Molecular view of equilibrium

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. 

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. 

Molecular view of a gasnsolution equilibrium, (a) At equilibrium, the rate of escape of gas molecules from the solution equals the rate of capture of gas molecules by the solution, (b) An increase in gas pressure causes more gas molecules to dissolve, throwing the system out of equilibrium, (c) The concentration of solute increases until the rates of escape and capture once again balance. 

Figure 12-11 is a molecular view of how a solute changes this liquid-vapor equilibrium of the solvent. The presence of a solute means that there are fewer solvent molecules at the surface of the solution. As a result, the rate of solvent evaporation from a solution is slower than the rate of evaporation of pure solvent. At equilibrium, the rate of condensation must be correspondingly slower than the rate of condensation for the pure solvent at equilibrium with its vapor. In other words, the vapor pressure drops when a solute is added to a liquid. A solute decreases the concentration of solvent molecules in the gas phase by reducing the rates of both evaporation and condensation. 

Molecular views of the rates of solid-liquid phase transfer of a pure liquid and a solution at the normal freezing point. The addition of solute does not change the rate of escape from the solid, but it decreases the rate at which the solid captures solvent molecules from the solution. This disrupts the dynamic equilibrium between escape and capture. 

The second part of Figure 14-1 shows a molecular view of what happens in the two bulbs. Recall from Chapter 5 that the molecules of a gas are in continual motion. The NO2 molecules in the filled bulb are always moving, undergoing countless collisions with one another and with the walls of their container. When the valve between the two bulbs is opened, some molecules move into the empty bulb, and eventually the concentration of molecules in each bulb is the same. At this point, the gas molecules are in a state of dynamic equilibrium. Molecules still move back and forth between the two bulbs, but the concentration of molecules in each bulb remains the same. 

The figure represents a molecular view of a gas-phase reaction that has reached equilibrium. Assuming that each molecule in the molecular view represents a partial pressure of 1.0 bar, determine for this... 

A molecular view of the solubility equilibrium for a solution of sodium chloride in water. At equilibrium, ions dissolve from the crystal surface at the same rate they are captured, so the concentration of ions in the solution remains constant. 

Observe a molecular view of dynamic equilibrium in your Chemistry 12 Electronic Learning Partner. 

FIGURE 11.8 A molecular view of Henry s law. (a) At a given pressure, an equilibrium exists in which equal numbers of gas particles enter and leave the solution, (b) When pressure is increased by pushing on the piston, more gas particles are temporarily forced into solution than are able to leave, so solubility increases until a new equilibrium is reached (c). 

Figure lo-i Macroscopic and molecular view of vapor-liquid equilibrium. 

The process is said to reach equilibrium.Theflasks,A,B,and C, present the molecular view of the process at positions A, B,and C on the curve. 

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. 

Figure 12-10 is a molecular view showing that the equilibrium concentration of a dissolved gas varies with the partial pressure of that gas. An increase in the partial pressure of gas results in an increase in the rate at which gas molecules enter the solution. This increases the concentration of gas in solution. The increased concentration in solution, in turn, results in an increase in the rate at which gas molecules escape from the solution. Equilibrium is reestablished when the solute concentration is high enough that the rate of escape equals the rate of capture. 

The molecular view represents a set of initial conditions for the reaction described in Example. Each molecule represents a partial pressure of 1.0 bar. Determine the equilibrium conditions and redraw the picture to illustrate those conditions. 

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). 

In this chapter, the diverse coupling constants and MEC components identified in the combined electronic-nuclear approach to equilibrium states in molecules and reactants are explored. The reactivity implications of these derivative descriptors of the interaction between the electronic and geometric aspects of the molecular structure will be commented upon within both the EP and EF perspectives. We begin this analysis with a brief survey of the basic concepts and relations of the generalized compliant description of molecular systems, which simultaneously involves the electronic and nuclear degrees-of-freedom. Illustrative numerical data of these derivative properties for selected polyatomic molecules, taken from the recent computational analysis (Nalewajski et al., 2008), will also be discussed from the point of view of their possible applications as reactivity criteria and interpreted as manifestations of the LeChatelier-Braun principle of thermodynamics (Callen, 1962). 

The direct detection of a complex from an equilibrium mixture is certainly the most obvious evidence of specific molecular interactions between components. Electrophoresis of an equilibrium mixture is an easily performed experiment, enabling the determination of complex formation parameters. When the dissociation kinetics of the complex is slow, the complex gives rise to a new peak in the electropherogram, in addition to the peaks of the free component molecules. Since the separation of the free components prevents the reformation of the complex inside the capillary, the complex peak should decrease in size during electrophoresis. The extent of this decrease depends on dissociation kinetics and separation time. In view of that fact, short analysis times, as obtained in CE, are required to detect less stable complexes, which would hardly be detected using previous formats of electrophoresis with longer separation times. 

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