Equilibrium yield, calculation pressure

The mass-action equations have been written in the same form as those given by Marynowski et al. (6) so that the equilibrium constants can be used directly. (Should more accurate data become available, the equilibrium yields calculated here will require revision.) The fourth equation, which applies to the heterogeneous equilibrium between carbon and nitrogen, is included for completeness but is unnecessary for the general solution. It can be shown that when the total pressure of the system is F, the partial pressure of cyanogen radicals is given by the equation ... 

The coordinates of thermodynamics do not include time, ie, thermodynamics does not predict rates at which processes take place. It is concerned with equilibrium states and with the effects of temperature, pressure, and composition changes on such states. For example, the equilibrium yield of a chemical reaction can be calculated for given T and P, but not the time required to approach the equilibrium state. It is however true that the rate at which a system approaches equilibrium depends direcdy on its displacement from equilibrium. One can therefore imagine a limiting kind of process that occurs at an infinitesimal rate by virtue of never being displaced more than differentially from its equilibrium state. Such a process may be reversed in direction at any time by an infinitesimal change in external conditions, and is therefore said to be reversible. A system undeigoing a reversible process traverses equilibrium states characterized by the thermodynamic coordinates. 

The results of the calculations show that with increasing pressure the equilibrium yield of ammonia is increasing and that the non-ideality of the gas mixtures has in this case a positive effect on the equilibrium conversion. 

Slanina et at. (1989) have considered the thermodynamics of the fullerenes in carbon vapour, and their work demonstrates that the C70/C60 ratio of approximately unity (ratios obtained vary roughly from 0.1 to 10) found in extracts from graphitic soot is incompatible with thermodynamic equilibrium being established between these two species when they were formed. In their work, the sum of the partial pressures of C60 and C70, PM 70, at which the species are present in equal concentrations at equilibrium was calculated, and PrM 70 is never larger than 10-13 bar below 5000 K. The observed C60 and C70 yields cannot be reached with such a small partial pressure of product. If the sum of the C60 and C70 partial pressures is raised, C70 rapidly becomes totally dominant at thermodynamic equilibrium. 

In cases in which the reaction quickly proceeds to equilibrium, the yields are easily estimated as the equilibrium yields. Under these circumstances, the only possibilities for process optimization are to change the temperature, pressure, or feed composition, so as to obtain a different equilibrium mixture. The calculation of reaction equilibrium is easily carried out using commercial process simulation programs. 

Fig. 8.8 The calculated effect of pressure and temperature upon the equilibrium yield of CCI4 from the dismutation of phosgene [ICI8,ICI9].

The experimentally determined S-L-V equilibrium data for salicylic acid (2-hydroxy-benzoic acid)-l-propanol-C02 were correlated by using the Stryjek-Vera modification of the Peng Robinson EOS in conjunction with Eq. (35) for the solid state fugacity of the solute (58,62), as described earlier. This procedure also yielded good agreement of the liquid phase compositions of salicylic acid in the temperature and pressure ranges of 273 to 367 K and 1.0 to 12.5 MPa. The P-Ttraces of S-L and L-V equilibria were calculated for a fixed solute concentration on C02-free basis, and subsequently the P-T trace for the S-L-V equilibrium was found from the point of intersection of these two lines. The liquid phase compositions of the solute as a function of pressure at a constant temperature at the condition of S-L-V equilibrium were calculated to assess the effect of pressure or addition of antisolvent on solute crystallization. It was reported that two isobaric points of the CO2 mole fraction could be observed on the curve of the S-L equilibrium temperature vs the CO2 mole fraction at constant temperature as it passes through a mini-... 

Use these constants to determine the equilibrium yields and conversions obtained at these temperatures when the total pressure in the system is 1.2 atm. Consider both the case in which water is supplied at a 2 1 mole ratio with CHCIF2 and the case in which the feed consists solely of CHCIF2. (There are thus four sets of conditions for which you are to calculate yields and conversions.)... 

HjO, 1 mole of CO, and 2 moles of NaCl at 50 C at 1 atm pressure. Let s further assume that the calculation of the electrolyte equilibrium yields ... 

Conversely, if is known, whether from measurements of the equilibrium yield at a pressure low enough to ensure that the factor exp. .. in equation (102) may safely be omitted, or from calorimetric measurements of Air (see Section 8) and of A5 (see Section 9) according to equation (15), or by use of a statistical-mechanical formula from spectroscopic measurements of molecular quantities usually supplemented by a calorimetric value of Air at any one temperature, then the yield at some other pressure can be calculated only if the integral in equation (102) can be evaluated. 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

In order to generate the starting material for a polymer that is used in water bottles, hydrogen is removed from the ethane in natural gas to produce ethene in the catalyzed reaction C,H6(g) H,(g) + C,ll4(g). Use the information in Appendix 2A to calculate the equilibrium constant for the reaction at 298 K. (a) If the reaction is begun by adding the catalyst to a flask containing C,H6 at 10.0 bar, what will be the partial pressure of the C,H4 at equilibrium (b) Identify three steps the manufacturer can take to increase the yield of product,... 

It is the equilibrium conditions of composition and activities (partial pressure for gases) that are calculated to assess the yield of a desired reaction. 

The next step involved cooling the reaction mixture to -196°C, removing the H2 at low pressure, and sealing the tube. This sealed tube was then used in the equilibrium measurements. When it warmed up, a fraction of the hydride complex reacted with benzene, yielding H2 and the phenyl complex, according to equilibrium 14.12. Therefore, the total amount of substance of H2 in equation 14.18 is given by the sum of the initial amount of substance of H2 (no) and the amount of substance of Sc(Cp )2Ph in equilibrium. The latter is easily calculated from the relative concentrations of Sc(Cp )2Ph and Sc(Cp )2H determined by H NMR, and the known initial concentration of Sc(Cp )2H (5.4 x 10-5x 1000/0.5 = 0.108 mol dm-3). To evaluate the initial amount of substance of H2, consider the experimental procedure before and after reaction 14.19 takes place. When this reaction occurs (at 25 °C) a certain amount of H2 remains in solution, and it can be calculated by an equation similar to 14.17. This amount will be equal to no, by assuming that (1) there is no further H2 solubilization when the tube is rapidly cooled to — 196 °C, and (2) only the H2 dissolved in the frozen reaction mixture is not removed by the evacuation procedure. 

Transition state theory yields rate coefficients at the high-pressure limit (i.e., statistical equilibrium). For reactions that are pressure-dependent, more sophisticated methods such as RRKM rate calculations coupled with master equation calculations (to estimate collisional energy transfer) allow for estimation of low-pressure rates. Rate coefficients obtained over a range of temperatures can be used to obtain two- and three-parameter Arrhenius expressions ... 

An extension of the procedure for calculating the deton velocities to include those expls which.yield solid carbon as a reaction product has been accomplished by the same investigators (See Ref 32) on the assumption that the volumes of solid and gas are additive, that the gas obeys eq 23 and that the solid has zero coefficients of thermal expansion and basic compression. The composition of the reaction products was assumed to be that of chemical equilibrium at the temp and pressure immediately behind the deton wave, and a numerical procedure, involving successive approximations, was developed for the determination of the composition from a consideration of the simultaneous equilibria involved. This method of calculation was briefly discussed in Ref 39, pp 86-7... 

Alternatively, experimental measurement of the variation of equilibrium continuous liquid holdup with position for a concentrated oil-in-water emulsion can be employed to infer the variation of disjoining pressure with film thickness. Since the continuous phase liquid holdup e is known as a function of position, xp, Op and r can be calculated using equations 7,21 and 24. Equation 24 will then yield the disjoining pressure II at the film thickness xp. ... 

Figures 1 to 3 present calculated equilibrium molar ratios of products to reactants as a function of temperature and total pressure of 1 and 100 atm. for the gas-carbon reactions (4), (7), and (5), (6), (4), (7), respectively. Up to 100 atm. over the temperature range involved, the fugacity coefficients of the gases are close to 1 therefore, pressures can be calculated directly from the equilibrium constant. From Fig. 1, it is seen that at temperatures above 1200°K. and at atmospheric pressure, the conversion of carbon dioxide to carbon monoxide by the reaction C - - COj 2CO essentially is unrestricted by equilibrium considerations. At elevated pressures, the possible conversion markedly decreases hence, high pressure has little utility for this reaction, since increased reaction rate can easily be obtained by increasing reaction temperature. On the other hand, for the reaction C -t- 2H2 CH4, the production of methane is seriously limited at one atmosphere pressure and practical operating temperatures, as seen in Fig. 2. Obviously, this reaction must be conducted at elevated pressures to realize a satisfactory yield of methane. For the carbon-steam reaction.

Condensation theory is based on thermodynamic equilibrium. More than a century s worth of experiments have yielded thermodynamic data (entropy and enthalpy of formation, plus heat capacity) for elements and compounds. Equations of state describing the stabilities of different compounds under various conditions can be calculated from these data, as briefly described in Box 7.1. Because liquids are not normally stable at the low pressures appropriate for space, the compounds in condensation calculations are generally solid minerals, but liquids can exist at higher pressures (achievable if areas of the nebula with enhanced dust concentrations relative to gas were vaporized). 

The gas pressure is next calculated from the concentration. The additional assumption is that the incremental gas pressure inside the sample is the same as the external gas pressure required to yield the same amount of dissolved gas within the polymer at equilibrium (from a solubility-external pressure isotherm). This procedure gives approxi-... 

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