Adiabatic reaction, definition

A second obvious problem with the ordinary definition of adiabatic reactions is the vagueness of the term product. If the product is what is actually isolated from a reaction flask at the end, few reactions are adiabatic. (Cf. Example 6.7.) If the product Is the first thermally equilibrated species that could in principle be isolated at sufficiently low temperature, many more can be considered adiabatic. A triplet Norrish II reaction is diabatic if an enol and an olefin are considered as products. It would have to be considered adiabatic, however, if the triplet 1,4-biradical, which might easily be observed, were considered the primary photochemical product. (See Section 7.3.2.)... 

In the other case, when the interaction Frp is very small the reaction is said to be non- adiabatic. The energy surfaces are perturbed only slightly as illustrated in Fig. 6.5b. The reactant system remains mostly on the reactant surface also when passing the crossing point and returns to its equilibrium state (see large arrow in Fig. 6.5b) without much electron transfer. Thus, s 1. According to these definitions, the Marcus model describes primarily adiabatic reactions. 

Equations 14.3-7 and 14.3-8 can be used to compute the steady-state outlet temperature of an adiabatic reactor whose effluent is in chemical equilibrium this temperature is called the adiabatic reaction temperature and will be designated here by Tad- By definition, the adiabatic reaction temperature must satisfy (1) the equilibrium relations... 

The general treatment of the theory of chemical reactions presented in this book is based on the usual adiabatic separation of nuclear and electronic motions which permits a definition of the potential energy as a function of internuclear distances This approach proves to be very useful for the study of electronically adiabatic reactions, provided a separation of the rotation of the reacting system, treated as a supermolecule, is possible. In general, such a separation seems to be a bad approximation /10/. A consideration of the coupling of the overall rotation with the internal motions of the system means taking into account the possibility of non-adiabatic transitions from one to another potential energy surface. This is still an unsolved problem of theoretical chemistry which is open for discussion. 

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

Vocabulary of Terms Used in Reactor Design. There are several terms that will be used extensively throughout the remainder of this text that deserve definition or comment. The concepts involved include steady-state and transient operation, heterogeneous and homogeneous reaction systems, adiabatic and isothermal operation, mean residence time, contacting and holding time, and space time and space velocity. Each of these concepts will be discussed in turn. 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

When a reaction is adiabatic, the electron is transferred every time the system crosses the reaction hypersurface. In this case the preexponential factor is determined solely by the dynamics of the inner-and outer-sphere reorganization. Consequently the reaction rate is independent of the strength of the electronic interaction between the reactant and the metal. In particular, the reaction rate should be independent of the nature of the metal, which acts simply as an electron donor and acceptor. Almost by definition adiabatic electron-transfer reactions are expected to be fast. 

Chemical reaction states, reactivity of states, 1467 Chemical reaction, as a basic step. 937. 1473 adiabatic, definition, 1497 at gas/solid interphase, 1371 heterogeneous, in solution. 1376 non-adiabatic, definition, 1497 reactivity of molecules in, 1473 velocity of. 1473... 

An assumption involving heat losses from the reactor is made in most treatments. The effect of heat transfer on the maximum reaction rates of a homogeneous reactor has been treated by DeZubay and Woodward (14). It was found that a lowering of the reactor surface temperature appreciably lowered the chemical reaction rates. Longwell and Weiss (43) found, for example, a loss equal to 5% of the maximum adiabatic heat liberated reduces the maximum heat release rate by more than 30%, while a 20% heat loss reduces the rate about 85%. One should not assume an adiabatic system without some definite knowledge of the magnitude of the heat losses. 

To reduce the number of parameters in the kinetic equations that are to be determined from experimental data, we used the following considerations. The values klt k2, and k4 that enter into the definition of the constant L, (236), are of analogous nature they indicate the fraction of the number of impacts of gas molecules upon a surface site resulting in the reaction. So the corresponding preexponential factors should be approximately the same (if these elementary reactions are adiabatic). Then, since k1, k2, and k4 are of the same order of magnitude, their activation energies should be almost identical. It follows that L can be considered temperature independent. 

To use this formula one can employ experimental or calculated adiabatic (or vertical, if the species from removal or addition of an electron are not stationary points) values of I and A. This same formula (Eq. 7.32) for / was elegantly derived by Mulliken (1934) [149] using only the definitions of I and A. Consider the reactions... 

Closely related to the above merit of VB methods, the unique definition of diabatic states also allows us to derive the energy profiles for diabatic states. Since for many reactions the whole process can be described with very few resonance structures, the comparison between the diabatic and adiabatic state energy profiles can yield insight into the nature governing the reactions [22-24]. In fact, even for complicated enzymatic reactions, simple VB ideas have shown unparalleled value [25, 26]. However, the further utilization of the VB ideas at the empirical and semi-empirical levels should be carefully verified by benchmark ab initio VB... 

Extending the theory to interpret or predict the rovibrational state distribution of the products of the unimolecular dissociation, requires some postulate about the nature of the motion after the unimolecularly dissociating system leaves the TS on its way to form products. For systems with no potential energy maximum in the exit channel, the higher frequency vibrations will tend to remain in the same vibrational quantum state after leaving the TS. That is, the reaction is expected to be vibrationally adiabatic for those coordinates in the exit channel (we return to vibrational adiabaticity in Section 1.2.9). The hindered rotations and the translation along the reaction coordinate were assumed to be in statistical equilibrium in the exit channel after leaving the TS until an outer TS, the PST TS , is reached. With these assumptions, the products quantum state distribution was calculated. (After the system leaves the PST TS, there can be no further dynamical interactions, by definition.)... 

There are several fundamental reasons why the GMH and adiabatic formulations are to be preferred over the traditionally employed diabatic formulation. The definition of the diabatic basis set is straightforward for intermolecular ET reactions when the donor and acceptor units are separated before the reaction and form a donor-acceptor complex in the course of diffusion in a liquid solvent. The diabatic states are then defined as those of separate donor and acceptor units. The current trend in experimental design of donor-acceptor systems, however, has focused more attention on intramolecular reactions where the donor and acceptor units are coupled in one molecule by a bridge.The direct donor-acceptor overlap and the mixing to bridge states both lead to electronic delocalization, with the result that the centers of electronic localization and localized diabatic states are ill-defined. It is then more appropriate to use either the GMH or adiabatic formulation. 

The normalized temperature t, given by equation (40), is a convenient independent variable only if it varies monotonically with distance through the flame. Although it is conceivable that nonmonotonic behavior of t could occur—for example, for flames in which endothermic reactions become dominant at the highest temperatures—no practical examples of adiabatic flames with temperature peaks or valleys are known the use of t seems appropriate from the viewpoint of monotonicity. The main limitation to the formulation given is assumption 7 to the effect that Cp i = Cp = constant. This assumption can be removed, with t = (T — Tq)I(T — Tq), merely at the expense of complicating the definition of / in equation (82), namely, /=Z7= 1 oo)/Cp(T — To), where each hj is a known function... 

---