Equilibrium macroscopic view

Thinking it Through When a reaction has reached equilibrium, it does not mean that all chemical activity has stopped. Rather, at equilibrium, the macroscopic view indicates constant (but seldom equal) concentrations for each substance, making Choice (D) the correct response. Choice (A) is a commonly held misconception, one that you will not choose if you remember the concept of dynamic equilibrium. It is also untrue that the total moles of products must equal the remaining moles of reactant, choice (B). The relative amounts of material present at equilibrium will depend greatly on the position of the equilibrium, revealed in quantitative problems by the value of the equilibrium constant. Choice (C) is based on another common misconception about equilibrium reactions. Addition of a catalyst, while it may increase the rate at which equilibrium is achieved, does not affect the position of equilibrium. 

A macroscopic view of equilibrium. The system we ll consider is the reversible gaseous reaction between colorless dinitrogen tetroxide and brown nitrogen dioxide ... 

A statistical ensemble can be viewed as a description of how an experiment is repeated. In order to describe a macroscopic system in equilibrium, its thennodynamic state needs to be specified first. From this, one can infer the macroscopic constraints on the system, i.e. which macroscopic (thennodynamic) quantities are held fixed. One can also deduce, from this, what are the corresponding microscopic variables which will be constants of motion. A macroscopic system held in a specific thennodynamic equilibrium state is typically consistent with a very large number (classically infinite) of microstates. Each of the repeated experimental measurements on such a system, under ideal... 

Relationships from thennodynamics provide other views of pressure as a macroscopic state variable. Pressure, temperature, volume and/or composition often are the controllable independent variables used to constrain equilibrium states of chemical or physical systems. For fluids that do not support shears, the pressure, P, at any point in the system is the same in all directions and, when gravity or other accelerations can be neglected, is constant tliroughout the system. That is, the equilibrium state of the system is subject to a hydrostatic pressure. The fiindamental differential equations of thennodynamics ... 

The macroscopic dielectric constant of liquid formic acid at 25° has the value 64, not much lower than that of water. Hence, from the simple electrostatic point of view, we should expect. /c for the proton transfer (211) carried out in formic acid solution, to have a value somewhat greater, but not much greater, than when the same proton transfer is carried out in water as solvent. In Table 12 we found that, in aqueous solution, the value of (./ + Jenv) rises from 0.3197 at 20°C to 0.3425 at 40°C. Measurements in formic acid at 25°C yielded for the equilibrium of (211) the value — kT log K = 4.70. Since for formic acid the number of moles in the b.q.s. is M = we find... 

Expressions (27) and (29) show how the rates of reaction (26) and its reverse, reaction (28), depend upon the concentrations. Now we can apply our microscopic view of the equilibrium state. Chemical changes will cease (on the macroscopic scale) when the rate of reaction (26) is exactly equal to that of reaction (28). When this is so, we can equate expressions (27) and (29) ... 

From a theoretical point of view, the equilibrium modulus very probably gives the best characterization of a cured rubber. This is due to the relationship between this macroscopic quantity and the molecular structure of the network. Therefore, the determination of the equilibrium modulus has been the subject of many investigations (e.g. 1-9). For just a few specific rubbers, the determination of the equilibrium modulus is relatively easy. The best example is provided by polydimethylsiloxane vulcanizates, which exhibit practically no prolonged relaxations (8, 9). However, the networks of most synthetic rubbers, including natural rubber, usually show very persistent relaxations which impede a close approach to the equilibrium condition (1-8). 

The next section is devoted to the analysis of the simplest transport property of ions in solution the conductivity in the limit of infinite dilution. Of course, in non-equilibrium situations, the solvent plays a very crucial role because it is largely responsible for the dissipation taking part in the system for this reason, we need a model which allows the interactions between the ions and the solvent to be discussed. This is a difficult problem which cannot be solved in full generality at the present time. However, if we make the assumption that the ions may be considered as heavy with respect to the solvent molecules, we are confronted with a Brownian motion problem in this case, the theory may be developed completely, both from a macroscopic and from a microscopic point of view. 

In view of the importance of macroscopic structure, further studies of liquid crystal formation seem desirable. Certainly, the rates of liquid crystal nucleation and growth are of interest in some applications—in emulsions and foams, for example, where formation of liquid crystal by nonequilibrium processes is an important stabilizing factor—and in detergency, where liquid crystal formation is one means of dirt removal. As noted previously and as indicated by the work of Tiddy and Wheeler (45), for example, rates of formation and dissolution of liquid crystals can be very slow, with weeks or months required to achieve equilibrium. Work which would clarify when and why phase transformation is fast or slow would be of value. Another topic of possible interest is whether the presence of an interface which orients amphiphilic molecules can affect the rate of liquid crystal formation at, for example, the surfaces of drops in an emulsion. 

The probability distribution in Figure 11.6 indicates that there are two stable states for the chemical reaction system of Equation (11.25). Since the system is open to species A, B, and C, these states are non-equilibrium steady states (NESS). A more careful discussion of the terminology is in order here. The concept of an NESS has different meanings depending on whether we are considering a macroscopic or a microscopic view. This difference is best understood in comparison to the term chemical equilibrium. From a macroscopic standpoint, an equilibrium simply means that the concentrations of all the chemical species are constant, and all the reactions have no net flux. However, from a microscopic standpoint, all the concentrations are fluctuating. 

It is in the treatment of such interacting transport processes, or coupled flows, that the methods of near-equilibrium thermodynamics yield a clear understanding of such phenomena, but only from a macroscopic or phenomenological point of view. These methods, as relevant to the present discussion, can be summarized with the following series of statements ... 

The topic arises from the following sequence of aspects of entropy when entropy is introduced on a thermodynamic basis the issue is the motion of heat (Jaynes, 1988), and the assessment involves calorimetry an entropy change is evaluated. When entropy is formalized with the classical view of statistical thermodynamics, the entropy is found by evaluating a configurational integral (Bennett, 1976). But a macroscopic physical system at a particular thermodynamic state has a particular entropy, a state function, and the whole description of the physical system shouldn t involve more than a mechanical trajectory for the system in a stationary, equilibrium condition. How are these different concepts compatible ... 

We shall start with a couple of such naive models for the liquid state, and for reactions occurring in solution. A molecular liquid in macroscopic equilibrium may be viewed as a large assembly of molecules incessantly colliding, and exchanging energy among collision partners and among in-... 

The kinetics of adsorption and desorption and the Elovich equation have been the matter of a comprehensive review by Aharoni and Tompkins in 1970 [14]. At that time, however, concepts now pervasive in physical chemistry of surfaces like fractality were not known, the mathematical theory of adsorption equilibrium on heterogeneous surfaces was at its beginning, and the notion of equilibrium surfaces had not demonstrated yet its usefulness in the understanding of adsorption phenomena on real surfaces. In view of these facts there is a space for another work, which however does not intend to be as comprehensive as that of Aharoni and Tompkins, but rather aims to study the Elovich behaviour met in new situations, to elucidate the theoretical origin of Eq. (3), and to relate the macroscopic empiric parameters te, and t and to microscopic quantities. 

---