Enthalpy profile

This difference in stabilization isreflectedinboththerateof carboiiylation and decarbonylation (Table 1). The free-enthalpy profiles for the car-bonylation of tertiary alkyl cations are shown in Fig. 1. 

If the variation in the physical properties is too large for these simple methods to be used it will be necessary to divide the temperature-enthalpy profile into sections and evaluate the heat-transfer coefficients and area required for each section. 

If the heat exchange involves desuperheating as well as condensation, then the exchanger can be divided into zones with linear temperature-enthalpy profiles in each zone. Figure 15.12a illustrates desuperheating and condensation on the shell-side of a horizontal condenser. The total heat transfer area is the sum of the values for each zone ... 

For multicomponent condensation, the condensation will not be isothermal, leading to a nonlinear temperature-enthalpy profile for the condensation. If this is the case, then the exchanger can be divided into a number of zones with the temperature-enthalpy profiles linearized in each zone. Each zone is then modeled separately and zones summed to obtain the overall area requirement1. 

Figure 19.3 Estimates of temperature-enthalpy profiles from existing exchanger heat duties and temperature.

Figure 19.4 Linearization of nonlinear temperature-enthalpy profiles.

Mechanistic details are very similar for DMSO and water exchange. The reaction proceeds through a distorted trigonal bipyramidal reactive intermediate [Li(DMSO)5]+ that is reached via a late transition state. The enthalpy profile (see Fig. 13) is in line with the experimentally observed very fast exchange process. The five-coordinate intermediate is computed to be 7.9kcalmol 1 less stable than [Li(DMS0)4]+ and free DMSO, while an overall activation barrier of only 8.4kcalmol 1 is computed. Obviously,... 

Moreover, ab initio calculations indicate that additions of chlorocarbenes to ethylene or TME lead to cyclopropanes either without the intermediacy of CACs,39 or via broad shallow wells for complexes that might occur in the reaction enthalpy profile but are not minima on the free energy surface.40 More recent calculations confirm these conclusions CACs are not predicted to be im-... 

Figure 3.2 An enthalpy profile for a unimolecular reaction in solution, involving the formation of a radical pair inside a solvent cage. Adapted from [61],...

Figure 21.9. (a) Experimental data on the thermal deazetization of DBH-ii2- (b) Schematic enthalpy profile for the reaction. The cyclopentane-l,3-dyl intermediate is calculated to have a C2-symmetry equilihrium structure. 

Fig. 5.4. Enthalpy profile for the electrophilic addition of Br2 (reactions proceeding towards the left) and for the electrophilic substitution by Br2 (reactions proceeding towards the right) of cyclohexene (top) and of benzene (bottom). Altogether, the facts presented here are likely to be prototypical of the chemoselectivity of all electrophilic reactions on alkenes versus benzenoid aromatic compounds. In detail, though, this need not be true both in the alkene and the aromatic compound AWSubstitution as well as AWadditio depend on the electrophile, which is why an electrophilic dependency can in principle also be expected for AAH = AWsubstitution - A//a(1(l t. ol. ...

Fig. 5.2. Enthalpy profile for the electrophilic addition of Br2 (reactions proceeding toward the left) and for the electrophilic substitution by Br2 (reactions proceeding toward the right) of cyclohexene (top) and of benzene (bottom).

Temperature versus enthalpy profiles similar to those shown in Figure 4-15 are obtained when starches are heated either in excess water, that is, when water stareh ratios are equal to two or greater, or under intermediate water content. The start of the endothermic peak at To corresponds to loss of birefringence, in the form of the typical Maltese cross, when the starch granule is viewed under polarized light. A single endotherm, such as that obtained under excess water conditions, is referred to as the... 

The differential enthalpy profile is usually seen to be a smooth function of resin loading which further supports the view that the... 

Figure 5.7 Differential enthalpy profiles for Nd -K ion exchange on styrenesulfon-ate cation exchange resins...

Figure 5.8 Differential enthalpy profiles for ion exchange on the zeolite, (Na-A) (Data from R. M. Barrer, L. V. C. Rees, and D. J. Ward, Proc. R. Soc. London, A, 1963, 273,180)...

Figure 3.9. Temperature-enthalpy profile for a stream that is vaporized and superheated.

Fig. 2 Hot composite curve. (A) Individual temperature-enthalpy profiles for hot streams. (B) Combination of profiles for two hot streams.

For equimolal overflow, the enthalpy profiles should be two vertical lines. Clearly, they are not vertical lines. The departure arises because the heat of vaporization of acetone and methanol are not quite equal. The following values were read from the ChemSep library ... 

Figure 12. Schematic enthalpy profile for a reaction of 02(1A() with a quencher Q leading to a negative experimental activation enthalpy in the pre-equilibrium region.

FIGURE 6.8 Laminar boundary layer enthalpy profile function on a uniform-temperature flat plate, C, = 1 [5]. 

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