Equilibrium composition

Example 8.2 Equilibrium compositions Consider the following chemical reaction 

Determine the equilibrium compositions in terms of the extent of the reaction. 

The enthalpy of reaction A//r can be calculated from the Gibbs-Helmholtz equation 

The standard enthalpy of reaction AH° and the standard Gibbs energy of reaction AG° can also be obtained from the standard enthalpy of formation of species / A// ,- and the standard Gibbs energy of formation of species / AG ,- by the following equations 

From Eqs. (8.10) and (8.17), we can relate the equilibrium constant with the standard enthalpy of reaction 

---

Determine the equilibrium composition of saturated solution of AgCl. Assume that the solubility of AgCl is influenced by the following reactions. 

D. R. Cmise, Theoretical Computation of Equilibrium Composition, Thermal Dynamic Properties, and Peformance Characteristics of Propellants Systems, NWC... 

S. Gordon and B. J. McBride, Computer Program for Calculation of Complex Equilibrium Compositions. Rocket Peformance Incident and Reflected Shocks and Chapman-]ouquetDetonations, NASA-Lewis Research Center, NASA, Airport, Md., Mar. 1976. 

Table 5. Equilibrium Composition of the Strong Phosphoric Acids ...

The MTDP process, which is similar to the Tatoray process, produces an equilibrium composition of xylene isomers. A -xylene yield of 24% in the xylene product is formed at 42—48 wt % toluene conversion over the heterogeneous catalyst at 390—495°C, 4.2 MPa (600 psig), 1 2 Hquid hourly space velocity, and 4 H2/hydrocarbon molar feed ratio. A new ZSM-5 catalyst, which has higher activity and stability than the current catalyst, has been reported (93). 

Table 3. Calculated Vapor—Liquid Equilibrium Composition for Propylene Hydration ...

The standard Gibbs energy change of reaction, is used ia the calculation of equilibrium compositions the standard heat of reaction, is used iu... 

For most LLE applications, the effect of pressure on the Yi < an be ignored, and thus Eq. (4-327) constitutes a set of N equations relating equilibrium compositions to each other and to temperature. For a given temperature, solution of these equations requires a single expression for the composition dependence of suitable for both liquid phases. Not all expressions for suffice, even in principle, because some cannot represent liquid/liquid phase splitting. The UNIQUAC equation is suitable, and therefore prediction is possible by the UNIFAC method. A special table of parameters for LLE calculations is given by Magnussen, et al. (Jnd E/ig Chem Process Des Dev, 20, pp. 331-339 [1981]). 

The standard Gibbs-energy change of reaction AG° is used in the calculation of equilibrium compositions. The standard heat of reaclion AH° is used in the calculation of the heat effects of chemical reaction, and the standard heat-capacity change of reaction is used for extrapolating AH° and AG° with T. Numerical values for AH° and AG° are computed from tabulated formation data, and AC° is determined from empirical expressions for the T dependence of the C° (see, e.g., Eq. [4-142]). 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

Table 1.1 Equilibrium composition of gas mixtures at 2300 K and 0.1 atmos pressure (mole fraetions of the major gases only)...

The principle of Le Chatelier shows that when the pressure applied to a gaseous system is increased, dre equilibrium composition will chairge in order to reduce tire number of gaseous molecules. In the case of tire steam reforming of metlrane, the partial pressures of methane and steam will increase as the pressure is increased. In the water-gas reaction, where tire number of molecules is the same on both sides of the equation, the effect of increasing... 

Table 4.3 Equilibrium composition in the steam-reforming reaetion at 900 K as afunetion of pressure (molar fraetion)...

The next stage in the zone-refining process is to move the furnace slowly and steadily to the right. The left-hand end of the bar will then cool and refreeze but with the equilibrium composition /cCq (Fig. 4.4c). As the furnace continues to move to the right the freezing solid, because it contains much less impurity than the liquid, rejects the surplus impurity into the liquid zone. This has the effect of inereasing the impurity concentration in the zone, which in turn then increases the impurity concentration in the next layer of freshly frozen solid, and so on (Fig. 4.4d). Eventually the concentrations ramp themselves up to the situation shown in Fig. 4.4(e). Flere, the solid ahead of the zone has exactly the same composition as the newly frozen solid behind the zone. This means that we have a steady state where as much impurity is removed from the... 

Equation (3.5) can be used to establish a one-to-one correspondence among all composition scales for which mass exchange is feasible. Since most environmental applications involve dilute systems, one can assume that these systems behave ideally. Hence, the transfer of the pollutant is indifferent to the existence of other species in the waste stream. In other words, even if two waste streams contain species that are not identical, but share the same composition of a particular pollutant, the equilibrium composition of the pollutant in an MSA will be the same for both waste streams. Hence, a single composition scale, y, can be used to represent the concentration of the pollutant in any waste stream. Next, (3.5) can be employed to generate Ns scales for the MSAs. For a given set of corresponding composition scales y,x, X2,..., xj,..., it is thermodynamically and practically feasible to transfer the pollutant from any waste stream to any MSA. In addition, it is also feasible to transfer the pollutant from any waste stream of a composition y/ to any MSA which has a composition less than the xy obtained from (3.5b). 

The first, and to this writing still only case of a ketone a-cleavage-recombi-nation sequence in the steroid field was reported by Butenandt, who found that 17-ketones epimerize at C-13. Ultraviolet irradiation of either stereoisomer produces an equilibrium mixture in which the thermodynamically more favored 13a-compound cf. (15)] with cw-fusion of rings C and D predominates at room temperature. As ultraviolet absorption energies and intensities of the two isomeric ketones are practically identical, the equilibrium composition depends largely on the rate of the competing recombination process from (14). For further examples of the photoisomerization at C-13 of 17-ketosteroids, see ref. 8, 12, 15 and 43. 

Gordon, S. and McBride, B. J. 1976. Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations. Report SP-273. Interim Revision, Report N78-17724. National Aeronautics and Space Administration, Washington, DC. 

Thermodynamic Isotope Effect. The change in equilibrium composition caused by isotopic substitution. 

Several techniques are available in the literature for evaluation of the flame temperature, exit temperature, equilibrium composition of combustion products, and performance parameters of energetic composites [11-13]. The optimum combination of the composite ingredients is determined by thermodynamic means, so as to arrive at a composition having maximum performance... 

Discarding Liebig s theoiy as worthless because it could not be subjected to experimental verification, OstvUd contended that a catalyst merely sped up a reaction that was already occurring at a very slow rate. He also indicated that a catalyst cannot change the equilibrium composition. By analogy, he considered... 

Wliile this definition does not address the question of how catalysts effect rate increases, it does ensure that a catalyst cannot cause the equilibrium composition to deviate from that of the uncatalyzed reaction. 

Step 4. To check the original assumed equilibrium composition in the evaporator, the total amount of propane and butane in the system must be determined. This total must be equal to the original charge. Therefore, the next step will be to calculate the volume of the total system. These calculations must necessarily be somewhat approximate because the exact installation conditions are not known. 

Thermodynamic equilibrium composition of Cs aromatics at three temperatures ... 

Fig. 7.83 The graphical method for obtaining equilibrium compositions from free energy vs. composition curves at a given temperature. Points of contact give equilibrium compositions Xi for phase I and X2 for phase II...

In Fig. 7.83 using the common tangent construction the equilibrium compositions of phase I-phase II at their boundary are found, from the points of contact, to be respectively Xg — A, and Xg = X2. 

---