The Rate of Chemical Change

The overall rate of chemical change at an electrode process depends on the current density, j (the cell current, /, divided by the electrode area. A) for the desired reaction and the selectivity of the chemical change. The latter is usually discussed in terms of the current efficiency, / , for the desired chemical change and is defined as the fraction of the charge passed used in the desired reaction. The space-time yield, Tst for n electrolytic reactor may be written 

It is important to differentiate between the extreme types of rate control. Under pure charge transfer control, the rate of electron supply/removal at the electrode surface dominates. The rate is very potential-dependent. The partial current for the desired reaction, /, is exponentially related to the overpotential r] = E- E ), and can be written as  

The overpotential essential to obtain the required current density can be decreased by an appropriate electrocatalyst (increasing the rate constant, k) or increasing the microscopic area of the electrode surface. In Equation (6.4), a is the transfer coefficient. 

Under complete mass transport control, the rate of reactant supply or product removal determines a limiting current, /l, and this is the maximum possible current for a given reaction. The limiting current, /l, is determined by the mass transport regime close to the electrode surface, characterized by the mass transfer coefficient, k, and related to the relative velocity, v, between the electrode and the electrolyte  

---

There are two principal chemical concepts we will cover that are important for studying the natural environment. The first is thermodynamics, which describes whether a system is at equilibrium or if it can spontaneously change by undergoing chemical reaction. We review the main first principles and extend the discussion to electrochemistry. The second main concept is how fast chemical reactions take place if they start. This study of the rate of chemical change is called chemical kinetics. We examine selected natural systems in which the rate of change helps determine the state of the system. Finally, we briefly go over some natural examples where both thermodynamic and kinetic factors are important. This brief chapter cannot provide the depth of treatment found in a textbook fully devoted to these physical chemical subjects. Those who wish a more detailed discussion of these concepts might turn to one of the following texts Atkins (1994), Levine (1995), Alberty and Silbey (1997). 

We may be able to infer information about the mechanism of chemical change from kinetics but not from thermodynamics the rate of chemical change is dependent on the path of reaction, as exemplified by the existence of catalysis thermodynamics, on the other hand, is not concerned with the path of chemical change, but only with state and change of state of a system. 

Arrhenius interpreted the equation by suggesting that there exists an equilibrium between normal molecules and what he called active molecules, and that only the active molecules undergo chemical change. The active molecules were supposed to be formed endothermically from the normal molecules. The rapid increase in the rate of chemical change with rising temperature is therefore caused by the shift in the equilibrium between the two kinds of molecules, and, since k is proportional to the number of active molecules, the equation d log k/dT = A/RT2 represents this shift in the ordinary thermodynamic way. A is the heat absorbed in the formation of an active molecule from a normal one and is therefore called the heat of activation. 

The facts that have just been described lend considerable support to the Lindemann theory. If this theory is to be applicable, the rate of activation and deactivation at higher pressures ought to be great compared with the rate of chemical change, in order that there may be little disturbance of the statistical equilibrium and hence an absolute rate of reaction directly proportional to the total concentration. At first some difficulty was felt about this point, but the solution appears to have been found, and indeed the solution itself constitutes a rather strong piece of evidence in favour of the theory. 

At high pressures, where the rate of activation and deactivation are large compared with the rate of chemical change, the value of [a] is simply nf(E), where f(E) is the fraction of the total number of molecules having energy greater than E. 

At low pressures the rate of chemical transformation is comparable with the rate of deactivation. The rate of activation is still given by total number of collisions xf(E), i. e. by V% it U ct2. to2. f(E). The rate of deactivation is very nearly equal to the number of collisions between activated molecules and normal molecules, i. e. to V2 ir u a2, to [a]. The rate of chemical change is 6 [a]. 

Solubility-Product.—It has already been mentioned on p. 14 that the rate of chemical change depends on the amount of each of the reacting substances present in unit volume. This last is generally termed the concentration of these substances, for the more concentrated the solution the greater the mass present in unit volume. Now, if two + ... 

Quantitative description of catalytic properties requires that the system under consideration be unambiguously described with respect to system boundaries (mass of catalyst mc, area of catalytic surface Ac, or volume of porous catalytic particle Vc) and conditions such as composition, pressure, temperature, prevailing at the boundary (control variables). A set of data characterizing a catalyst must permit the prediction of material balance of the system containing the catalyst at steady state under at least one set of control variables. It is sometimes possible to represent a number of experimental observations by rate equation or a set of rate equations which may or may not be based on a mechanistic model. The model has to fulfil the above criteria within a certain range of validity which should be indicated. The catalytic system should be characterized with respect to the rate of chemical change (activity) and with respect to product composition selectivity). 

The transition state is of strategic importance within the field of chemical reactivity. Owing to its location in the region of the highest energy point on the most accessible route between reactants and products it commands both the direction and the rate of chemical change. Questions of selectivity ( Which way is it to the observed product ) and efficiency ( How easy is it to get there ) may be answered by a knowledge of the structure and properties of the transition state. 

Mr. Harcourt, whose refusal to lecture separately to women students had hastened their admission to university lectures, had equally strong objections to allowing chaperones in his laboratory an arrangement was therefore arrived at, by which, at times when Miss Rich was in the laboratory, Miss Seward carried out research with Mr. W. H. Pendlebury on the rate of chemical change.56... 

Temperature is, of course, only one of a number of variables which may influence the rates of chemical changes in crystals. Other possible variables include a, pressure of volatile product (most significant in reversible reactions), reactant pressure (in gas-solid reactions), etc. Thus the overall rate equation applicable to the decomposition of a solid may be a function of several variables [5] ... 

We first review the thermodynamic principles necessary to describe equilibrium systems. A discussion of electrochemistry is also included. Next, the rates of chemical changes, or chemical kinetics, are examined. Finally, we examine selected natural systems in which thermodynamic and kinetic factors are important. 

Reaction rates can be controlled by the rate of conversion of the reactants or by nonchemical rate processes such as the rate of diflusion of reactants or the rate of heat transfer. In the study of chemical kinetics we will be interested in the rates of chemical change governed by the speed of chemical processes. Any investigation of reaction rates meant for mechanistic studies must first establish that this is what we are measuring. Fortunately, it is relatively easy to check for extraneous effects before the kinetic investigation is undertaken. The effects that are most likely to cause problems involve diffusion of mass and heat in catalyst particles and mixing in the reactor. 

The rate of chemical change how fast do chemical reactions go ... 

Describing the rates at which chemical reactions occur is the subject of chemical kinetics. It is the study of the rates at which chemical compounds interact with one another to produce new chemical species, and the insight into factors governing chemical reactivity that derives therefrom. The rates of chemical change span an enormous range of time... 

For extended coverage of figures of merit that may be used to quantify cell performance, the reader is referred elsewhere [1,3]. However, at this point emphasis will be placed on two critical parameters, namely cell potential and the rate of chemical change. 

Mass transport processes in the liquid phase are always very slow in comparison with those in the gas phase. This will cause both mass transport limitations on the rate of chemical changes in the reactor and the creation of reaction layers at the solid-fluid interface to be much more troublesome. 

In the second aspect, we again picture the catalytic material itself to have spatially invariant properties, but now we ask questions about the stability of a spatially uniform reaction state to spatial perturbations. This stability question is similar to that posed in studies of hydrodynamic stability and of the other reaction-diffusion problems considered by Turing [62], Prigogine [63,64], Nicolis [63], Othmer and Scriven [65,66] and their co-workers. Prigogine and his co-workers labeled this phenomena "symmetry-breaking" instabilities. The key idea is that since there is a finite rate of transport, the complex interactions between the rate of communication by diffusive transport and the rate of chemical change may make it dynamically impossible for a spatially uniform state to be sustained. 

---