Endothermic reactions, temperature dependence

In the case of fast highly exothermic or endothermic reactions, temperature gradients inside the porous catalyst and temperature differences between the fluid phase and catalyst surface cannot be neglected. Depending on the physical properties of the fluid and the solid catalyst, important temperature gradients may occur. The relative importance of internal to external temperature profiles can be estimated based on the relationships presented in Sections 2.6.1.2 and 2.6.2.2. According to Equation 2.158 the temperature difference between bulk and outer pellet surface is ... 

Reaction 1 is highly exothermic. The heat of reaction at 25°C and 101.3 kPa (1 atm) is ia the range of 159 kj/mol (38 kcal/mol) of soHd carbamate (9). The excess heat must be removed from the reaction. The rate and the equilibrium of reaction 1 depend gready upon pressure and temperature, because large volume changes take place. This reaction may only occur at a pressure that is below the pressure of ammonium carbamate at which dissociation begias or, conversely, the operating pressure of the reactor must be maintained above the vapor pressure of ammonium carbamate. Reaction 2 is endothermic by ca 31.4 kJ / mol (7.5 kcal/mol) of urea formed. It takes place mainly ia the Hquid phase the rate ia the soHd phase is much slower with minor variations ia volume. 

For an endothermic reaction AH/ is positive for an exothermic reaction it is negative. The temperature dependence of AH/ is given by dAHf... 

Most chemical reactions are greatly affected by temperature. The previous chapters discussed reactions at isothermal condition, however, industrial reactors often operate under non-isothermal condition. This is because chemical reactions strongly depend on temperature, either absorbing (i.e., endothermic) or generating (i.e., exothermic) a large amount of heat. 

The evolution of a. star after it leaves the red-giant phase depends to some extent on its mass. If it is not more than about 1.4 M it may contract appreciably again and then enter an oscillatory phase of its life before becoming a white dwarf (p. 7). When core contraction following helium and carbon depletion raises the temperature above I0 K the y-ray.s in the stellar assembly become sufficiently energetic to promote the (endothermic) reaction Ne(y,a) 0. The a-paiticle released can penetrate the coulomb barrier of other neon nuclei to form " Mg in a strongly exothermic reaction ... 

We can see from Table 9.2 that the equilibrium constant depends on the temperature. For an exothermic reaction, the formation of products is found experimentally to be favored by lowering the temperature. Conversely, for an endothermic reaction, the products are favored by an increase in temperature. 

Most of the chemical reactions in the process industry are temperature dependent. They are either exothermic or endothermic. As a consequence, it is often necessary to remove the heat generated by an exothermic reaction to control the reaction temperature and to avoid thermal runaway reactions or to suppress endothermic by-product reactions, for instance [8]. 

Figure 3.3 The temperature dependence of AC0, AH0, and T AS0 over large temperature ranges the behaviour (A) for negative AS0, (B) positive AS0 and (C) variation of In K with 1/7" for exothermic and endothermic reactions.

For cases where AH0 is essentially independent of temperature, plots of in Ka versus 1/T are linear with slope —(AH°/R). For cases where the heat capacity term in equation 2.2.7 is appreciable, this equation must be substituted in either equation 2.5.2 or equation 2.5.3 in order to determine the temperature dependence of the equilibrium constant. For exothermic reactions (AH0 negative) the equilibrium constant decreases with increasing temperature, while for endothermic reactions the equilibrium constant increases with increasing temperature. 

The value of E - y is called the open-circuit voltage of the cell, which is related to the composition of the product. Note that the steam conversion ratio, X, depends on the open-circuit voltage, and is not affected by the pressure or flow rate of the reactant. Also, the open-circuit voltage decreases with increasing temperature because of the endothermic nature of the reaction. However, due to the temperature dependence of the logarithmic term in Equation 4.5, this effect decreases with the value of X. 

Our initial work on reaction thermal effects involved CFD simulations of fluid flow and heat transfer with temperature-dependent heat sinks inside spherical particles. These mimicked the heat effects caused by the endothermic steam reforming reaction. The steep activity profiles in the catalyst particles were approximated by a step change from full to zero activity at a point 5% of the sphere radius into the pellet. 

Free energy variations with temperature can also be used to estimate reaction enthalpies. However, few studies devoted to the temperature dependence of adsorption phenomena have been published. In one such study of potassium octyl hydroxamate adsorption on barite, calcite and bastnaesite, it was observed that adsorption increased markedly with temperature, which suggested the enthalpies were endothermic (26). The resulting large positive entropies were attributed to loosening of ordered water structure, both at the mineral surface and in the solvent surrounding octyl hydroxamate ions during the adsorption process, as well as hydrophobic chain association effects. 

AN melts at 443 K and begins to gasify above 480 K. The decomposition process of AN is temperature-dependent At low temperatures, i. e. around 480 K, the gasification process of AN is the endothermic (-178 kJ mol" ) reversible reaction represented by[i5]... 

For each reaction in a surface chemistry mechanism, one must provide a temperature dependent reaction probability or a rate constant for the reaction in both the forward and reverse directions. (The user may specify that a reaction is irreversible or has no temperature dependence, which are special cases of the general statement above.) To simulate the heat consumption or release at a surface due to heterogeneous reactions, the (temperature-dependent) endothermicity or exothermicity of each reaction must also be provided. In developing a surface reaction mechanism, one may choose to specify independently the forward and reverse rate constants for each reaction. An alternative would be to specify the change in free energy (as a function of temperature) for each reaction, and compute the reverse rate constant via the reaction equilibrium constant. 

The equilibrium constant for the reaction between methanol on surface sites and internal sites, K, is the most complex in its temperature and acetylation dependence. In some coals temperature dependences shift about from exothermic to endothermic reactions, and no overall pattern for high rank and low rank coals seems to exist. 

Thermal explosions may be expected to develop whenever the rate of heat liberation in an exothermic reaction exceeds the rate of heat dissipation by conduction and convection. (An endothermic reaction can never cause a thermal explosion.) Because of the exponential dependence of the reaction rate on temperature, the rate increases rapidly as the temperature rises, until an explosion results. There is little difference, therefore, in the temporal behavior prior to explosion, between explosions that develop as a result of a thermal acceleration of the reaction rate, or those that occur by virtue of a catastrophic build-up of reactive reaction intermediates. 

Fig. 1. A new process (Urea Technologies) developed for the Tennessee Valley Authority operates at considerable energy savings. Urea is produced in an overall exothermic reaction of ammonia and carbon dioxide at elevated pressure and temperature. In a highly exothermic reaction, ammonium carbamate is first formed as an intermediate compound, followed by its dehydration to urea and water, which is a slightly endothermic reaction. The conversion of CO2 and NH3 to urea depends oil the ammonia-to-caibon dioxide ratio, temperature, and water-to-carbon dioxide ratio, among other factors. The new process makes maximum use of the heat created in the initial reaction, including heat recycling. 1 Urea Technologies and Tennessee Valley Authority)...

The equation Kc = kf/kr also helps explain why equilibrium constants depend on temperature. Recall from Section 12.10 that rate constants increase as the temperature increases, in accord with the Arrhenius equation k = Ae E RT. In general, the forward and reverse reactions have different values of the activation energy, so kf and kT increase by different amounts as the temperature increases. The ratio kf/kT = Kc is therefore temperature-dependent. For an exothermic reaction, which has AE = Ea(forward) — Ea(reverse) < 0, Ea(reverse) is greater than Ea(forward). Consequently, kT increases by more than kf increases as the temperature increases, and so Kc = kt/kr for an exothermic reaction decreases as the temperature increases. Conversely, Kc for an endothermic reaction increases as the temperature increases. 

The composition of an equilibrium mixture can be altered by changes in concentration, pressure (volume), or temperature. The qualitative effect of these changes is predicted by Le Chatelier s principle, which says that if a stress is applied to a reaction mixture at equilibrium, net reaction occurs in the direction that relieves the stress. Temperature changes affect equilibrium concentrations because Kc is temperature-dependent. As the temperature increases, Kc for an exothermic reaction decreases, and Kc for an endothermic reaction increases. 

Temperature profiles are established so that conversion and yield objectives are achieved while not exceeding heat transfer capacity limitations. These optimum temperature profiles depend on the chemistry. For example, if the reaction is reversible and exothermic, the temperature profile may ramp up to a high temperature to get the reactions going and then drop off with time to avoid the decrease in the chemical equilibrium constant at high temperature. If the reaction is reversible and endothermic, the temperature profile would rise to the highest possible temperature as quickly as possible because the chemical equilibrium constant increases with temperature. 

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