Equilibrium yield, calculation temperature

Both the integrated and differential forms show that a plot of log K against 1/T should yield a straight line with a slope equal to -AH0/2.303 R. Thus, a measured value of AH0 can be employed to calculate the equilibrium constant at temperatures other than that for which it is given. Conversely, it is possible to use measurements of the equilibrium constant at a number of temperatures to evaluate the standard enthalpy change for the reaction. 

For example, classic thermodynamic methods predict that the maximum equUi-brium yield of ammonia from nitrogen and hydrogen is obtained at low temperatures. Yet, under these optimum thermodynamic conditions, the rate of reaction is so slow that the process is not practical for industrial use. Thus, a smaller equilibrium yield at high temperature must be accepted to obtain a suitable reaction rate. However, although the thermodynamic calculations provide no assurance that an equUibrium yield will be obtained in a finite time, it was as a result of such calculations for the synthesis of ammonia that an intensive search was made for a catalyst that would allow equilibrium to be reached. 

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. 

Fundamental thermodynamic and kinetic studies of the decomposition reaction (1) have confirmed that hydrogen sulphide is a stable sulphide and that the dissociation is thermodynamically unfavorable below 1800°K. Nevertheless, some decomposition does, of course, occur below these temperatures and equilibrium hydrogen yields range from less than 1% at 750°K through about 5% at 1000°K to almost 30% at 1400°K. [These values are based on equilibrium product calculations which considered all possible sulphur/hydrogen species which could be present at equilibrium including various sulphur vapor species (S S to S ), and sulphanes (H2Sx) as well as H2S, H and The values which are... 

Columns between Ke and y(H2) may contain intermediate quantities in the calculation of yni First test your program for the conditions of part (a) and verify that it is correct. Then try a variety of values of the input variables and draw conclusions about the conditions (reactor temperature and feed composition) that maximize the equilibrium yield of hydrogen. 

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-... 

Figure 4.10 shows the mole fraction of 14 species in gas phase equilibrium calculated from thermodynamic data [180]. The figure shows that the equilibrium yield of ethyne is low below 1373 K, but the yield increases strongly with increasing temperature. The figure also shows that the ethene yield also is low at all temperatures, less than 5% over the entire temperature range [179],... 

The output data from reformer II for the process gas and the calculated results of the dusty gas model and simplified models I and II are presented in Table 6.16. The measured and calculated temperatures, pressures and concentrations of the process gas at the exit of reformer II are in good agreement (Table 6.16). AH models give almost the same exit conversion and yield for methane and carbon dioxide. This unit is operating relatively close to thermodynamic equilibrium, though it is slightly shifted away from equilibrium compared with unit I. 

Figures 3 and 4 are the predicted profiles of vapor and liquid composition along the column with 43 ml of catalyst and a reflux flow rate of 22 g/tnin. It is important to note that both the liquid and vapor concentration profiles for acetone in the column are relatively high and hence it is favorable for the formation of DAA. The equilibrium constants calculated from the equilibrium conversion data [9,10] are given in Figure 5, which indicates that at 54 °C, the Ac conversion at equilibrium conversion is only 4.3 wt %. In order to carry out the aldol condensation of acetone in the CD column, the temperature at the reaction zone of the CD column will be near the boiling point of Ac in order to maintain liquid vapor equilibrium. Our CD experimental results show that a maximum concentration of 55 wt% of DAA concentration was obtained which clearly exceeds the equilibrium conversion. The aldol condensation of Ac to produce DAA is an excellent example to demonstrate that in situ separation in a CD column results in an increased yield for equilibrium limited reactions.

From Figs. 10-2d and e, it can be calculated that at 400°C in the case of a larger paraffin, e.g., hexane there is a spontaneous tendency to decompose or crack, yielding a smaller paraffin and smaller olefin, e.g., propane and propylene. At 100°C, such a reaction does not tend to occur. Therefore, if a relatively large olefin were to be hydrogenated to a paraffin of the same molecular weight, apparently it would be desirable to carry out such a reduction at lower temperatures for two pertinent reasons (1) the equilibrium yield is better, (2) decomposition or side reactions are less likely to be troublesome. Because of this preferred lower-temperature operation, catalysts must be available to operate at these lower temperatures. Such hydrogenation catalysts are known, as was pointed out elsewhere in this chapter. 

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.)... 

In accordance with the thermodynamics of the reaction system, at low temperatures silicon-poor phases are formed, while at high temperatures silicides with a high silicon content are generated. Each of the phases present reaches its catalytic activity after an induction period, in which the thermodynamically stable silicide, corresponding to the temperature of reaction, is formed. The yield of trichlorosilane is independent of the phase used it corresponds to the equilibrium value calculated for the present temperature. It is concluded that the catalytic reaction proceeds almost without kinetic hindrance and that silicon has a high mobility in the eatalyst system [ I -3]. 

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. 

To calculate the number of moles of H2 at equilibrium we can use the ICE method, and to assess the effect of temperature on the equilibrium yield of H2 we can apply Le Chatelier s principle. 

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. 

Thermal Effects in Addition Polymerizations. Table 13.2 shows the heats of reaction (per mole of monomer reacted) and nominal values of the adiabatic temperature rise for complete polymerization. The point made by Table 13.2 is clear even though the calculated values for T dia should not be taken literally for the vinyl addition polymers. All of these pol5Tners have ceiling temperatures where polymerization stops. Some, like polyvinyl chloride, will dramatically decompose, but most will approach equilibrium between monomer and low-molecular-weight polymer. A controlled polymerization yielding high-molecular-weight pol)mier requires substantial removal of heat or operation at low conversions. Both approaches are used industrially. 

Here K is the thermodynamic chemical equilibrium constant. If AH is constant, direct integration yields an explicit expression. If AH is a function of temperature, as described in Sec. 1.3.3, then its dependancy on Cp can be easily included and integration is again straight forward. A calculation with varying AH and Cp being functions of temperature is given in the simulation example REVTEMP. 

When all the violet dye is off the column, begin to collect and evaporate 10-ml. fractions. Two or three fractions, which on evaporation yield little or no residue, will precede the appearance of the 7-benzene hexachloride. Continue to collect 10-ml. fractions and evaporate until no more 7-benzene hexachloride is obtained. Stop the column operation, dissolve the several 7-benzene hexachloride residues with a minimum quantity of n-hexane, and pour into a tared 125-ml. Erlenmeyer flask. Evaporate under vacuum, using the solvent evaporator, at 60° and finally at room temperature for 5 minutes with a high vacuum pump. Release the vacuum, wipe the flask with a clean, moist towel, and weigh after allowing the flask to come to equilibrium near the balance. Calculate the percentage of 7-benzene hexachloride in the original sample. 

Once we have determined the entropy and enthalpy of polymerization, we can calculate the free energy of the process at a variety of temperatures. The only time this is problematic is when we are working near the temperatures of transition as there are additional entropic and enthalpic effects due to crystallization. From the free energy of polymerization, we can predict the equilibrium constant of the reaction and then use this and Le Chatelier s principle to design our polymerization vessels to maximize the percent yield of our process. 

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