Species-Dependent Definition

4 DEFINITIONS OF REACTION RATE 1.4.1 Species-Dependent Definition 

In order to be useful in reactor design and analysis, the reaction rate must be an intensive variable, i.e., one that does not depend on the size of the system. Also, it is very convenient to define the reaction rate so that it refers explicitly to one of the chemical species that participates in the reaction. The reference species usually is shown as part of the symbol for the reaction rate, and the reference species should be specified in the units of the reaction rate. 

Consider a system in which one stoichiometrically simple reaction is taking place. Let s define a reaction rate r,- as 

The subscript i refers to the species whose rate of formation is rj. The denominator of the right-hand side of Eqn. (1-11) is what makes r, an intensive variable. We will return to this denominator momentarily. 

Several things are obvious about this definition of r,. First, if i actually is being formed, r,- will be positive. However, we may want i to be a reactant, which is being consumed (disappearing). In this case, the value of r,- would be negative. An alternative, mathematically equivalent, definition can be used when i is a reactant  

---

The species-dependent definition of reaction rate will be used throughout the remainder of this text. 

This definition is therefore independent of the choice of coordinate origin only when the charges sum to zero. The dipole moment of a charged species depends on the coordinate origin, which must be quoted when reporting such quantities. 

The recognised definition of an ionic liquid is an ionic material that is liquid below 100 °C but leaves the significant question as to what constitutes an ionic material. Some authors limit the definition to cations with discrete anions e.g. BF4-, NO3. This definition excludes the original work on chloroaluminate systems and the considerable work on other eutectic systems and is therefore unsatisfactory. Systems with anionic species formed by complex equilibria are difficult to categorise as the relative amounts of ionic species depend strongly on the composition of the different components. 

The survival of all species depends on the integrity of its reproductive system. Reproductive toxicology may be defined as the study of the effects of physical and chemical agents on the reproductive and neuroendocrine systems of adult males and females, as well as those of the embryo, fetus, neonate, and prepubertal animal. This chapter focuses primarily on the potential sites of toxic insult in the reproductive systems of adult mammals, the biochemical mechanisms of such toxicants, and the manifestations that may result. The latter part of the above definition is a subspecialty of developmental toxicology (Chapter 34) and is discussed only in brief. 

The color of the chromium(III) species depends on anions in solution that can form complexes with Cr. Frequently the ion is green, so there is a definite color change from orange to green during the reaction. 

One more effect should be taken into account. Because the miscibility of two species depends on the ratio of their molecular mass, the situation arises where, on the change of the outer conditions, the system remains in a thermodynamically stable state for some fractions of definite molecular mass, while already undergoing the phase separation for other fractions. Although this point has practically not been dealt with in the hterature, its role in the formation of a non-equilibrimn frozen structure should be essential. It means that the state of a system turns out to be dependent on its history. Thus, again, the phase diagram by itself yields a poor indication of the system state within the region of immiscibility bomid by the spinodal or binodal curve. 

Anyhow, the polycation-induced RBC toxicity depends definitely on the nature and the structure of the polycations. In other words, RBC might be a useful tool to anticipate the in vivo relative toxicity. However, in vivo, the interactions between RBC and proteins and polycations also depend on other factors such as the polycation local concentration and the blood flow rate, and thus on the experimental injection conditions. Such a behavior has already been observed once since a defined solution of Q-P(TDAE)n was foimd less lethal when slowly perfused than when given i.v.. Similarly to the effect of the order of mixing the interacting species, the influence of the i.v. administration conditions well agree with the involvement of a thermodynamically unbalanced formation ofpolyelectrolyte complexes. 

This is the situation exploited by the so-called isolation method to detennine the order of the reaction with respect to each species (see chapter B2.1). It should be stressed that the rate coefficient k in (A3,4,10) depends upon the definition of the in the stoichiometric equation. It is a conventionally defined quantity to within multiplication of the stoichiometric equation by an arbitrary factor (similar to reaction enthalpy). 

Over the next few years, both the mid-infrared and the far-infrared spectra for Ar-HF and Ar-HCl were extended to numerous other bands and to other isotopic species (most importantly those containing deuterium). In 1992, Hutson [18, 39] combined all the available spectroscopic data to produce definitive potential energy surfaces that included both the angle dependence and the dependence on the HF/HCl monomer vibrational quantum number v... 

Fn some cases, r-allylpalladium complex formation by retention syn attack) has been observed. The reaction of the cyclic allyiic chloride 33 with Pd(0) affords the 7r-allylpalladium chlorides 34 and 35 by retention or inversion depending on the solvents and Pd species. For example, retention is observed in benzene, THF, or dichloromethane with Pd2(dba)3. However, the complex formation proceeds by inversion in these solvents with Pd(Ph3P)4, whereas in MeCN and DMSO it is always inversion[33]. The syn attack in this case may be due to coordination of Pd to chlorine in 33, because Pd is halophilic. The definite syn attack in complex formation has been observed using stereoche-mically biased substrates. The reaction of the cxoallylic diphenylphosphino-acetate 36 with phenylzinc proceeds smoothly to give 37. The reaction can be explained by complex formation by a syn mechanism[31]. However, these syn attacks are exceptional, and normally anti attack dominates. 

Normality makes use of the chemical equivalent, which is the amount of one chemical species reacting stoichiometrically with another chemical species. Note that this definition makes an equivalent, and thus normality, a function of the chemical reaction in which the species participates. Although a solution of 1T2S04 has a fixed molarity, its normality depends on how it reacts. 

The previous definitions can be interpreted in terms of ionic-species diffusivities and conductivities. The latter are easily measured and depend on temperature and composition. For example, the equivalent conductance A is commonly tabulated in chemistry handbooks as the limiting (infinite dilution) conductance and at standard concentrations, typically at 25°C. A = 1000 K/C = ) + ) = +... 

One chemical will be a solvent for another if the molecules are able to co-exist on a molecular scale, i.e. the molecules show no tendency to separate. In these circumstances we say that the two species are compatible. The definition concerns equilibrium properties and gives no indication of the rate of solution which will depend on other factors such as temperature, the molecular size of the solvent and the size of voids in the solute. 

Climate is often viewed as the aggregate of all of the elements of weather, with quantitative definitions being purely physical. However, because of couplings of carbon dioxide and many other atmospheric species to both physical climate and to the biosphere, the stability of the climate system depends in principle on the nature of feedbacks involving the biosphere. For example, the notion that sulfate particles originating from the oxidation of dimethylsulfide emitted by marine phytoplankton can affect the albedo (reflectivity) of clouds (Charlson et ai, 1987). At this point these feedbacks are mostly unidentified, and poorly quantified. 

A free radical (often simply called a radical) may be defined as a species that contains one or more unpaired electrons. Note that this definition includes certain stable inorganic molecules such as NO and NO2, as well as many individual atoms, such as Na and Cl. As with carbocations and carbanions, simple alkyl radicals are very reactive. Their lifetimes are extremely short in solution, but they can be kept for relatively long periods frozen within the crystal lattices of other molecules. Many spectral measurements have been made on radicals trapped in this manner. Even under these conditions, the methyl radical decomposes with a half-life of 10-15 min in a methanol lattice at 77 K. Since the lifetime of a radical depends not only on its inherent stabihty, but also on the conditions under which it is generated, the terms persistent and stable are usually used for the different senses. A stable radical is inherently stable a persistent radical has a relatively long lifetime under the conditions at which it is generated, though it may not be very stable. 

When the system contains more than one component it is important to be able to explore the distribution of the different components both locally and at long range. One way in which this can be achieved is to evaluate the distribution function for the different species. For example in a binary mixture of components A and B there are four radial distribution functions, g (r), g (r), g (r) and g (r) which are independent under certain conditions. More importantly they would, with the usual definition, be concentration dependent even in the absence of correlations between the particles. It is convenient to remove this concentration dependence by normalising the distribution function via the concentrations of the components [26]. Thus the radial distribution function of g (r) which gives the probability of finding a molecule of type B given one of type A at the origin is obtained from... 

---