View of Equilibrium

Phase equilibrium can be viewed as a dynamic process on the molecular level. We will discuss this perspective by considering a system containing a pure species in vapor-liquid equilibrium, but the principles can be applied to liquid-solid, vapor-solid, and even solid-solid phase equilibria. 

Vapor-liquid equilibrium depends on two counteracting processes occurring at the phase boundary marked by the liquid surface. The liquid-phase molecules with enough 

If effects such as surface tension or gravitational electric, or magnetic fields are important, the system is confronted with other driving forces that the criteria for equilibrium must also include. 

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Le Chatelier s Principle permits the chemist to make qualitative predictions about the equilibrium state. Despite the usefulness of such predictions, they represent far less than we wish to know. It is a help to know that raising the pressure will favor production of NH3 in reaction (10a). But how much will the pressure change favor NH3 production Will the yield change by a factor of ten or by one-tenth of a percent To control a reaction, we need quantitative information about equilibrium. Experiments show that quantitative predictions are possible and they can be explained in terms of our view of equilibrium on the molecular level. 

The double arrow represents the condition of equilibrium that exists between the non-ionized and the ionized species of the electrolyte. Since ionization of strong electrolytes is practically complete there will not be much gain in studying this type of reaction from the point of view of equilibrium. Equilibria involving weak electrolytes, where there is only partial ionization, are of considerable importance. 

Students may have a compartmentalised view of equilibrium - as somehow involving two disconnected sides of a reaction (Griffiths, 1994). For instance, they make a distinction between a left and a right side within an equilibrium system and then believe that both sides can act independently from one another (Johnstone et al., 1977. This study involved upper secondary school students from Scotland). 

Students holding a compartmentalised view of equilibrium often believe that the effect of imposing a constraint, such as changing temperature or pressure, on a system at equilibrium causes a change in the amounts of substances on only one side of the equation (Jonnstone et al., 1977). 

Chromium monosiUcide, formed by a peritectic reaction [10] (this point is essential for a critical evaluation of the results jErom the point of view of equilibrium of the samples studied), is characterized by an effective magnetic moment (/leff) which varies in the temperature range investigated and corresponds to a change of the number of unpaired electrons per metal atom from about 1.3 to about 2.5 [4,6] (these figures are only estimates, since in this case it is possible only to refer nominally to the validity of the Curie-Weiss law in each narrow temperature range). 

This completes our description of the thermodynamic basis functions in terms of the configurational and momenta density functions obtained directly from the equilibrium solution to the Liouville equation. As will be shown in the next chapter, the nonequilibrium counterparts (local in space and time) of the thermodynamic basis functions can also be obtained directly from the Liouville equation, thus, providing a unified molecular view of equilibrium thermodynamics and chemical transport phenomena. Before moving on, however, we conclude this chapter by noting some important aspects of the equilibrium solution to the Liouville equation. 

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

A qmntitiative view of equilibrium a constant ratio of constants. Let s see how reactant and product concentrations affect this process. At a particular temperature, when the system reaches equilibrium, we have... 

An enlarged view of a crystal is shown in Fig. VII-11 assume for simplicity that the crystal is two-dimensional. Assuming equilibrium shape, calculate 711 if 710 is 275 dyn/cm. Crystal habit may be changed by selective adsorption. What percentage of reduction in the value of 710 must be effected (by, say, dye adsorption selective to the face) in order that the equilibrium crystal exhibit only (10) faces Show your calculation. 

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 ... 

We can sample the energy density of radiation p(v, T) within a chamber at a fixed temperature T (essentially an oven or furnace) by opening a tiny transparent window in the chamber wall so as to let a little radiation out. The amount of radiation sampled must be very small so as not to disturb the equilibrium condition inside the chamber. When this is done at many different frequencies v, the blackbody spectrum is obtained. When the temperature is changed, the area under the spechal curve is greater or smaller and the curve is displaced on the frequency axis but its shape remains essentially the same. The chamber is called a blackbody because, from the point of view of an observer within the chamber, radiation lost through the aperture to the universe is perfectly absorbed the probability of a photon finding its way from the universe back through the aperture into the chamber is zero. 

Charge diagrams suggest that the 2-amino-5-halothiazoles are less sensitive to nucleophilic attack on 5-position than their thiazole counterpart. Recent kinetic data on this reactivity however, show, that this expectation is not fulfilled (67) the ratio fc.. bron.c.-2-am.noih.azoie/ -biomoth.azoie O"" (reaction with sodium methoxide) emphasizes the very unusual amino activation to nucleophilic substitution. The reason of this activation could lie in the protomeric equilibrium, the reactive species being either under protomeric form 2 or 3 (General Introduction to Protomeric Thiazoles). The reactivity of halothiazoles should, however, be reinvestigated under the point of view of the mechanism (1690). 

Bicucine, C20H19O7N, H2O. This alkaloid has m.. 222° (dec.) and — 115 4° (N/10, KHO) but in N/HCl it shows mutarotation — 145° to — 100°,due to the formation of an equilibrium mixture of bicucine and bicuculline. Alkaline permanganate oxidises it to 3 4-methylene-dioxyphthalic acid, isolated as the ethylimide. In view of its formation from bicuculline by the action of alkali, Manske has suggested for its formula (II) or (III), the former representing it as the nomarceine (p. 208) analogue of bicuculline, whilst (III) makes it the hydroxy-acid corresponding to the lactone, bicuculline and is preferred. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

Energy calculations and geometry optimizations ignore the vibrations in molecular systems. In this way, these computations use an idealized view of nuclear position. In reality, the nuclei in molecules are constantly in motion. In equilibrium states, these vibrations are regular and predictable, and molecules can be identified by their characteristic spectra. 

Horvath, J. and Novak, M., Potential/pH Equilibrium Diagrams of Some Me-S-HjO Ternary Systems and Their Interpretation from the Point of View of Metallic Corrosion , Corros. Sci., 4, 159 (1964)... 

This area will be passivated by the increase in pH due to the cathodically produced OH ions, and partially cathodically protected by the electrons liberated by the anodic processes within the pit. The tubercle thus results in an occluded cell with the consequent acidification of the anodic sites. Wranglen considers that in view of the fact that crystals of FeClj -4H20 are sometimes observed at the bottom of a pit the solution within the pit is a saturated solution of that salt, and that this will correspond with an equilibrium pH of about 3-5. 

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) ... 

We see in Table 11-IV that the equilibrium view of acid strengths suggests that we regard water itself as a weak acid. It can release hydrogen ions and the extent to which it does so is indicated in its equilibrium constant, just as for the other acids. We shall see that this type of comparison, stimulated by our equilibrium considerations, leads us to a valuable generalization of the acid-base concept. 

Reaction (19) is carried out at a high temperature (about 500°C in the contact process). How does temperature affect equilibrium, according to Le Chatelier s Principle In view of your answer, propose an explanation of why the temperature is kept high. 

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