Equilibrium phase changes

Example 8.2 Use Figure 8.9 to predict the phase changes that would occur when solid Sn at p = 0.1 MPa is compressed isothermally to p = 15 GPa at (a) 7 = 600 K (b) 7 = 550 K and (c) 7 = 250 K. Assume that the equilibrium phase changes occur rapidly enough to keep up with the change in pressure. 

For any equilibrium phase change for a pure substance represented by A = B... 

The important role of volume fraction on the structure of rigid sphere dispersions has been uncovered recently as the volume fraction of hard spheres is increased, the equilibrium phase changes from a disordered fluid to coexistence with a crystalline phase (0.494<<0.545), then to fully crystalline ( = 0.545), and finally to a glass (0 = 0.58) (Pham et al. 2002). 

For equilibrium phase changes at constant temperature, pressure, and particle number, the Gibbs free energy does not change, as shown in the next example. 

Complexity of the catalytic process itself. The catalytic processes are very complicated. One of the factors that influences catalyst properties includesnon-linearity of surface catalytic reactions which is rarely taken into considerations. The catalyst surface has a feature of fractional-dimension structures where the distributions of the active center on surface show multi-fractional-dimension characteristics. At the same time, there is a non-equilibrium phase change and space-time ordered structures such as the chemical oscillation and chaos during a certain process. 

Two phases of a single substance can be at equilibrium with each other at a fixed temperature that depends on the pressure. For example, liquid and gaseous water can be at equilibrium with each other at 100.00°C if the pressure is 1.000 atm (760.0 torr), and can be at equilibrium with each other at 25.00°C if the pressure is 23.756 torr. If an equilibrium phase change is carried out at constant pressure and temperatureEq. (3.3-2) apphes. Since the pressure is constant, q is equal to AH, and... 

Fig. 11.10. Changes during the tempering of martensite. There is a large driving force trying to moke the martensite transform to the equilibrium phases of or + Fe3C. Increasing the temperature gives the atoms more thermal energy, allowing the transformation to take place.

Another technique that can be used to account for the presence of liquids is to assume that the water and oil in the stream pass through the choke with no phase change or loss of temperature. The gas is assumed to cool to a temperature given in Figure 4-8. The heat capacity of the liquids is then used to heat the gas to determine a new equilibrium temperature. 

The use of kinetic inhibitors and/or anti-agglomcrators in actual fieid operations is a new and evolving technology. These are various formulations of chemicals that can be used in a mixture of one or more kinetic inhibitors and/or anti-agglomerators. At the current time, to get an optimum mixture for a specific application it is necessary to set up a controlled bench test using the actual fluids to be inhibited and determine the resulting equilibrium phase line. As the mixture of chemicals is changed, a family of equilibrium phase lines will develop. This will result m an initial determination of a near optimum mixture of chemicals. 

We have encountered equilibrium before—in our we considered the liquid-gas equilibrium that consideration of phase changes. In Section 5-1.2 fixes the vapor pressure of a liquid, and in Sec-142... 

For chemical reactions, just as for phase changes, at equilibrium, microscopic processes continue but in a balance which gives no macroscopic changes. 

Experience indicates that the Third Law of Thermodynamics not only predicts that So — 0, but produces a potential to drive a substance to zero entropy at 0 Kelvin. Cooling a gas causes it to successively become more ordered. Phase changes to liquid and solid increase the order. Cooling through equilibrium solid phase transitions invariably results in evolution of heat and a decrease in entropy. A number of solids are disordered at higher temperatures, but the disorder decreases with cooling until perfect order is obtained. Exceptions are... 

Changing the pressure will have a similar effect. If we increase p by dp, the solid melts. This process can be reversed at any time by decreasing the pressure by dp. Note that at p = 1 atm (101.325 kPa), only at T = 273.15 K can the phase change be made to occur reversibly because this is the temperature where solid and liquid are in equilibrium at this pressure. If we tried to freeze liquid water aip— atm and a lower temperature such as 263.15 K, the process, once started, would proceed spontaneously and could not be reversed by an infinitesimal change in p or T. 

The consequences of these equations are seen in Figure 5.8 in which and are plotted against temperature at a fixed pressure. At the temperature T(h Ma = Mb and the two phases are in equilibrium. For T > To, ma > Mb and B is the stable phase. For T < To, /xB > and A is the stable phase. It can be seen from these relationships that n is a potential that drives the flow of mass in a phase change. Mass flows from the phase with high potential to the phase with low potential. When the two potentials are equal, equilibrium is established and there is no net flow of mass. 

A pressure displacement dp and a temperature displacement d T are made on the system. This causes changes in the chemical potentials dp,, and dp / If the phases are to remain in equilibrium, these changes must be equal so that... 

Solution (a) At 7 — 600 K, liquid Sn freezes at 3 GPa to form solid III. Apparently, no other phase changes occur with increasing pressure, (b) At 550 K, liquid Sn freezes to form solid II at 1.5 GPa, then changes to solid III at 3.5 MPa. (c) At 250 K, solid I converts to solid II at 0.3 GPa, which presumably would convert to solid III at approximately 11 MPa. (The equilibrium line stops at 10 GPa.)... 

As mentioned earlier, the physical properties of a liquid mixture near a UCST have many similarities to those of a (liquid + gas) mixture at the critical point. For example, the coefficient of expansion and the compressibility of the mixture become infinite at the UCST. If one has a solution with a composition near that of the UCEP, at a temperature above the UCST, and cools it, critical opalescence occurs. This is followed, upon further cooling, by a cloudy mixture that does not settle into two phases because the densities of the two liquids are the same at the UCEP. Further cooling results in a density difference and separation into two phases occurs. Examples are known of systems in which the densities of the two phases change in such a way that at a temperature well below the UCST. the solutions connected by the tie-line again have the same density.bb When this occurs, one of the phases separates into a shapeless mass or blob that remains suspended in the second phase. The tie-lines connecting these phases have been called isopycnics (constant density). Isopycnics usually occur only at a specific temperature. Either heating or cooling the mixture results in density differences between the two equilibrium phases, and separation into layers occurs. 

Although this section provides only a brief introduction to equilibrium, the principles presented here arc critically important, because the tendency of reactions to proceed toward equilibrium is the basis of much of chemistry. The material in this section lays the foundation for the next five chapters, including phase changes, the reactions of acids and bases, and redox reactions. 

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,... 

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