Species, chemical equilibrium

Analogous considerations apply to spatially distributed reacting media where diffusion is tire only mechanism for mixing chemical species. Under equilibrium conditions any inhomogeneity in tire system will be removed by diffusion and tire system will relax to a state where chemical concentrations are unifonn tliroughout tire medium. However, under non-equilibrium conditions chemical patterns can fonn. These patterns may be regular, stationary variations of high and low chemical concentrations in space or may take tire fonn of time-dependent stmctures where chemical concentrations vary in botli space and time witli complex or chaotic fonns. 

An example of enhanced ion production. The chemical equilibrium exists in a solution of an amine (RNH2). With little or no acid present, the equilibrium lies well to the left, and there are few preformed protonated amine molecules (ions, RNH3+) the FAB mass spectrum (a) is typical. With more or stronger acid, the equilibrium shifts to the right, producing more protonated amine molecules. Thus, addition of acid to a solution of an amine subjected to FAB usually causes a large increase in the number of protonated amine species recorded (spectrum b). 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

Based on Eq. (4.6.8), the retiction rate is positive if species A is being formed (since Ca increases with time), and negative if A is reacting (since Ca decreases with time). The rate is zero if the system is at chemical equilibrium. 

As the molecular weight of H2SO4 is 98.078 it follows that 1 kg contains 10.196 mol hence the predominant ions are present to the extent of about 1 millimole per mole of H2SO4 and the total concentration of species in equilibrium with the parent acid is 4.16 millimole per mole. Many of the physical and chemical properties of anhydrous H2SO4 as a nonaqueous solvent stem from these equilibria. 

Chemical reactions involving gases carried out in closed containers resemble in many ways the H20(/)-H20(g) system. The reactions are reversible reactants are not completely consumed. Instead, an equilibrium mixture containing both products and reactants is obtained. At equilibrium, forward and reverse reactions take place at the same rate. As a result, the amounts of all species at equilibrium remain constant with time. 

Our sun is, of course, a star. It is a relatively cool star and, as such, contains a number of diatomic molecules (see Figure 25-3). There are many stars, however, with still lower surface temperatures and these contain chemical species whose presence can be understood in terms of the temperatures and the usual chemical equilibrium principles. For example, as the star temperature drops, the spectral lines attributed to CN and CH become more prominent. At lower temperatures, TiO becomes an important species along with the hydrides MgH, SiH, and A1H, and oxides ZrO, ScO, YO, CrO, AlO, and BO. 

In terms of levels, nnderstanding the notion of chemical equilibrium involves being able to mentally translate between the macro level, conceived in terms of the observable properties (e g. colour) the sub-micro level, conceived as being identities of the specific species involved and their associated behaviour the symbolic... 

This model is similar to the associated species model in that a chemical equilibrium is assumed between existing species, and it is different in that in the latter only a nonassociated ionic species is assumed to be the electrically conducting species. 

The dynamic dissociation model resembles the association (or dissociation) model in that electrically conducting species are assumed to he nonassociated species, and it differs from the association model in that in the dynamic dissociation model the dissociation process itself is the electrically conducting process, while in the association model, the amount of the dissociated species is constant according to the chemical equilibrium. 

Here the square brackets indicate the concentration of the chemical species within the bracket. That is, [A] means the concentration of A, and so forth. [A]" means the concentration of A raised to the a power, where a is the value of the coefficient of A in the balanced equation for the chemical equilibrium. The value of the ratio of concentration terms is symbolized by the letter K, called the equilibrium constant. For example, for the reaction of nitrogen and hydrogen referred to in Sec. 19.3,... 

In Eyring s formulation of the problem he assumes that an equilibrium exists between the activated complex species and the reactant molecules. This equilibrium is said to exist at all times, regardless of whether or not a true chemical equilibrium has been established between the reactants and products. Although the... 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

Note The above potentials, E, are for pH 7 at equal concentrations of oxidised and reduced species. These equilibrium values are as important as stability constants and solubility products for an understanding of cellular chemical systems. These are free energy changes in volts, E, and where n3E is in kilocalories. The [Fe3+]/[Fe2+] is related to an equilibrium constant, K (see Section 4.17). 

Recently, Muha (83) has found that the concentration of cation radicals is a rather complex function of the half-wave potential the concentration goes through a maximum at a half-wave potential of about 0.7 V. The results were obtained for an amorphous silica-alumina catalyst where the steric problem would not be significant. To explain the observed dependence, the presence of dipositive ions and carbonium ions along with a distribution in the oxidizing strengths of the surface electrophilic sites must be taken into account. The interaction between the different species present is explained by assuming that a chemical equilibrium exists on the surface. 

Fowle and Fein (1999) measured the sorption of Cd, Cu, and Pb by B. subtilis and B. licheniformis using the batch technique with single or mixed metals and one or both bacterial species. The sorption parameters estimated from the model were in excellent agreement with those measured experimentally, indicating that chemical equilibrium modeling of aqueous metal sorption by bacterial surfaces could accurately predict the distribution of metals in complex multicomponent systems. Fein and Delea (1999) also tested the applicability of a chemical equilibrium approach to describing aqueous and surface complexation reactions in a Cd-EDTA-Z . subtilis system. The experimental values were consistent with those derived from chemical modeling. 

We can find the reaction s equilibrium point from Equation 3.3 as soon as we know the form of the function representing chemical potential. The theory of ideal solutions (e.g., Pitzer and Brewer, 1961 Denbigh, 1971) holds that the chemical potential of a species can be calculated from the potential pg of the species in its pure form at the temperature and pressure of interest. According to this result, a species chemical potential is related to its standard potential by... 

The governing equations are composed of two parts mass balance equations that require mass to be conserved, and mass action equations that prescribe chemical equilibrium among species and minerals. Water Aw, a set of species, 4/, the min-... 

Because Schottky defects are present as equilibrium species, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX ... 

The mixture we have just described, even with a chemical reaction, must obey thermodynamic relationships (except perhaps requirements of chemical equilibrium). Thermodynamic properties such as temperature (T), pressure (p) and density apply at each point in the system, even with gradients. Also, even at a point in the mixture we do not lose the macroscopic identity of a continuum so that the point retains the character of the mixture. However, at a point or infinitesimal mixture volume, each species has the same temperature according to thermal equilibrium. 

Here we are considering the dynamic equilibrium between molecular species in the gas phase and the adsorbed gas species on a surface. Let us consider the following quasi-chemical equilibrium between the species B in the gas, Bg, and the available sites at the surface of the adsorbate ... 

The fundamental law of chemical equilibrium is the law of mass action, formulated in 1864 by Cato Maximilian Guldberg and Peter Waage. It has since been redefined several times. Consider the equilibrium between the four chemical species A, B, C and D ... 

For elementary chemical reactions, it is sometimes possible to assume that all chemical species reach their chemical-equilibrium values much faster than the characteristic time scales of the flow. Thus, in this section, we discuss how the description of a turbulent reacting flow can be greatly simplified in the equilibrium-chemistry limit by reformulating the problem in terms of the mixture-fraction vector. 

The exp-6 potential has also proved successful in modeling chemical equilibrium at the high pressures and temperatures characteristic of detonation. However, to calibrate the parameters for such models, it is necessary to have experimental data for product molecules and mixtures of molecular species at high temperature and pressure. Static compression and sound-speed measurements provide important data for these models. 

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