Phases dynamic equilibrium

Hoover W G 1985 Canonical dynamics equilibrium phase-space distributions Phys. Rev. A 31 1695-7... 

Hoover W G 1985. Canonical Dynamics Equilibrium Phase-space Distributions. Physical Revic A31 1695-1697. 

The Clapeyron equation expresses the dynamic equilibrium existing between the vapor and the condensed phase of a pure substance ... 

This description of the dynamics of solute equilibrium is oversimplified, but is sufficiently accurate for the reader to understand the basic principles of solute distribution between two phases. For a more detailed explanation of dynamic equilibrium between immiscible phases the reader is referred to the kinetic theory of gases and liquids. 

Additional evidence that a dynamic equilibrium exists between an enamine, N-hemiacetal, and aminal has been presented by Marchese (41). It should be noted that no acid catalysts were used in the reactions of aldehydes and amines discussed thus far. The piperidino enamine of 2-ethylhexanal (0.125 mole), morpholine (0.375 mole), and p-toluene-sulfonic acid (1.25 x 10 mole) diluted with benzene to 500 ml were refluxed for 5 hr. At the end of this time the enamine mixture was analyzed by vapor-phase chromatography, which revealed that exchange of the amino residue had occurred in a ratio of eight morpholine to one piperidine. Marchese proposed a scheme [Eqs. (4), (5) and (6)] to account for these... 

Vapor pressure is an important property of liquids, and to a much lesser extent, of solids. If a liquid is allowed to evaporate in a confined space, tlie pressure of Uie vapor phase increases as Uie amount of vapor increases. If Uiere is sufficient liquid present, Uie pressure in Uie vapor space eventually comes to equal exacUy Uie pressure exerted by the liquid at its own surface. At Uiis point, a dynamic equilibrium exists in wliich vaporization and condensation take place at equal rates and Uie pressure in Uie vapor space remains constant. The pressure exerted at equilibrium is called Uie vapor pressure of the liquid. Solids, like liquids, also exert a vapor pressure. EvaporaUon of solids (sublimaUon) is noUccable only for Uie few solids characterized by appreciable vapor pressures. 

It is clear that pure" anhydrous sulfuric acid, far from being a single substance in the bulk liquid phase, comprises a dynamic equilibrium involving at least seven well-defined species. The... 

W.G. Hoover, Canonical dynamics Equilibrium phase-space distributions,... 

When a solid, such as ice, is in contact with its liquid form, such as water, at certain conditions of temperature and pressure (at 0°C and 1 atm for water), the two states of matter are in dynamic equilibrium with each other, and there is no tendency for one form of matter to change into the other form. When solid and liquid water are at equilibrium, water molecules continually leave solid ice to form liquid water, and water molecules continually leave the liquid phase to form ice. However there is no net change, because these processes occur at the same rate and so balance each other. 

Whenever we see the symbol it means that the species on both sides of the symbol are in dynamic equilibrium with each other. Although products (water molecules in the gas phase) are being formed from reactants (water molecules in the liquid phase), the products are changing back into reactants at a matching rate. With this picture in mind, we can now define the vapor pressure of a liquid (or a... 

The vapor pressure of a given phase of a substance is the pressure exerted by its vapor when the vapor is in dynamic equilibrium with the condensed phase. 

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

A phase diagram summarizes the regions of pressure and temperature at which each phase of a substance is most stable. The phase boundaries show the conditions under which two phases can coexist in dynamic equilibrium with each other. Three phases coexist in mutual equilibrium at a triple point. 

A feature of the phase diagram in Fig. 8.12 is that the liquid-vapor boundary comes to an end at point C. To see what happens at that point, suppose that a vessel like the one shown in Fig. 8.13 contains liquid water and water vapor at 25°C and 24 Torr (the vapor pressure of water at 25°C). The two phases are in equilibrium, and the system lies at point A on the liquid-vapor curve in Fig. 8.12. Now let s raise the temperature, which moves the system from left to right along the phase boundary. At 100.°C, the vapor pressure is 760. Torr and, at 200.°C, it has reached 11.7 kTorr (15.4 atm, point B). The liquid and vapor are still in dynamic equilibrium, but now the vapor is very dense because it is at such a high pressure. 

Like phase changes, chemical reactions tend toward a dynamic equilibrium in which, although there is no net change, the forward and reverse reactions are still taking place, but at matching rates. What actually happens when the formation of ammonia appears to stop is that the rate of the reverse reaction,... 

Wet towels hung on a clothesline eventually dry, because the continual motion of molecules in liquid water allows some molecules to escape from the liquid phase (Figure 2-9aV A wet towel left in a closed washing machine, however, stays wet for a long time. This is because water molecules that escape from the surface of the towel remain within the washing chamber (Figure 2-9b). The number of water molecules in the gas phase increases, and the towel recaptures some of these molecules when they collide with its surface. The system soon reaches a condition of dynamic equilibrium in which, for every water molecule that leaves the surface of the towel, one water molecule returns from the gas phase to the towel (Figure 2-9cV Under these conditions, the towel remains wet indefinitely. 

Summarizing, once this system has reached dynamic equilibrium, molecules continue to leave the liquid phase for the gas phase, but the liquid captures equal numbers of molecules from the gas. The amount of water in each phase remains the same (equilibrium) even though molecules continue to move back and forth between the gas and the liquid (dynamic). As with dye dispersed in water, no net change occurs after equilibrium is established. 

C02-0037. Iodine is an element whose molecules can move directly from the solid to the gas phase. A sample of solid iodine in a stoppered flask stood undisturbed for several years. As the photo shows, crystals of solid iodine grew on the sides of the flask. Use the principle of dynamic equilibrium to explain at the molecular level what happened. Include an observation about the color of the atmosphere inside the flask. 

C02-0097. The element bromine exists as diatomic molecules and is a liquid under normal conditions. Bromine evaporates easily, however, giving a red-brown color to the gas phase above liquid bromine, as shown in the photo. Draw molecular pictures showing liquid bromine, the gas above it, and the dynamic equilibrium between the phases. 

When a solution is saturated, there is dynamic equilibrium. Solute molecules move back and forth between the solute phase and the solution phase at equal rates. 

Several observations show that saturated solutions are at dynamic equilibrium. For example, if O2 gas enriched in the oxygen-18 isotope is introduced into the gas phase above water that is saturated with oxygen gas, the gas in the solution eventually also becomes enriched in the heavier isotope. As another example, if finely divided ciystalline salt is in contact with a saturated solution of the salt, the small crystals slowly disappear and are replaced by larger crystals. Each of these observations shows that molecules are moving between the two phases, yet the concentrations of the saturated solutions remain constant. 

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 addition of solutes decreases the freezing point of a solution. In the solution, solvent molecules collide with crystals of solid solvent less frequently than they do in the pure solvent. Consequently, fewer molecules are captured by the solid phase than escape from the solid to the liquid. Cooling the solution restores dynamic equilibrium because it simultaneously reduces the number of molecules that have sufficient energy to break away from the surface of the solid and increases the number of molecules in the liquid with small enough kinetic energy to be captured by the solid. 

The effect of a solute on the boiling point of a solution is opposite to its effect on the freezing point. A nonvolatile solute inereases the boiling point of a solution. This is because the solute blocks some of the solvent molecules from reaching the surface of the solution and thus decreases the rate of escape into the gas phase. To get back to dynamic equilibrium, the solution must be heated so that more molecules acquire sufficient energy to escape from the liquid phase. 

C14-0122. At its triple point, a dynamic equilibrium can exist among all three phases of matter. Draw a molecular picture of argon that shows what happens at the triple point. What is AG for each of the processes under these conditions Describe the matter and energy dispersal taking place for each of the processes. 

Given that, under the defined conditions, there is no interfacial kinetic barrier to transfer from phase 2 to phase 1, the concentrations immediately adjacent to each side of the interface may be considered to be in dynamic equilibrium throughout the course of a chronoamperometric measurement. For high values of Kg the target species in phase 2 is in considerable excess, so that the concentration in phase 1 at the target interface is maintained at a value close to the initial bulk value, with minimal depletion of Red in phase 2. Under these conditions, the response of the tip (Fig. 11, case (a)] is in agreement with that predicted for other SECM diffusion-controlled processes with no interfacial kinetic barrier, such as induced dissolution [12,14—16] and positive feedback [42,43]. A feature of this response is that the current rapidly attains a steady state, the value of which increases... 

The results of the unsteady-state reactivity tests and of the catalysts characterization allow us to propose a model for the active layer of VPP under reaction conditions, illustrated in Figure 55.5. In this model, the surface is in dynamic equilibrium with the gas phase, and its nature is a function of both reaction... 

Hoover WG (1985) Canonical dynamics equilibrium phase-space distributions. Phys Rev A 31(3) 1695—1697... 

An interesting extension of the original methodology was proposed by Lopes and Tildesley to allow the study of more than two phases at equilibrium [21], The extension is based on setting up a simulation with as many boxes as the maximum number of phases expected to be present. Kristof and Liszi [22, 23] have proposed an implementation of the Gibbs ensemble in which the total enthalpy, pressure and number of particles in the total system are kept constant. Molecular dynamics versions of the Gibbs ensemble algorithm are also available [24-26]. 

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