resulting from the heat source. The density of the hot water is less than that of the cold water, so that a convection process is set up in order to achieve uniform density. Convection results in cold water moving down into the hot region so that the flow of water molecules assists the flow of heat. The changes which occur in this system cannot be understood without considering both processes. A system undergoing an irreversible change involving an electrolyte is electrolysis in an electrochemical cell. When current flows between two copper electrodes in an aqueous solution of CuSO4 the charge in solution is carried by migration of Cu2+ ions moving in one direction and SO42− ions moving in the opposite. At the cathode, the incoming Cu2+ ions are reduced to metallic copper, thereby lowering the concentration of these ions in the electrode’s vicinity. At the anode, Cu metal is oxidized to produce Cu2+ ions in the solution, so that the local concentration of cations is increased.

The Electrical Double Layer

In examining the properties of the metal | solution interface, two limiting types of behavior are found, namely, the ideal polarizable interface and the ideally nonpolarizable interface. In the former case, the interface behaves as a capacitor so that charge can be placed on the metal using an external voltage source. This leads to the establishment of an equal and opposite charge on the solution side. The total system in which charge is separated in space is called the electrical double layer and its properties are characterized by electrostatic equilibrium. An electrical double layer exists in general at any interface at which there is a change in dielectric properties. It has an important influence on the structure of the interface and on the kinetics of processes occurring there. The classical example of an ideally polarizable interface is a mercury electrode in an electrolyte solution which does not contain mercury ions, for example, aqueous KCl. The charge on the mercury surface is altered using an external voltage source placed between the polarizable electrode and non-polarizable electrode, for example, a silver | silver chloride electrode in contact with the same solution. Within well-defined limits, the charge can be changed in both the negative and positive directions. When the mercury electrode is positively charged, there is an excess of anions in the solution close to the electrode. The opposite situation occurs when the electrode is negatively charged. An important point of reference is the point of zero charge (PZC), which occurs when the charge on the electrode is exactly zero. The properties of the electrical double layer in solution depend on the nature of the electrolyte and its concentration. In many electrolytes, one or more of the constituent ions are specifically adsorbed at the interface. Specific adsorption implies that the local ionic concentration is determined not just by electrostatic forces but also by specific chemical forces. For example, the larger halide ions are chemisorbed on mercury due to the covalent nature of the interaction between a mercury atom and the anion. Specific adsorption can also result from the hydrophobic nature of an ion.

Liquids and Solutions at Interfaces

When the properties of liquids and solutions are considered, attention is normally focused on the bulk of the phase, and the properties of the system at its boundaries are ignored. Significant effects are associated with the region near the surface of a liquid phase and an understanding of these is an important part of solution chemistry. As a simple example, consider a beaker of pure water at room temperature in a closed inert environment. As has been seen in the consideration of liquid structure, the properties of water are strongly influenced by hydrogen bonding between neighboring molecules, and to a lesser extent by dipole–dipole interactions. As an observer at the molecular level, one would find that the molecules near the boundaries of the water phase have different properties. There are two boundaries in this system, the water | air interface and the water | glass interface. At the water | air interface, the important feature is the termination of intermolecular interactions, so that molecules must adjust to an environment where the number of nearest neighbors is reduced. At the water | glass interface, water molecules meet the components of glass, a supercooled liquid with silicon dioxide as the major component. Interaction between water and silicon dioxide is different from interaction among water molecules. It is clear that the molecular environment at these interfaces is very different than it is in the bulk. As a result, local properties are different. Now imagine that the water in the beaker is dispersed as a fog, that is to say, as many very small droplets for which the ratio of surface area to volume is much larger than for the water in the beaker. It is obvious that the thermodynamic properties of the fog, a colloidal system, are very different from those of the water as a macrosystem in a beaker. In order to create the fog considerable work must be done to form a system with a much larger surface area. This means that the Gibbs energy of a fog containing the same number of water molecules as the beaker of water is much higher.

The Thermodynamics of Liquid Solutions

Chemistry in the laboratory very often involves the use of liquid solutions. This is especially true in chemical analysis, where the amount of analyte is easily manipulated when it is dissolved in a solution. Solutions are often the medium for chemical reactions which form the basis of titrations. Other simple analytical procedures are based on absorption spectroscopy, which is used to determine the concentrations of an analyte in solution. Most liquid solutions, also called liquid mixtures, are non-ideal. This follows from the fact that the components are in intimate contact with one another, and that the forces between the various species are usually not the same. As a result, the physical properties of the solution, for example, the vapor pressure of a given component, are usually not simply related to its concentration. This non-ideality leads to the concept of the activity of a solution component. As far as the analytical chemist is concerned, only concentration is ultimately of interest. Thus, if an analysis is based on the measurement of a physical property which in turn depends on the activity of a component, it is very important that the relationship between activity and concentration be understood for the system in question. Activity and its relationship to concentration is defined within the context of chemical thermodynamics. Using the laws which govern phase equilibria and the laboratory observations relating to these processes one can develop a detailed understanding of this relationship. In this chapter the macroscopic concepts of chemical thermodynamics which are relevant to solutions are reviewed. In addition, some simple models based on molecular concepts are discussed. The examples chosen are mainly limited to non-electrolyte solutions, especially those involving polar molecules. Concentration of one component in a two-component system can be expressed in several ways: as a weight/weight ratio, as a volume/volume ratio, or as a weight/volume ratio. Physical chemists clearly prefer to express concentration as a weight/weight ratio because then one has the possibility of estimating the number of moles of both components in the solution. In this case, solution composition is independent of temperature and pressure. On the other hand, the analytical chemist prefers to use a weight/volume ratio.

Electrolyte Solutions

Electrolyte solutions are important in all branches of chemistry, but especially in analytical chemistry, and biochemistry. These systems by their nature are always non-ideal, and represented an early challenge to theoreticians interested in describing their thermodynamic properties. The solute components are ions, cations, and anions, which carry opposite charges and thus interact very differently with one another. The existence of electrolyte solutions depends on the polar properties of the solvent through which the individual ions are stabilized. When one recognizes the molecular nature of the solvent, one must also consider the interactions between solvent dipoles and the ion. This results in changes in solvent structure in the immediate vicinity of the ions. It follows that a complete description of an electrolyte solution at the molecular level requires the consideration of ion–dipole, ion–ion, and dipole–dipole interactions. In addition to these simple electrostatic interactions, one must also consider the role of hydrogen bonding in protic solvents like water. In very dilute electrolyte solutions, the most important consideration is ion– dipole interactions. One expects these interactions to be different for cations and anions. This follows from the fact that the solvent molecule is not a simple dipole in the electrostatic sense but instead it has a chemical structure which is different at each end of the molecular dipole. Each ion interacts locally with four to six solvent molecules in its immediate surroundings. In the case of water, the concentration of water molecules in the pure liquid is 55.5 M; it follows that the number of water molecules experiencing direct interaction with ions in dilute solutions represents a small fraction of the total number. As the electrolyte concentration increases, ion–ion interactions become more important in determining the thermodynamic properties of the solution. The electrostatic field of an ion is long ranged, decreasing with the reciprocal of the distance from the charge center of the ion. As a result a given ion has an ionic atmosphere in which the concentration of oppositely charged ions in its vicinity is slightly greater on the average than that of ions of the same charge.

The Structure of Liquids

It is well known from studies of the properties of matter that the liquid state is much more complex than either the gaseous or solid states. Studies of the properties of gases quickly lead to the ideal gas law, which describes the properties of real gases at low pressures and high temperatures. This success is clearly due to the fact that the molecules in a dilute gas are far from one another so that the effects of intermolecular forces and of the finite volume occupied by the gas molecules are negligible. As the pressure of a gas is increased and its temperature lowered, the effects of non-ideality become apparent, and the equation of state becomes more complex. These changes are those required to convert the gas to a liquid. As the molecules come closer together, the influence of intermolecular forces becomes greater and the free volume available for the gas molecules is significantly reduced because of the space occupied by the molecules themselves. The statistical mechanical description of a gas relies upon the concept that the molecules are in constant movement with trajectories determined by collisions with the walls of the container and with other molecules. The probability of finding another molecule in the immediate vicinity of a given molecule is extremely low and does not vary significantly with distance from the reference molecule. On the other hand, solids are characterized by a very ordered structure in which each ion or molecule is surrounded by a fixed number of neighbors whose nature and orientation are determined by the interparticle forces in the crystal. These may be chiefly ion–ion interactions, as in an ionic crystal, or intermolecular forces, as in a molecular crystal. Because of the high state of order in crystals it is a reasonably straightforward problem to calculate their thermodynamic properties on the basis of quite simple statistical mechanical models. One way of conceptualizing a liquid is as a very disordered solid. If one disrupts the structure of the nearest neighbors around a reference molecule in a molecular crystal, the effect of the disruption extends quite far.

Charge Transfer Equilibria at Interfaces

Processes in which charge is transferred from one phase to another at an interface make up an important class of interfacial reactions. Well-known examples are the reactions which occur at the electrodes of an electrochemical cell. These are electron transfer reactions, oxidation taking place at one electrode and reduction at the other. The early study of electrochemical cells provided valuable thermodynamic information about the redox processes occurring in them. When an electrochemical cell is a source of energy, for example, a battery, chemical energy is converted to electrical energy. When electrical energy is driven into an electrochemical cell from an external source, electrode reactions producing products of commercial interest are possible. Thus the general subject discussed here is of considerable practical importance. Another important class of interfacial charge transfer processes occurs at the membrane | solution interface. Some solute species can move into the membrane phase, whereas others cannot. When ions are involved in membrane selectivity, a potential drop is established at the interface. Ion transfer processes at membranes are extremely important in living organisms and form the basis for the functioning of the nervous system. Membranes are also involved in ion selective electrodes such as the ubiquitous pH electrode. These electrodes are often used in modern analytical techniques based on potentiometry. In the present chapter, the relationship between the electrode potential and the activity of the solution components in the cell is examined in detail. The connection between the Galvani potential difference at the electrode solution interface and the electrode potential on the standard redox scale is discussed. This leads to an examination of the extrathermodynamic assumption which allows one to define an absolute electrode potential. Ion transfer processes at the membrane | solution interface are then examined. Diffusion potentials within the membrane and the Donnan potentials at the interface are illustrated for both liquid and solid state membranes. Specific ion electrodes are described, and their various modes of sensing ion activities in an analyte solution discussed. The structure and type of membrane used are considered with respect to its selectivity to a particular ion over other ions.

Spectroscopic Studies of Liquid Structure and Solvation

Spectroscopy involves the study of the interactions of electromagnetic radiation with matter. In the case of liquids, radiation of a wide range of frequencies, and thus energies, has been used, all the way from radio-frequency waves to X-rays. Experiments involving neutrons, which are associated with very short wavelengths, are also important. In the spectroscopic experiment the incident radiation may be either absorbed or scattered and the experimental information is obtained by examining the intensity and direction of the radiation after it has passed through the sample. Several spectroscopic techniques will be considered in this chapter. X-ray and neutron diffraction techniques are powerful tools for studying the structure of liquids and have been introduced in chapter 2. They may also be used to study the structure of solutions and determine distribution functions for both the solute and solvent. The feasibility of these experiments depends on the number of different nuclei involved in the system. UV-visible spectroscopy is mainly used to study electronic transitions in polyatomic species. These species are often complex ions formed between the electrolyte and the solvent, or between the cation and one or more anions. Vibrational spectroscopy involves electromagnetic radiation of lower energy, usually in the infrared region. It is used to study intramolecular vibrational modes and how they are altered by the environment in solution. It can also be used to study the bonds formed between solute and solvent in the solvation process. Finally, nuclear magnetic resonance spectroscopy and its application to the study of solvation will be discussed. This is a particularly powerful technique because it provides information about the environment of a given nucleus, and experiments specific to a given nucleus can be carried out provided the nucleus has a non-zero magnetic moment. Several other spectroscopic techniques are commonly used [G1] but those considered here provide a representative picture of what can be learnt from those experiments. One should remember that the atoms and molecules in liquids are not motionless but in a state of flux determined by the intermolecular interactions and temperature. From the study of microwave spectroscopy discussed in chapter 4, it was found that rotational diffusion processes in liquids are characterized by relaxation times the order of a few picoseconds.

Polar Solvents

Polar solvents are those liquids whose relative permittivity is sufficiently high that electrolytes can be dissolved in them. The best-known example of such a liquid is water. The oxygen end of this simple molecule is electron-rich and can stabilize cations. The hydrogen atoms are electron-poor and thus are involved in the solvation of anions. The structure of pure water is very much influenced by the hydrogen bonding between the negative end of the molecular dipole at oxygen and a hydrogen atom on an adjacent molecule. The special properties of water as a solvent for electrolytes are the central reason for its importance in living systems. There are many other solvents which can be classified as polar. Some of them, such as the alcohols, have the same polar group as the water molecule, namely, the hydroxyl group –OH. These solvents are also involved in hydrogen bonding, and are generally classified as protic. Other examples of protic solvents are simple amides such as formamide and acetamide. In these systems, the protic group is –NH2, the hydrogen atom being involved in hydrogen bonding with the oxygen atom in the carbonyl group on an adjacent molecule. There are other polar solvents which are not protic. These involve liquids with large dipole moments. Some examples are acetonitrile, propylene carbonate, and dimethylsulfoxide. In each case, the solvent molecule possesses an electronegative group which is rich in electrons. The opposite end of the molecule is electron deficient but does not have acidic hydrogen atoms which can participate in hydrogen bonding. This class of solvents is called aprotic. In this chapter, the properties of polar solvents are discussed, especially as they relate to the formation of electrolyte solutions. Polar solvents are arbitrarily defined here as those liquids with a relative permittivity greater than 15. Solvents with zero dipole moment and a relative permittivity close to unity are non-polar. These include benzene, carbon tetrachloride, and cyclohexane. Solvents with relative permittivities between 3 and 5 are weakly polar, and those with values between 5 and 15 are moderately polar. The latter systems are not considered in the discussion in this chapter.