Chemical equilibrium, requirement

Chemical equilibrium requires that, if species exist in adjoining phases, their electrochemical potentials must be equal, e.g., for electrons... 

In introductory chemistry lessons, chemical reactions are usually associated with observable phenomena (e.g., change of colour, evolution and absorption of heat, precipitation of a solid, evolution of a gas) and chemical reactions are presented as proceeding to completion, taking place in one direction (Andersson, 1990). The introduction of chemical equilibrium at a later stage, however, demonstrates the reversibility of chemical reactions and the possibility that chemical reactions do not proceed to completion. Moreover, the dynamic nature of chemical equilibrium requires students to assume that two opposite chemical reactions are taking place, in spite of the fact that this cannot be deduced from observation. As a consequence, the introduction of chemical equilibrium requires students to revise their initial conception of chemical reactions. This is illustrated in Table 1. 

The condition of chemical equilibrium requires that the chemical potential is the same throughout the system and is thus given by its value for the bulk solution, where the composition is... 

Few chemical reactions proceed in only one direction. Most are, at least to some extent, reversible reactions, that is, they can proceed in either the forward or reverse direction. At the start of a reversible reaction, the reaction proceeds toward the formation of products. As soon as some product molecules are formed, the reverse reaction begins to take place and reactant molecules are formed from product molecules. Eventually, the rates of product and reactant formation will equalize, and the systan will have attained a state of chemical equilibrium in which the concentrations of the reactants and products no longer change. Like physical equilibrium (discussed in Chapters 5 and 8), chemical equilibrium is a dynamic process. However, the transformations involved in chemical equilibrium require the breaking and formation of chemical bonds, whereas physical equilibrium involves the transfer of intact molecules between different physical phases of a substance and no ch ical bonds are broken in the process. 

An understanding of chemical equilibrium requires that students understand reversible reactions and their dynamic nature. In the pre-test and the pre-interview, students had the pre-instructional conceptions that reactions go in one direction and that at least one of the reactants would completely react. The first lesson used experiments (van Driel et al., 1998) resulting in anomalous data. Experiment 1 involved the iron(lII)-thiocyanate equilibrium and was intended to show the presence of unreacted iron(lll) and thiocyanate ions and the incompleteness of the reaction. The use of anomalous data or discrepant events to create cognitive conflict causing students to be dissatisfied with their current conceptions and to adopt a target concept has been advocated by many educational researchers (Posner, Strike,... 

When two parts of a system are in mechanical equilibrium, their volumes need not be the same, but pressure, an intensive field, must be the same. For thermal equilibrium, temperature must be the same. Chemical equilibrium requires equality of chemical potential. This was a very important discovery by Gibbs. Consider the example,... 

Figure3.9 shows a beaker containing the pure liquid A. Immersed in the liquid is a tube with its lower end closed to the liquid by a membrane. The membrane allows A to permeate into the tube and vice versa. Inside the tube there is a binary mixture of two components A and B. The latter however is held back inside the tube by the membrane. What happens As far as A is concerned the two subsystems, the pure solvent outside the tube and the binary mixture inside the tube, do exchange A-moles and therefore chemical equilibrium requires...

It follows that, because phase equilibrium requires that the chemical potential p. be the same in the solution as in the gas phase, one may write for the chemical potential in the solution ... 

The mechanism of ion polymerization in formaldehyde crystals proposed by Basilevskii et al. [1982] rests on Semenov s [1960] assumption that solid-phase chain reactions are possible when the arrangement of the reactants in the crystal prepares the configuration of the future chain. The monomer crystals capable of low-temperature polymerization fulfill this condition. In the initial equilibrium state the monomer molecules are located in the lattice sites and the creation of a chemical bond requires surmounting a high barrier. However, upon creation of the primary dimer cation, the active center shifts to the intersite, and the barrier for the addition of the next link... 

Thus, the mean temperature of the atmosphere, which is about 20°C at sea level, falls steadily to about —55° at an altitude of 10 km and then rises to almost 0°C at 50 km before dropping steadily again to about —90° at 90 km. Concern was expressed in 1974 that interaction of ozone with man-made chlorofluorocarbons would deplete the equilibrium concentration of ozone with potentially disastrous consequences, and this was dramatically confirmed by the discovery of a seasonally recurring ozone hole above Antarctica in 1985. A less prominent ozone hole was subsequently detected above the Arctic Ocean. The detailed physical and chemical conditions required to generate these large seasonal depletions of ozone are extremely complex but the main features have now been elucidated (see p. 848). Several accounts of various aspects of the emerging story, and of the consequent international governmental actions to... 

What Do We Need to Know Already The concepts of chemical equilibrium are related to those of physical equilibrium (Sections 8.1-8.3). Because chemical equilibrium depends on the thermodynamics of chemical reactions, we need to know about the Gibbs free energy of reaction (Section 7.13) and standard enthalpies of formation (Section 6.18). Ghemical equilibrium calculations require a thorough knowledge of molar concentration (Section G), reaction stoichiometry (Section L), and the gas laws (Ghapter 4). 

Conditions of phase equilibrium require that the chemical potential of polymer in each phase and that of solvent in each phase be equal ... 

Another general type of behavior that occurs in polymer manufacture is shown in Figure 3. In many polymer processing operations, it is necessary to remove one or more solvents from the concentrated polymer at moderately low pressures. In such an instance, the phase equilibrium computation can be carried out if the chemical potential of the solvent in the polymer phase can be computed. Conditions of phase equilibrium require that the chemical potential of the solvent in the vapor phase be equal to that of the solvent in the liquid (polymer) phase. Note that the polymer is essentially involatile and is not present in the vapor phase. 

Table 16-2 List of input components for the simplest case of the acid-base balance of unpolluted marine clouds. Also shown are the mass conservation statements, chemical equilibrium expressions and constants, and the requirement for charge balance...

For t vo systems in chemical equilibrium we can calculate the equilibrium constant from the ratio of partition functions by requiring the chemical potentials of the t vo systems to be equal. 

From the equilibrium requirement that the chemical potential involving all ionic species be uniform throughout the phase boundary, the distribution of ions within the electrical double layer can be expressed by the Boltzmann equation ... 

In practice, measurement of the individual rate constants or equilibrium constants for these various chemical steps requires specialized methodologies, such as transient state kinetics (see Johnson, 1992, Copeland, 2000, and Fersht, 1999, for discussion of such methods) and/or a variety of biophysical methods for measuring equilibrium binding (Copeland, 2000). These specialized methods are beyond the scope of the present text. More commonly, the overall rate of reaction progress after ES complex formation is quantified experimentally in terms of a composite rate constant given the symbol km. 

One of the interests in confined polymers arises from adsorption behavior— that is, the intake or partitioning of polymers into porous media. Simulation of confined polymers in equilibrium with a bulk fluid requires simulations where the chemical potentials of the bulk and confined polymers are equal. This is a difficult task because simulations of polymers at constant chemical potential require the insertion of molecules into the fluid, which has poor statistics for long chains. Several methods for simulating polymers at constant chemical potential have been proposed. These include biased insertion methods [61,62], novel simulation ensembles [63,64], and simulations where the pore is physically connected to a large bulk reservoir [42]. Although these methods are promising, so far they have not been implemented in an extensive study of the partitioning of polymers into porous media. This is a fruitful avenue for future research. 

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-... 

Hi/9)2, so that material equilibrium requires pi)i = 1)2- The statistical parameters thus possess the essential property of chemical potentials. 

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. 

Predictions of high explosive detonation based on the new approach yield excellent results. A similar theory for ionic species model43 compares very well with MD simulations. Nevertheless, high explosive chemical equilibrium calculations that include ionization are beyond the current abilities of the Cheetah code, because of the presence of multiple minima in the free energy surface. Such calculations will require additional algorithmic developments. In addition, the possibility of partial ionization, suggested by first principles simulations of water discussed below, also needs to be added to the Cheetah code framework. 

The analysis of Ref. [42] as well as the NJL-type model investigation of Ref. [43] are based on a comparison of homogeneous phases. The neutrality conditions can, however, also be fulfilled giving up the requirement of separately neutral phases and to consider mixed phases in chemical equilibrium which are only neutral in total. This procedure has been pushed forward by Glendenning in the context of the quark-hadron phase transition in neutron stars where a similar problem related to electrical neutrality occurs [44], For the case of electrically and color neutral quark matter the phase boundaries are... 

Let us start by giving a brief introduction into the general method of constructing mixed phases by imposing the Gibbs conditions of equilibrium [23, 18]. From the physical point of view, the Gibbs conditions enforce the mechanical as well as chemical equilibrium between different components of a mixed phase. This is achieved by requiring that the pressure of different components inside the mixed phase are equal, and that the chemical potentials (p and ne) are the same across the whole mixed phase. For example, in relation... 

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