Equilibrium yield temperature

Although the left to right reaction is exothermic, hence giving a better equilibrium yield of sulphur trioxide at low temperatures, the reaction is carried out industrially at about 670-720 K. Furthermore, a better yield would be obtained at high pressure, but extra cost of plant does not apparently justify this. Thus the conditions are based on economic rather than theoretical grounds (cf Haber process). 

The reaction is reversible and strongly exothermic. The equilibrium yield of CH3OH decreases as the temperature increases. Hence, a low temperature and increased pressure will be kept. 

The temperature affects the equilibrium yield primarily through its influence on the equilib-... 

Other reactions will have somewhat different forms for the curve of Qq versus T. For example, in the case of a reversible exothermic reaction, the equilibrium yield decreases with increasing temperature. Since one cannot expect to exceed the equilibrium yield within a reactor, the fraction conversion obtained at high temperatures may be less than a subequilibrium value obtained at lower temperatures. Since the rate of energy release by reaction depends only on the fraction conversion attained and not on the position of equilibrium, the value of Qg will thus be lower at the higher temperature than it was at a lower temperature. Figure 10.2 indicates the general shape of a Qg versus T plot for a reversible exothermic reaction. For other reaction networks, different shaped plots of Qg versus T will exist. 

In order to minimize the required reactor volume for a given type of reactor and level of conversion, one must always operate with the reactor at a temperature where the rate is a maximum. For irreversible reactions the reaction rate always increases with increasing temperature, so the highest rate occurs at the highest permissible tepiperature. This temperature may be selected on the basis of constraints established by the materials of construction, phase changes, or side reactions that become important at high temperatures. For reversible reactions that are endothermic the same considerations apply, since both the reaction rate and the equilibrium yield increase with increasing temperature. 

The constraint of thermodynamic equilibrium for the butene dehydrogenation reaction is effectively removed since hydrogen is converted to water by oxidation. Equilibrium yields then approach 100% over the complete temperature and partial pressure range of interest. 

At a given temperature and pressure eqs. (4.7) and (4.8) must be solved simultaneously to determine the compositions of the two phases a and P that correspond to coexistence. At isobaric conditions, a plot of the composition of the two phases in equilibrium versus temperature yields a part of the equilibrium T, x-phase diagram. 

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 reaction is exothermic, hence the highest equilibrium yield is obtained at low temperatures and high pressures. The catalyst functions by inducing the formation of a nitrogen complex with the catalyst surface this complex is far more readily hydrogenated to NH3 than is nitrogen with its triple bond (Somorjai and Salmeron, 1986). 

Chemistry The first topic to examine is the chemical reactions one wants to run and all the reactions that can occur. One immediately looks up the A and AGr,- to determine the heat release or absorption and the equilibrium composition. Equilibrium considerations also govern the temperature and pressure necessary for an acceptable equilibrium yield. This was the subject of Chapter 2. 

These reactors operate below room temperature to attain a high equilibrium yield, and refrigeration equipment is a major component of an alkylation process. 

The above reaction is highly exothermic. The stoichiometric proportion of gaseous mixture at equilibrium flame temperature is cooled to 200°C, whereupon the elements combine rapidly to form HCl with over 99% yield. 

It is implicit in reaction 9.4 that the equilibrium yield of ammonia is favored by high pressures and low temperatures (Table 9.1). However, compromises must be made, as the capital cost of high pressure equipment is high and the rate of reaction at low temperatures is slow, even when a catalyst is used. In practice, Haber plants are usually operated at 80 to 350 bars and at 400 to 540 °C, and several passes are made through the converter. The catalyst (Section 6.2) is typically finely divided iron (supplied as magnetite, Fe304 which is reduced by the H2) with a KOH promoter on a support of refractory metallic oxide. The upper temperature limit is set by the tendency of the catalyst to sinter above 540 °C. To increase the yield, the gases may be cooled as they approach equilibrium. 

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. 

At temperatures of about 4000°K., the free energy of formation of acetylene from its elements approaches zero, and the equilibrium yield of acetylene is appreciable. The system is complicated, however, by other reactions and phase changes which occur at these high temperatures. Carbon sublimes at about 4000°K., various species of carbon Ci, C2, and Ca are formed, and dissociation of molecular hydrogen occurs. 

Methanol synthesis from waste C02 streams has the potential to contribute to the limitation of worldwide C02 emissions and to serve as an alternative carbon source to fossil fuels if a renewable source of hydrogen is available (see Section 5.3.1). The main obstacle to methanol synthesis from C02-rich streams is thermodynamics. The equilibrium yield of methanol from 25% C0/C02 75% H2 mixtures of varying C0/C02 ratio is shown in Figure 5.3.5. For pure CO, a one-pass methanol yield of nearly 55% can be obtained at 525 K, while pure C02 would only yield 18%. Besides the addition of CO, this equilibrium limitation can be overcome by operating at lower temperatures (an option that requires more active catalysts), implementing higher recycle ratios, or product extraction (an option that requires higher capital investment) [8]. 

Many industrial reactions are not carried to equilibrium. In this circumstance the reactor design is based primarily on reaction rate. However, the choice of operating conditions may still be determined by equilibrium considerations as already illustrated with respect to the oxidation of sulfur dioxide. In addition, the equilibrium conversion of a reaction provides a goal by which to measure improvements in the process. Similarly, it may determine whether or not an experimental investigation of a new process is worthwhile. For example, if the thermodynamic analysis indicates that a yield of only 20 percent is possible at equilibrium and a 50 percent yield is necessary for the process to be economically attractive, there is no purpose to an experimental study. On the other hand, if the equilibrium yield is 80 percent, an experimental program to determine the reaction rate for various conditions of operation (catalyst, temperature, pressure, etc.) may be warranted. 

Equation (15.17) gives the effect of temperature on the equilibrium constan hence on the equilibrium yield. If A H° is negative, i.e., if the reaction is exot] the equilibrium constant decreases as the temperature increases. Convers increases with T for an endothermic reaction. 

It is easy to see from Equation (2.2.5) that if ( 2 i) > 0 then the reaction is exothermic and likewise if ( 2 — 1) < 0 it is endothermic (refer to Appendix A for temperature dependence of A c). In a typical situation, the highest yields of products are desired. That is, the ratio (CsCw/C CB%q will be as large as possible. If the reaction is endothermic. Equation (2.2.5) suggests that in order to maximize the product yield, the reaction should be accomplished at the highest possible temperature. To do so, it is necessary to make exp[( 2 — i)/(/ T)] as large as possible by maximizing (RgT), since ( 2 — 1) is negative. Note that as the temperature increases, so do both the rates (forward and reverse). Thus, for endothermic reactions, the rate and yield must both increase with temperature. For exothermic reactions, there is always a trade-off between the equilibrium yield of products and the reaction rate. Therefore, a balance between rate and yield is used and the T chosen is dependent upon the situation. 

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. 

A liquid mixture of n-hexane (HX) and n-heptane (HP) at a high pressure is abruptly exposed to a lower pressure, A portion of the mixture evaporates, yielding a vapor mixture relatively rich in hexane (the more volatile of the two feed components) and a residual liquid mixture relatively rich in heptane. The two product streams are in equilibrium at temperature F and pressure P their compositions are related by Raoult s law (Section 6.4b). 

During metamorphism and recrystallization, oxygen isotopes are redistributed among mineral phases, according to the mass-dependent equilibrium fractionations corresponding to the peak metamorphic temperature. The measured mineral-pair fractionations (usually for major minerals olivine, pyroxene, and feldspar) can then be used for metamorphic thermometry, yielding temperatures of 600 °C for an L4 chondrite, and 850 50 °C for several type-5 and type-6 chondrites (Clayton et al., 1991). Isotopic equilibration, even in type-6 chondrites, involves oxygen atom transport only over distances of a few millimeters (Olsen et al., 1981). 

Equations 4 and 7 of Table 2.2 suggest that a plot of the logarithm of the equilibrium constant (or a representative equilibrium activity) of a reaction versus the reciprocal of absolute temperature can yield information concerning AH°. For many reactions ACp is close to zero and AH° is essentially independent of temperature, and a linear plot of log K versus JT is obtained over an appreciable temperature range. The equilibrium constant can then be computed readily by the simple relationship of equation 3 in Table 2.2. When ACp is constant over a range of temperature, equation 6 of Table 2.2 can be used to compute the equilibrium constant-temperature coefficient. 

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. 

Isomerization of 1-hexene. Figure 6 shows simulated equilibrium yields and conversions of 1-hexene versus temperature at the specified pressure. Cracking products were not considered in our analysis. Increase in temperature is seen to cause a slight decrease in equilibrium conversion and to have little effect on the isomer selectivities. Simulated equilibrium conversion at 250 C and 7,250 psia is 97.2%. This value compares with the experimental value of 40% obtained by Tiltsher et al. (16) in a catalytic flow reactor. Clearly, there is room for improving the experimentally reported conversion. 

In a gas-phase reaction, it is observed that the equilibrium yield of products is increased by lowering the temperature and by reducing the volume. 

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