Equihbrium

For all reversible secondary reactions, deliberately feeding BYPRODUCT to the reactor inhibits its formation at the source by shifting the equihbrium of the secondary reaction. This is achieved in practice by separating and recycling BYPRODUCT rather than separating and disposing of it directly. 

The general case of two compounds forming a continuous series of solid solutions may now be considered. The components are completely miscible in the sohd state and also in the hquid state. Three different types of curves are known. The most important is that in which the freezing points (or melting points) of all mixtures lie between the freezing points (or melting points) of the pure components. The equilibrium diagram is shown in Fig. 7, 76, 1. The hquidus curve portrays the composition of the hquid phase in equihbrium with sohd, the composition of... 

We define Fj to be the mole fraction of component 1 in the vapor phase and fi to be its mole fraction in the liquid solution. Here pj and p2 are the vapor pressures of components 1 and 2 in equihbrium with an ideal solution and Pi° and p2° are the vapor pressures of the two pure liquids. By Dalton s law, Plot Pi P2 Pi/Ptot these are ideal gases and p is propor-... 

Pos twe-Tone Photoresists. The ester, carbonate, and ketal acidolysis reactions which form the basis of most positive tone CA resists are thought to proceed under specific acid catalysis (62). In this mechanism, illustrated in Figure 22 for the hydrolysis of tert-huty acetate (type A l) (63), the first step involves a rapid equihbrium where the proton is transferred between the photogenerated acid and the acid-labile protecting group ... 

However, the formal differences between microemulsions and macroemulsions are well defined. A microemulsion is a single, thermodynamically stable, equihbrium phase a macroemulsion is a dispersion of droplets or particles that contains two or more phases, which are Hquids or Hquid crystals (48). 

When power is appHed to an electronic scale, it warms up and is somewhat unstable until thermal equiHbrium is reestabHshed. The manufacturer s recommendations with regard to warm-up period should be followed. 

Where there is a temperature difference between the object to be weighed and the surrounding air, air currents will be induced close to the object s surface (12). These can be significant if extreme accuracy is required. Objects should be allowed to reach thermal equiHbrium in the laboratory before weighing. Just as important, the balance should be designed to minimize the temperature rise inside the weighing chamber. In extreme cases, the object should be placed inside the chamber until it reaches thermal equiHbrium before weighing. Needless to say, drafts must be avoided. 

If a 1-kg stainless weight (m = 1, OOOg, = 8,000 kg/m ) is added to one pan of the balance in Figure 1, and material with a density of 1,000 kg/m is added to the other until equiHbrium is reached, the amount of the material needed is 1001.05 g, using equation 5. Thus, it takes 1001.05 g of this material to counterbalance 1,000 g of stainless steel, because of the buoyancy effects on the dissimilar volumes. 

As shown in Figure 1, the equiHbrium concentration is affected slightly by temperature (11). The actual concentration is affected by the reaction rate and the initial concentration of each isomer. Deviations beyond equiHbrium can be achieved when zeoHtes are used, owing to shape selectivity (see Molecularsieves). The thermal isomerization of the three xylenes has been studied at 1000°C (12). Side reactions predominated, and only a small percentage of xylenes was interconverted. 

Transalkylation is also catalyzed by acids, but requires more severe conditions than isomerization. As shown below, the methyl migration is intermolecular and ultimately produces a mixture of aromatic compounds ranging from benzene to hexamethylbenzene. The overall equiHbrium constants for all possible methylbenzenes have been deterrnined experimentally and calculated theoretically (Fig. 2 and Table 3). 

Mobil s Low Pressure Isomerization Process (MLPI) was developed in the late 1970s (123,124). Two unique features of this process are that it is Operated at low pressures and no hydrogen is used. In this process, EB is converted to benzene and diethylbenzene via disproportionation. The patent beheved to be the basis for the MLPI process (123) discusses the use of H-ZSM-5 zeoHte with an alumina binder. The reaction conditions described are start-of-mn temperatures of 290—380°C, a pressure of 273 kPa and WHSV of 5—8.5/h. The EB conversion is about 25—40% depending on reaction conditions, with xylene losses of 2.5—4%. The PX approach to equiHbrium is about 99 ndash 101%. The first commercial unit was Hcensed in 1978. A total of four commercial plants have been built. 

A second Mobil process is the Mobil s Vapor Phase Isomerization Process (MVPI) (125,126). This process was introduced in 1973. Based on information in the patent Hterature (125), the catalyst used in this process is beHeved to be composed of NiHZSM-5 with an alumina binder. The primary mechanism of EB conversion is the disproportionation of two molecules of EB to one molecule of benzene and one molecule of diethylbenzene. EB conversion is about 25—40%, with xylene losses of 2.5—4%. PX is produced at concentration levels of 102—104% of equiHbrium. Temperatures are in the range of 315—370°C, pressure is generally 1480 kPa, the H2/hydrocatbon molar ratio is about 6 1, and WHSV is dependent on temperature, but is in the range of 2—50, although normally it is 5—10. 

Mobil s High Temperature Isomerization (MHTI) process, which was introduced in 1981, uses Pt on an acidic ZSM-5 zeoHte catalyst to isomerize the xylenes and hydrodealkylate EB to benzene and ethane (126). This process is particularly suited for unextracted feeds containing Cg aHphatics, because this catalyst is capable of cracking them to light paraffins. Reaction occurs in the vapor phase to produce a PX concentration slightly higher than equiHbrium, ie, 102—104% of equiHbrium. EB conversion is about 40—65%, with xylene losses of about 2%. Reaction conditions ate temperature of 427—460°C, pressure of 1480—1825 kPa, WHSV of 10—12, and a H2/hydtocatbon molar ratio of 1.5—2 1. Compared to the MVPI process, the MHTI process has lower xylene losses and lower formation of heavy aromatics. 

A more general way of expressing solubiHties is through the vapor—Hquid equiHbrium constant m defined by... 

The value of m, also known as equiHbrium K value, is widely employed to represent hydrocarbon vapor—Hquid equiHbria in absorption and distillation... 

Fig. 3. The two-film concept and x are the concentrations in the bulk of the phases jy and x are the actual interfacial concentrations at equiHbrium ...

The experimentally observed rates of mass transfer are often proportional to the displacement from equiHbrium and the rate equations for the gas and Hquid films are... 

Mass transfer rates may also be expressed in terms of an overall gas-phase driving force by defining a hypothetical equiHbrium mole fractionjy as the concentration which would be in equiHbrium with the bulk Hquid concentration = rax ) ... 

The relationship of the overall gas-phase mass transfer coefficient to the individual film coefficients maybe found from equations 4 and 5, assuming a straight equiHbrium line ... 

A representation of the various concentrations and driving forces in a.j—x diagram is shown in Eigure 4. The point representing the interfacial concentrations x ) must He on the equiHbrium curve since these concentrations are at equiHbrium. The point representing the bulk concentrations (y, Xj may be anywhere above the equiHbrium line for absorption or below it for desorption. The slope of the tie line connecting the two points is given by equations 4 and 5 ... 

Rapid Approximate Design Procedure for Curved Operating and Equilibrium Lines. If the operating or the equihbrium line is nonlinear, equation 56 is of Httie use because will assume a range of values over the tower. The substitution of effective average values for m and... 

The principles outlined so far may be used to calculate the tower height as long as it is possible to estimate the temperature as a function of Hquid concentration. The classical basis for such an estimate is the assumption that the heat of solution manifests itself entirely in the Hquid stream. It is possible to relate the temperature increase experienced by the Hquid flowing down through the tower to the concentration increase through a simple enthalpy balance, equation 68, and thus correct the equiHbrium line in ajy—a diagram for the heat of solution as shown in Figure 9. 

Fig. 9. Simple model of adiabatic gas absorption. A, nonisotherm a1 equihbrium line for overall gas-phase driving force y = B, nonisotherm a1...

Fig. W.y—x diagram for adiabatic absorption of acetone into water. A, isothermal equihbrium line at equihbrium line for simple model of adiabatic...

Fig. 12. Correlatioa of AT. The three lines represeat the best fit of a mathematical expressioa obtaiaed by multidimensional nonlinear regressioa techniques for 99, 95, and 90% recovery the poiats are for 99% recovery. = mean molar heat capacity of Hquid mixture, average over tower AY = VA2 slope of equiHbrium line for solute, to be taken at Hquid feed temperature mg = slope of equilibrium line for solvent.

Fig. 16. Correlation of the Hquid concentration at which the inflection point of the nonisothermal equihbrium occurs (45).

---