Systems and Equilibrium

In this brief review of dynamics in condensed phases, we have considered dense systems in various situations. First, we considered systems in equilibrium and gave an overview of how the space-time correlations, arising from the themial fluctuations of slowly varying physical variables like density, can be computed and experimentally probed. We also considered capillary waves in an inliomogeneous system with a planar interface for two cases an equilibrium system and a NESS system under a small temperature gradient. 

In the context of chemical kinetics, the eigenvalue technique and the method of Laplace transforms have similar capabilities, and a choice between them is largely dependent upon the amount of algebraic labor required to reach the final result. Carpenter discusses matrix operations that can reduce the manipulations required to proceed from the eigenvalues to the concentration-time functions. When dealing with complex reactions that include irreversible steps by the eigenvalue method, the system should be treated as an equilibrium system, and then the desired special case derived from the general result. For such problems the Laplace transform method is more efficient. 

Conceptualizing a geochemical model is a matter of defining (1) the nature of equilibrium to be maintained, (2) the initial composition and temperature of the equilibrium system, and (3) the mass transfer or temperature variation to occur over the course of the reaction process envisioned. 

The fugacities of gases such as CO2 and O2 can be buffered (Fig. 2.1 see Chapter 14) so that they are held constant over the reaction path. In this case, mass transfer between the equilibrium system and the gas buffer occurs as needed to maintain the buffer. Adding acid to a C02-buffered system, for example, would be likely to dissolve calcite,... 

In this chapter we consider how to construct reaction models that are somewhat more sophisticated than those discussed in the previous chapter, including reaction paths over which temperature varies and those in which species activities and gas fugacities are buffered. The latter cases involve the transfer of mass between the equilibrium system and an external buffer. Mass transfer in these cases occurs at rates implicit in solving the governing equations, rather than at rates set explicitly by the modeler. In Chapter 16 we consider the use of kinetic rate laws, a final method for defining mass transfer in reaction models. 

Our goal in this chapter is to help you master the concept of chemical equilibria, the mathematical representations that we use in equilibrium systems and the manipulation of equilibrium by factors such as temperature and pressure. Chapters 15 and 16 will rely on the basic concepts presented in this chapter. Mastering them here will make things much easier later. Mastering these concepts will require, you guessed it, Practice, Practice, Practice. 

Changes in pressure are only significant if there are gases involved. The pressure may be changed by changing the volume of the container or by changing the concentration of a gaseous species. If the container becomes smaller, the pressure increases because there are an increased number of collisions on the inside walls of the container. This stresses the equilibrium system and it will shift in order to reduce the pressure. A shift towards the side of the equation that has the least number of moles of gas will accomplish this. If the container... 

Our goal in this chapter is to help you continue learning about acid-base equilibrium systems and, in particular, buffers and titrations. If you are a little unsure about equilibria and especially weak acid-base equilibria, review Chapters 14 and 15. You will also learn to apply the basic concepts of equilibria to solubility and complex ions. Two things to remember (1) The basic concepts of equilibria apply to all the various types of equilibria, and (2) Practice, Practice, Practice. 

This is equivalent to dividing the original particle into four equal pieces. From Doyle s data, this was obviously not the case since a few very small droplets of higher charge-to-mass ratio were ejected from the large droplet. One may conclude, therefore, that an atomizing system is not an equilibrium system and that the approach leading to Eq. (55) is not valid. 

Assume that such an equilibrium can exist in some crevice in an automotive cylinder or manifold. Determine whether raising the temperature decreases or increases the amount of carbon present. Determine the Kp for this equilibrium system and the effect of raising the pressure on the amount of carbon formed. 

Your teacher will give you a table that lists four equilibrium systems and the changes you will make to each system. In the appropriate column, record your predictions for each test. If you predict that the change will cause the system to re-attain equilibrium by shifting toward the reactants, record left. If you predict that the system will re-establish equilibrium by shifting toward the products, record right. ... 

The calculation of the affinity scale, in terms of differences in free-energy content between the various ionic forms of these materials, implies that one is dealing with equilibrium systems and that the reaction is both reversible and stoichiometric, i.e., hydrolysis phenomena are absent in the zeolite. Within certain limits, these conditions are generally met however, it is apparent that some discrepancies between experimental data have sometimes been attributed (1) to a failure in the fulfillment of one or more of these basic prerequisites. 

Figure 5. Schematic of an external EM field interaction with the equilibrium system and the dissipative subsystem. a(w) and are the attenuation function and the biological-response function for the equilibrium system, respectively aBIsM and [hns(i ) are the same functions, respectively, for the dissipative subsystem,- m is the frequency of the EM field.

In 1888 the French chemist Henri Le Chatelier studied equilibrium systems and came up with an idea for describing what happens to an equilibrium when it is stressed by a change. There are times when it is important to take a qualitative look at a chemical reaction to see how it responds to changes. 

You will see this topic appear twice, once in this chapter and once the next chapter. For now, you will see how this phenomenon affects acid-base equilibria. In the next chapter, you will see its effects on solubility equilibria. The common-ion effect is not too different from what its name suggests. If you have an equilibrium system and add a solute to it that contains one of the ions in the equilibrium, it will cause the equilibrium to shift. That is the common-ion effect (common because the solute has an ion in common with the equilibrium system). From a conceptual standpoint, this can be addressed using Le Chatelier s Principle. For example, consider our favorite equilibrium system below ... 

Cyclopentadienyltin(II) chloride and bromide can be made by the exchange reaction shown in Eq. (2) (79). This is apparently an equilibrium system, and the product is determined by the relative solubility of the reagents present. It is not possible to synthesize the iodide this way because it is too soluble in THF (31). 

Intensive properties that specify the state of a substance are time independent in equilibrium systems and in nonequilibrium stationary states. Extensive properties specifying the state of a system with boundaries are also independent of time, and the boundaries are stationary in a particular coordinate system. Therefore, the stationary state of a substance at ary point is related to the stationary state of the system. 

The surface elasticity force is considered as the most important factor of stability of steady-state foams [113]. In the model of Malysa [123] it is assumed that a dynamic foam is a non-equilibrium system and phenomena occurring in the solution have an influence on the formation and stability of the foam. The foam collapse takes place only at the top of the foam bubbles at thickness larger than 100 nm, where fl = 0. So, the lifetime of the bubbles at the... 

These strategies capitalize on the perturbation of an equilibrium system and the measure of the return of the system to equilibrium they are valuable because they apply almost universally to solutions and can shed light on the multi-step association process. Unfortunately they are technologically demanding and expensive even when commercially available. Additionally, only very experienced and capable practitioners can exploit the potential of these strategies since ion-pairing is detected by the observation and appraisal of new features in spectra. 

Liu Z.-K. and Agren J. (1995) Thermodynamics of constrained and unconstrained equilibrium systems and their phase rules. J. Phase Equil. 16, 30-35. 

The NO2-N2O4 equilibrium system is shown at three different temperatures. Temperature changes put stress on equilibrium systems and cause either the forward or reverse reaction to be favored. 

CD-ROM Simulation Exploration of Equilibrium Systems and the Equilibrium Constant. 

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