Equilibrium molecular view

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. 

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... 

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. 

The problem asks for the equilibrium pressures and a molecular view illustrating the equilibrium conditions. 

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). 

With T-i lower than Tz, the most probable molecular speed u-, is less than U2. (Note the similarity to Figure 5.12) The fraction of molecules with enough energy to escape the liquid (shaded area) is greater at the higher temperature. The molecular views show that at the higher T, equilibrium is reached with more gas molecules in the same volume and thus at a higher vapor pressure. 

Hydrolysis is the principal degradation mechanism for the condensation polymers. From the point of view of chemistry, the equilibrium molecular weight of these polymers is determined by the H O concentration at given temperature, T. However, owing to the moisture absorption from the air, the reaction equilibrium is shifted toward depolymerization. The rate of hydrolytic depolymerization depends on the moisture content, T and the presence of catalyst. Since these polymers are also subject to free-radical and oxidative processes (that lead to formation of unsaturations, hence the... 

Shaw [17-20] developed the first method of simulating chemical reactions that did not require specification of chemical potentials or chemical potential differences. This was an important step forward in modeling chemical reactants because it avoided the problems associated with specifying or calculating chemical potentials, and allowed computation of chemical equilibrium in the natural isothermal-isobaric ensemble for the first time. Shaw s method is called the Na(omspT ensemble, indicating that the method was derived from an atomic, rather than a molecular view point. As originally presented [17], the method was limited to reactions that conserve the total number of molecules. Shaw applied this method to computation of the equilibrium composition for the reaction... 

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

Dobmskin [57] proposed a model for the adsorption equilibria of multicomponent vapor mixtures based on the concept of TVFM and an adsorbed phase model in which the adsorbate-adsorbent interactions predominate over the lateral interaction between adsorbed molecules. The proportions of the component in the adsorbed phase are determined by a statistical distribution based on Frenkel s [70] mechanism and kinetic gas theory [71,72]. In Dobruskin s study, the equilibrium is viewed as a dynamic process in which the average molecular residence time T is the reciprocal of the rate constant for desorption, k. For adsorption of a binary mixture in an elementary volume dW, the ratio of the average times between two components is... 

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. 

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. 

Conservation laws at a microscopic level of molecular interactions play an important role. In particular, energy as a conserved variable plays a central role in statistical mechanics. Another important concept for equilibrium systems is the law of detailed balance. Molecular motion can be viewed as a sequence of collisions, each of which is akin to a reaction. Most often it is the momentum, energy and angrilar momentum of each of the constituents that is changed during a collision if the molecular structure is altered, one has a chemical reaction. The law of detailed balance implies that, in equilibrium, the number of each reaction in the forward direction is the same as that in the reverse direction i.e. each microscopic reaction is in equilibrium. This is a consequence of the time reversal syimnetry of mechanics. 

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. 

Furthermore, about 1920 the idea had become prevalent that many common crystals, such as rock salt, consisted of positive and negative ions in contact. It then became natural to suppose that, when this crystal dissolves in a liquid, the positive and negative ions go into solution separately. Previously it had been thought that, in each case when the crystal of an electrolyte dissolves in a solvent, neutral molecules first go into solution, and then a certain large fraction of the molecules are dissociated into ions. This equilibrium was expressed by means of a dissociation constant. Nowadays it is taken for granted that nearly all the common salts in aqueous solution are completely dissociated into ions. In those rare cases where a solute is not completely dissociated into ions, an equilibrium is sometimes expressed by means of an association constant that is to say, one may take as the starting point a completely dissociated electrolyte, and use this association constant to express the fact that a certain fraction of the ions are not free. This point of view leads directly to an emphasis on the existence of molecular ions in solution. When, for example, a solution contains Pb++ ions and Cl- ions, association would lead directly to the formation of molecular ions, with the equilibrium... 

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. 

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